math related research topics for high school

12 Math Project Ideas for Middle and High School Students

By János Perczel

Co-founder of Polygence, PhD from MIT

6 minute read

Mathematics serves as the foundation for most fields of science, such as physics, engineering, computer science, and economics. It equips you with critical problem-solving skills and the ability to break down complex problems into smaller, more manageable parts. It helps you avoid ambiguity and communicate in what is often called “the universal language,” so-called because its principles and concepts are the same worldwide. Beyond the fact that studying math can open up many career opportunities, some mathematicians also simply find beauty in the equations and proofs themselves.

In this post, we’ll give you ideas for different math research and passion projects and talk about how you can showcase your project.

How do I find my math passion project focus?

Because math is so foundational in the sciences, there are many different directions you can take with your math passion project. Decide which topics within mathematics most speak to you. Maybe you’re more interested in how math is used in sports statistics, how you can harness math to solve global problems, or perhaps you’re curious about how math manifests itself in the physical realm. Once you find a topic that interests you, then you can begin to dive deeper. 

Keep in mind that some passion projects may require more technical skills, such as computer programming, whereas others may just explore theoretical concepts. The route you take is totally up to you and what you feel comfortable with, but don’t be afraid to pursue a project if you don’t currently have the technical skills for it. You can view it as an opportunity to learn new skills while also exploring a topic you’re excited about.

Do your own research through Polygence!

Polygence pairs you with an expert mentor in your area of passion. Together, you work to create a high quality research project that is uniquely your own.

What are the best math project ideas?

1. the mathematical properties of elections.

In recent years, there has been a lot of discussion about which election mechanism is most effective at achieving various goals. Proposed mechanisms in United States elections include majority elections, the electoral college, approval voting, and ranked-choice voting. All of these mechanisms have benefits and drawbacks, and it turns out that no perfect election mechanism exists. Look at the work being done by mathematicians to understand when elections fail, and what can be done to improve them. Choose the strongest mechanism and use evidence to support your claim.

Idea by math research mentor Grayson

2. Knot theory

A knot is simply a closed loop of string. Explore how mathematicians represent knots on a page. Learn how knots can be combined, and how to find knots that can't be created by combining other knots. You can learn techniques for determining whether or not two knots are distinct, in the sense that neither can be deformed to match the other. You can also study related objects, such as links and braids, and research the application of knots in the physical sciences.

Idea by math research mentor Alex

3. Bayesian basketball win prediction system

The Bayes’ Rule is crucial to modern statistics (as well as data science and machine learning). Using a Bayesian model to predict the probability distribution of basketball performance statistics, you can attempt to predict a team’s win and loss rate versus another team by drawing samples from these distributions and computing correlation to win or loss. Your project could be as simple or as complicated as you want. Based on your interest and comfort level, you could use simple normal models, mixture models, Gibbs sampling , and hidden Markov models. You can also learn how to code a fairly simple simulation in R or Python. Then, you’ll need to learn how to interpret the significance of statistical results and adjust results over time based on the success/failure of your model over time.

Idea by math research mentor Ari

4. Finding value in Major League Baseball free agency

Here’s another sports-related project idea. Every offseason, there are hundreds of professional baseball players who become free agents and can be signed by any team. This project involves determining which players might be a good "value" by deciding which statistics are most important to helping a team win relative to how players are generally paid. After deciding which stats are the most important, a ranked list of "value" can be produced based on expected salaries.

Idea by math research mentor Dante

5. Impact of climate change on drought risk

Are you interested in environmental economics, risk analysis, or water resource economics?

You can use historical data on precipitation, temperature, soil moisture, drought indicators, and meteorological models that simulate atmospheric conditions to train a machine-learning model that can assess the likelihood and intensity of droughts in different regions under different climate scenarios. You can also explore your assessments' potential adaptation strategies and policy implications. This project would require some skills in data processing, machine learning, and meteorological modeling.

Idea by math research mentor Jameson

Go beyond crunching numbers

Interested in Math? We'll match you with an expert mentor who will help you explore your next project.

6. Making machines make art 

You can program a computer to create an infinite number of images, music, video game levels, 3D objects, or text using techniques like neural style transfer, genetic algorithms, rejection sampling, Perlin noise , or Voronoi tessellation . Your challenge then is to create a functioning content generator that you could then showcase on a website, research conference, or even in a gallery exhibition.

Idea by math research mentor Sam

7. Measuring income inequality and social mobility

If you’re interested in the intersection of mathematics and public policy, here’s an idea. Use data from the World Bank, the Organization for Economic Co-operation and Development (OECD), and other sources to calculate the Gini coefficient and the intergenerational elasticity of income for different countries and regions over time. Explore the factors that influence these measures and their implications for economic development and social justice. You will need to have some skills in data collection, analysis, and visualization.

8. Rocket (fuel) science

Rockets are mainly made out of fuel. When the fuel burns, it gets heated and expelled out, producing thrust. Fuel is heavy and, for long-range space missions, we need to carry around the fuel for the rest of the mission the whole way. It is important that the fuel gives us the most bang for our buck (i.e., the most acceleration per unit of fuel). Compare the amount of fuel (weight) required to get to various celestial objects and back using current electric and chemical propulsion technologies . Then do a cost analysis and compare how long it would take.

Idea by math research mentor Derek

9. COVID-19 and the global financial crisis

It is shocking how the economic effects of COVID-19 have far outweighed the ones from the Global Financial Crisis in 2007-08 . How much is the difference in terms of employment? Production? Let's go to the data!

Idea by math research mentor Alberto

10. Modeling polarization in social networks

We've all seen or heard about nasty political arguments and echo chambers on social media, but how and why do these happen? To try and find out, construct a mathematical and/or computational model of how people with different opinions interact in a social network. When do people come to a consensus, and when do they become more strongly divided? How can we design social networks with these ideas in mind?

Idea by math research mentor Emily

11. The world of mathematics

The history of mathematics dates all the way back to the very first civilizations and followed throughout history all over the globe. This development leads us to our way of living and thinking today. Rarely taught in math courses, the origins of math can provide clear insight into the necessities of learning math and the broad applications that math has in the world. Conduct research on a chosen time period, location, or figure in mathematics and describe the impacts this innovation or innovator had on the development of math as we know it today.

Idea by math research mentor Shae

12. Simulating the stock market

Here’s an idea for a beginner-to-intermediate statistics and programming project centered around Monte Carlo simulations. Monte Carlo simulations are random methods for modeling the outcome of a complicated process. These methods are used in finance all the time. How could you code a program that uses the Monte Carlo technique to "simulate" the stock market? You will need some familiarity with statistics, basic finance, and basic programming in any language to complete this project.

Idea by math research mentor Sahil

How can I showcase my math project?

After you’ve done the hard work of completing your mathematics passion project, it’s also equally important to showcase your accomplishments . You can see that in many of the project ideas above, there is a clear topic, but how you want to present the project is open-ended. You could try to publish a research paper , create a podcast or infographic, or even create a visual representation of your concept. You’ll find that although many project ideas can simply be summarized in a paper, projects can also be showcased in other creative ways.

Polygence Scholars Are Also Passionate About

What are some examples of math passion projects completed by polygence students.

There are several examples of math projects Polygence students have completed through enrolling in our programs; we’ll highlight two here.

Ahmet's mathematical passion project offers detailed breakdowns of the first introduced quantum algorithm Deutsch-Jozsa, and the first quantum algorithm proven to be faster than classical algorithms, Grover’s Algorithm. It also includes a side-by-side comparison of the quantum algorithms and their classical counterparts. He uploaded his paper on Github and plans to submit it to an official publication soon.

Anna’s finance project provides an overview of topics related to personal finance, covering tax and benefits, tax-deferred savings, interest rates, cost of living, investing, insurance, and housing to help young adults manage their savings. To further her understanding of how different areas of finance influence one's life consumption, she created a life consumption plan for a hypothetical person and produced a paper. 

How can I get guidance and support on my math project?

In this post, we covered how to find the right mathematics project for you, shared a dozen ideas for physics passion projects, and discussed how to showcase your project.

If you have a passion for math–or are generally curious about exploring mathematical concepts–and are interested in pursuing a passion project, Polygence’s programs are a great place to start. You’ll be paired with a mathematics research mentor with whom you’ll be able to meet one-on-one. Through these virtual mentorship sessions, your mentor can help you learn new concepts, troubleshoot issues you encounter along the way to bringing your math project to completion, and brainstorm with you on how to showcase your passion project .

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181 Mathematics Research Topics From PhD Experts

If you are reading this blog post, it means you are looking for some exceptional math research topics. You want them to be original, unique even. If you manage to find topics like this, you can be sure your professor will give you a top grade (if you write a decent paper, that is). The good news is that you have arrived at just the right place – at the right time. We have just finished updating our list of topics, so you will find plenty of original ideas right on this page. All our topics are 100 percent free to use as you see fit. You can reword them and you don’t need to give us any credit.

And remember: if you need assistance from a professional, don’t hesitate to reach out to us. We are not just the best place for math research topics for high school students; we are also the number one choice for students looking for top-notch research paper writing services.

Our Newest Research Topics in Math

We know you probably want the best and most recent research topics in math. You want your paper to stand out from all the rest. After all, this is the best way to get some bonus points from your professor. On top of this, finding some great topics for your next paper makes it easier for you to write the essay. As long as you know at least something about the topic, you’ll find that writing a great paper or buy phd thesis isn’t as difficult as you previously thought.

So, without further ado, here are the 181 brand new topics for your next math research paper:

Cool Math Topics to Research

Are you looking for some cool math topics to research? We have a list of original topics for your right here. Pick the one you like and start writing now:

• Roll two dice and calculate a probability
• Discuss ancient Greek mathematics
• Is math really important in school?
• Discuss the binomial theorem
• The math behind encryption
• Game theory and its real-life applications
• Analyze the Bernoulli scheme
• What are holomorphic functions and how do they work?
• Describe big numbers
• Solving the Tower of Hanoi problem

Undergraduate Math Research Topics

If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics:

• Methods to count discrete objects
• The origins of Greek symbols in mathematics
• Methods to solve simultaneous equations
• Real-world applications of the theorem of Pythagoras
• Discuss the limits of diffusion
• Use math to analyze the abortion data in the UK over the last 100 years
• Discuss the Knot theory
• Analyze predictive models (take meteorology as an example)
• In-depth analysis of the Monte Carlo methods for inverse problems
• Squares vs. rectangles (compare and contrast)

Number Theory Topics to Research

Interested in writing about number theory? It is not an easy subject to discuss, we know. However, we are sure you will appreciate these number theory topics:

• Discuss the greatest common divisor
• Explain the extended Euclidean algorithm
• What are RSA numbers?
• Discuss Bézout’s lemma
• In-depth analysis of the square-free polynomial
• Discuss the Stern-Brocot tree
• Analyze Fermat’s little theorem
• What is a discrete logarithm?
• Gauss’s lemma in number theory
• Analyze the Pentagonal number theorem

Math Research Topics for High School

High school students shouldn’t be too worried about their math papers because we have some unique, and quite interesting, math research topics for high school right here:

• Discuss Brun’s constant
• An in-depth look at the Brahmagupta–Fibonacci identity
• What is derivative algebra?
• Describe the Symmetric Boolean function
• Discuss orders of approximation in limits
• Solving Regiomontanus’ angle maximization problem
• What is a Quadratic integral?
• Define and describe complementary angles
• Analyze the incircle and excircles of a triangle
• Analyze the Bolyai–Gerwien theorem in geometry
• Math in our everyday life

Complex Math Topics

If you want to give some complex math topics a try, we have the best examples below. Remember, these topics should only be attempted by students who are proficient in mathematics:

• Mathematics and its appliance in Artificial Intelligence
• Try to solve an unsolved problem in math
• Discuss Kolmogorov’s zero-one law
• What is a discrete random variable?
• Analyze the Hewitt–Savage zero-one law
• What is a transferable belief model?
• Discuss 3 major mathematical theorems
• Describe and analyze the Dempster-Shafer theory
• An in-depth analysis of a continuous stochastic process
• Identify and analyze Gauss-Markov processes

Easy Math Research Paper Topics

Perhaps you don’t want to spend too much time working on your next research paper. Who can blame you? Check out these easy math research paper topics:

• Define the hyperbola
• Do we need to use a calculator during math class?
• The binomial theorem and its real-world applications
• What is a parabola in geometry?
• How do you calculate the slope of a curve?
• Define the Jacobian matrix
• Solving matrix problems effectively
• Why do we need differential equations?
• Should math be mandatory in all schools?
• What is a Hessian matrix?

Logic Topics to Research

We have some interesting logical topics for research papers. These are perfect for students interested in writing about math logic. Pick one right now:

• Discuss the reductio ad absurdum approach
• Discuss Boolean algebra
• What is consistency proof?
• Analyze Trakhtenbrot’s theorem (the finite model theory)
• Discuss the Gödel completeness theorem
• An in-depth analysis of Morley’s categoricity theorem
• How does the Back-and-forth method work?
• Discuss the Ehrenfeucht–Fraïssé game technique
• Discuss Aleph numbers (Aleph-null and Aleph-one)
• Solving the Suslin problem

Algebra Topics for a Research Paper

Would you like to write about an algebra topic? No problem, our seasoned writers have compiled a list of the best algebra topics for a research paper:

• Discuss the differential equation
• Analyze the Jacobson density theorem
• The 4 properties of a binary operation in algebra
• Analyze the unary operator in depth
• Analyze the Abel–Ruffini theorem
• Epimorphisms vs. monomorphisms: compare and contrast
• Discuss the Morita duality in algebraic structures
• Idempotent vs. nilpotent in Ring theory
• Discuss the Artin-Wedderburn theorem
• What is a commutative ring in algebra?
• Analyze and describe the Noetherian ring

Math Education Research Topics

There is nothing wrong with writing about math education, especially if your professor did not give you writing prompts. Here are some very nice math education research topics:

• What are the goals a mathematics professor should have?
• What is math anxiety in the classroom?
• Teaching math in UK schools: the difficulties
• Computer programming or math in high school?
• Is math education in Europe at a high enough level?
• Common Core Standards and their effects on math education
• Culture and math education in Africa
• What is dyscalculia and how does it manifest itself?
• When was algebra first thought in schools?
• Math education in the United States versus the United Kingdom

Computability Theory Topics to Research

Writing about computability theory can be a very interesting adventure. Give it a try! Here are some of our most interesting computability theory topics to research:

• What is a multiplication table?
• Analyze the Scholz conjecture
• Explain exponentiating by squaring
• Analyze the Myhill-Nerode theorem
• What is a tree automaton?
• Compare and contrast the Pushdown automaton and the Büchi automaton
• Discuss the Markov algorithm
• What is a Turing machine?
• Analyze the post correspondence problem
• Discuss the linear speedup theorem
• Discuss the Boolean satisfiability problem

Interesting Math Research Topics

We know you want topics that are interesting and relatively easy to write about. This is why we have a separate list of our most interesting math research topics:

• What is two-element Boolean algebra?
• The life of Gauss
• The life of Isaac Newton
• What is an orthodiagonal quadrilateral?
• Tessellation in Euclidean plane geometry
• Describe a hyperboloid in 3D geometry
• What is a sphericon?
• Discuss the peculiarities of Borel’s paradox
• Analyze the De Finetti theorem in statistics
• What are Martingales?
• The basics of stochastic calculus

Applied Math Research Topics

Interested in writing about applied mathematics? Our team managed to create a list of awesome applied math research topics from scratch for you:

• Discuss Newton’s laws of motion
• Analyze the perpendicular axes rule
• How is a Galilean transformation done?
• The conservation of energy and its applications
• Discuss Liouville’s theorem in Hamiltonian mechanics
• Analyze the quantum field theory
• Discuss the main components of the Lorentz symmetry
• An in-depth look at the uncertainty principle

Geometry Topics for a Research Paper

Geometry can be a very captivating subject, especially when you know plenty about it. Check out our list of geometry topics for a research paper and pick the best one today:

• Most useful trigonometry functions in math
• The life of Archimedes and his achievements
• Trigonometry in computer graphics
• Using Vincenty’s formulae in geodesy
• Define and describe the Heronian tetrahedron
• The math behind the parabolic microphone
• Discuss the Japanese theorem for concyclic polygons
• Analyze Euler’s theorem in geometry

Math Research Topics for Middle School

Yes, even middle school children can write about mathematics. We have some original math research topics for middle school right here:

• Finding critical points in a graph
• The basics of calculus
• What makes a graph ultrahomogeneous?
• How do you calculate the area of different shapes?
• What contributions did Euclid have to the field of mathematics?
• What is Diophantine geometry?
• What makes a graph regular?
• Analyze a full binary tree

Math Research Topics for College Students

As you’ve probably already figured out, college students should pick topics that are a bit more complex. We have some of the best math research topics for college students right here:

• What are extremal problems and how do you solve them?
• Discuss an unsolvable math problem
• How can supercomputers solve complex mathematical problems?
• An in-depth analysis of fractals
• Discuss the Boruvka’s algorithm (related to the minimum spanning tree)
• Discuss the Lorentz–FitzGerald contraction hypothesis in relativity
• An in-depth look at Einstein’s field equation
• The math behind computer vision and object recognition

Calculus Topics for a Research Paper

Let’s face it: calculus is not a very difficult field. So, why don’t you pick one of our excellent calculus topics for a research paper and start writing your essay right away:

• When do we need to apply the L’Hôpital rule?
• Discuss the Leibniz integral rule
• Calculus in ancient Egypt
• Discuss and analyze linear approximations
• The applications of calculus in real life
• The many uses of Stokes’ theorem
• Discuss the Borel regular measure
• An in-depth analysis of Lebesgue’s monotone convergence theorem

Simple Math Research Paper Topics for High School

This is the place where you can find some pretty simple topics if you are a high school student. Check out our simple math research paper topics for high school:

• The life and work of the famous Pierre de Fermat
• What are limits and why are they useful in calculus?
• Explain the concept of congruency
• The life and work of the famous Jakob Bernoulli
• Analyze the rhombicosidodecahedron and its applications
• Calculus and the Egyptian pyramids
• The life and work of the famous Jean d’Alembert
• Discuss the hyperplane arrangement in combinatorial computational geometry
• The smallest enclosing sphere method in combinatorics

Business Math Topics

If you want to surprise your professor, why don’t you write about business math? We have some exceptional topics that nobody has thought about right here:

• Is paying a loan with another loan a good approach?
• Discuss the major causes of a stock market crash
• Best debt amortization methods in the US
• How do bank loans work in the UK?
• Calculating interest rates the easy way
• Discuss the pros and cons of annuities
• Basic business math skills everyone should possess
• Business math in United States schools
• Analyze the discount factor

Probability and Statistics Topics for Research

Probability and statistics are not easy fields. However, you can impress your professor with one of our unique probability and statistics topics for research:

• What is the autoregressive conditional duration?
• Applying the ANOVA method to ranks
• Discuss the practical applications of the Bates distribution
• Explain the principle of maximum entropy
• Discuss Skorokhod’s representation theorem in random variables
• What is the Factorial moment in the Theory of Probability?
• Compare and contrast Cochran’s C test and his Q test
• Analyze the De Moivre-Laplace theorem
• What is a negative probability?

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251+ Math Research Topics [2024 Updated]

Mathematics, often dubbed as the language of the universe, holds immense significance in shaping our understanding of the world around us. It’s not just about crunching numbers or solving equations; it’s about unraveling mysteries, making predictions, and creating innovative solutions to complex problems. In this blog, we embark on a journey into the realm of math research topics, exploring various branches of mathematics and their real-world applications.

How Do You Write A Math Research Topic?

Writing a math research topic involves several steps to ensure clarity, relevance, and feasibility. Here’s a guide to help you craft a compelling math research topic:

• Identify Your Interests: Start by exploring areas of mathematics that interest you. Whether it’s pure mathematics, applied mathematics, or interdisciplinary topics, choose a field that aligns with your passion and expertise.
• Narrow Down Your Focus: Mathematics is a broad field, so it’s essential to narrow down your focus to a specific area or problem. Consider the scope of your research and choose a topic that is manageable within your resources and time frame.
• Review Existing Literature: Conduct a thorough literature review to understand the current state of research in your chosen area. Identify gaps, controversies, or unanswered questions that could form the basis of your research topic.
• Formulate a Research Question: Based on your exploration and literature review, formulate a clear and concise research question. Your research question should be specific, measurable, achievable, relevant, and time-bound (SMART).
• Consider Feasibility: Assess the feasibility of your research topic in terms of available resources, data availability, and research methodologies. Ensure that your topic is realistic and achievable within the constraints of your project.
• Consult with Experts: Seek feedback from mentors, advisors, or experts in the field to validate your research topic and refine your ideas. Their insights can help you identify potential challenges and opportunities for improvement.
• Refine and Iterate: Refine your research topic based on feedback and further reflection. Iterate on your ideas to ensure clarity, coherence, and relevance to the broader context of mathematics research.
• Craft a Title: Once you have finalized your research topic, craft a compelling title that succinctly summarizes the essence of your research. Your title should be descriptive, engaging, and reflective of the key themes of your study.
• Write a Research Proposal: Develop a comprehensive research proposal outlining the background, objectives, methodology, and expected outcomes of your research. Your research proposal should provide a clear roadmap for your study and justify the significance of your research topic.

By following these steps, you can effectively write a math research topic that is well-defined, relevant, and poised to make a meaningful contribution to the field of mathematics.

251+ Math Research Topics: Beginners To Advanced

• Prime Number Distribution in Arithmetic Progressions
• Diophantine Equations and their Solutions
• Applications of Modular Arithmetic in Cryptography
• The Riemann Hypothesis and its Implications
• Graph Theory: Exploring Connectivity and Coloring Problems
• Knot Theory: Unraveling the Mathematics of Knots and Links
• Fractal Geometry: Understanding Self-Similarity and Dimensionality
• Differential Equations: Modeling Physical Phenomena and Dynamical Systems
• Chaos Theory: Investigating Deterministic Chaos and Strange Attractors
• Combinatorial Optimization: Algorithms for Solving Optimization Problems
• Computational Complexity: Analyzing the Complexity of Algorithms
• Game Theory: Mathematical Models of Strategic Interactions
• Number Theory: Exploring Properties of Integers and Primes
• Algebraic Topology: Studying Topological Invariants and Homotopy Theory
• Analytic Number Theory: Investigating Properties of Prime Numbers
• Algebraic Geometry: Geometry Arising from Algebraic Equations
• Galois Theory: Understanding Field Extensions and Solvability of Equations
• Representation Theory: Studying Symmetry in Linear Spaces
• Harmonic Analysis: Analyzing Functions on Groups and Manifolds
• Mathematical Logic: Foundations of Mathematics and Formal Systems
• Set Theory: Exploring Infinite Sets and Cardinal Numbers
• Real Analysis: Rigorous Study of Real Numbers and Functions
• Complex Analysis: Analytic Functions and Complex Integration
• Measure Theory: Foundations of Lebesgue Integration and Probability
• Topological Groups: Investigating Topological Structures on Groups
• Lie Groups and Lie Algebras: Geometry of Continuous Symmetry
• Differential Geometry: Curvature and Topology of Smooth Manifolds
• Algebraic Combinatorics: Enumerative and Algebraic Aspects of Combinatorics
• Ramsey Theory: Investigating Structure in Large Discrete Structures
• Analytic Geometry: Studying Geometry Using Analytic Methods
• Hyperbolic Geometry: Non-Euclidean Geometry of Curved Spaces
• Nonlinear Dynamics: Chaos, Bifurcations, and Strange Attractors
• Homological Algebra: Studying Homology and Cohomology of Algebraic Structures
• Topological Vector Spaces: Vector Spaces with Topological Structure
• Representation Theory of Finite Groups: Decomposition of Group Representations
• Category Theory: Abstract Structures and Universal Properties
• Operator Theory: Spectral Theory and Functional Analysis of Operators
• Algebraic Number Theory: Study of Algebraic Structures in Number Fields
• Cryptanalysis: Breaking Cryptographic Systems Using Mathematical Methods
• Discrete Mathematics: Combinatorics, Graph Theory, and Number Theory
• Mathematical Biology: Modeling Biological Systems Using Mathematical Tools
• Population Dynamics: Mathematical Models of Population Growth and Interaction
• Epidemiology: Mathematical Modeling of Disease Spread and Control
• Mathematical Ecology: Dynamics of Ecological Systems and Food Webs
• Evolutionary Game Theory: Evolutionary Dynamics and Strategic Behavior
• Mathematical Neuroscience: Modeling Brain Dynamics and Neural Networks
• Mathematical Physics: Mathematical Models in Physical Sciences
• Quantum Mechanics: Foundations and Applications of Quantum Theory
• Statistical Mechanics: Statistical Methods in Physics and Thermodynamics
• Fluid Dynamics: Modeling Flow of Fluids Using Partial Differential Equations
• Mathematical Finance: Stochastic Models in Finance and Risk Management
• Option Pricing Models: Black-Scholes Model and Beyond
• Portfolio Optimization: Maximizing Returns and Minimizing Risk
• Stochastic Calculus: Calculus of Stochastic Processes and Itô Calculus
• Financial Time Series Analysis: Modeling and Forecasting Financial Data
• Operations Research: Optimization of Decision-Making Processes
• Linear Programming: Optimization Problems with Linear Constraints
• Integer Programming: Optimization Problems with Integer Solutions
• Network Flow Optimization: Modeling and Solving Flow Network Problems
• Combinatorial Game Theory: Analysis of Games with Perfect Information
• Algorithmic Game Theory: Computational Aspects of Game-Theoretic Problems
• Fair Division: Methods for Fairly Allocating Resources Among Parties
• Auction Theory: Modeling Auction Mechanisms and Bidding Strategies
• Voting Theory: Mathematical Models of Voting Systems and Social Choice
• Social Network Analysis: Mathematical Analysis of Social Networks
• Algorithm Analysis: Complexity Analysis of Algorithms and Data Structures
• Machine Learning: Statistical Learning Algorithms and Data Mining
• Deep Learning: Neural Network Models with Multiple Layers
• Reinforcement Learning: Learning by Interaction and Feedback
• Natural Language Processing: Statistical and Computational Analysis of Language
• Computer Vision: Mathematical Models for Image Analysis and Recognition
• Computational Geometry: Algorithms for Geometric Problems
• Symbolic Computation: Manipulation of Mathematical Expressions
• Numerical Analysis: Algorithms for Solving Numerical Problems
• Finite Element Method: Numerical Solution of Partial Differential Equations
• Monte Carlo Methods: Statistical Simulation Techniques
• High-Performance Computing: Parallel and Distributed Computing Techniques
• Quantum Computing: Quantum Algorithms and Quantum Information Theory
• Quantum Information Theory: Study of Quantum Communication and Computation
• Quantum Error Correction: Methods for Protecting Quantum Information from Errors
• Topological Quantum Computing: Using Topological Properties for Quantum Computation
• Quantum Algorithms: Efficient Algorithms for Quantum Computers
• Quantum Cryptography: Secure Communication Using Quantum Key Distribution
• Topological Data Analysis: Analyzing Shape and Structure of Data Sets
• Persistent Homology: Topological Invariants for Data Analysis
• Mapper Algorithm: Method for Visualization and Analysis of High-Dimensional Data
• Algebraic Statistics: Statistical Methods Based on Algebraic Geometry
• Tropical Geometry: Geometric Methods for Studying Polynomial Equations
• Model Theory: Study of Mathematical Structures and Their Interpretations
• Descriptive Set Theory: Study of Borel and Analytic Sets
• Ergodic Theory: Study of Measure-Preserving Transformations
• Combinatorial Number Theory: Intersection of Combinatorics and Number Theory
• Additive Combinatorics: Study of Additive Properties of Sets
• Arithmetic Geometry: Interplay Between Number Theory and Algebraic Geometry
• Proof Theory: Study of Formal Proofs and Logical Inference
• Reverse Mathematics: Study of Logical Strength of Mathematical Theorems
• Nonstandard Analysis: Alternative Approach to Analysis Using Infinitesimals
• Computable Analysis: Study of Computable Functions and Real Numbers
• Graph Theory: Study of Graphs and Networks
• Random Graphs: Probabilistic Models of Graphs and Connectivity
• Spectral Graph Theory: Analysis of Graphs Using Eigenvalues and Eigenvectors
• Algebraic Graph Theory: Study of Algebraic Structures in Graphs
• Metric Geometry: Study of Geometric Structures Using Metrics
• Geometric Measure Theory: Study of Measures on Geometric Spaces
• Discrete Differential Geometry: Study of Differential Geometry on Discrete Spaces
• Algebraic Coding Theory: Study of Error-Correcting Codes
• Information Theory: Study of Information and Communication
• Coding Theory: Study of Error-Correcting Codes
• Cryptography: Study of Secure Communication and Encryption
• Finite Fields: Study of Fields with Finite Number of Elements
• Elliptic Curves: Study of Curves Defined by Cubic Equations
• Hyperelliptic Curves: Study of Curves Defined by Higher-Degree Equations
• Modular Forms: Analytic Functions with Certain Transformation Properties
• L-functions: Analytic Functions Associated with Number Theory
• Zeta Functions: Analytic Functions with Special Properties
• Analytic Number Theory: Study of Number Theoretic Functions Using Analysis
• Dirichlet Series: Analytic Functions Represented by Infinite Series
• Euler Products: Product Representations of Analytic Functions
• Arithmetic Dynamics: Study of Iterative Processes on Algebraic Structures
• Dynamics of Rational Maps: Study of Dynamical Systems Defined by Rational Functions
• Julia Sets: Fractal Sets Associated with Dynamical Systems
• Mandelbrot Set: Fractal Set Associated with Iterations of Complex Quadratic Polynomials
• Arithmetic Geometry: Study of Algebraic Geometry Over Number Fields
• Diophantine Geometry: Study of Solutions of Diophantine Equations Using Geometry
• Arithmetic of Elliptic Curves: Study of Elliptic Curves Over Number Fields
• Rational Points on Curves: Study of Rational Solutions of Algebraic Equations
• Galois Representations: Study of Representations of Galois Groups
• Automorphic Forms: Analytic Functions with Certain Transformation Properties
• L-functions: Analytic Functions Associated with Automorphic Forms
• Selberg Trace Formula: Tool for Studying Spectral Theory and Automorphic Forms
• Langlands Program: Program to Unify Number Theory and Representation Theory
• Hodge Theory: Study of Harmonic Forms on Complex Manifolds
• Riemann Surfaces: One-dimensional Complex Manifolds
• Shimura Varieties: Algebraic Varieties Associated with Automorphic Forms
• Modular Curves: Algebraic Curves Associated with Modular Forms
• Hyperbolic Manifolds: Manifolds with Constant Negative Curvature
• Teichmüller Theory: Study of Moduli Spaces of Riemann Surfaces
• Mirror Symmetry: Duality Between Calabi-Yau Manifolds
• Kähler Geometry: Study of Hermitian Manifolds with Special Symmetries
• Algebraic Groups: Linear Algebraic Groups and Their Representations
• Lie Algebras: Study of Algebraic Structures Arising from Lie Groups
• Representation Theory of Lie Algebras: Study of Representations of Lie Algebras
• Quantum Groups: Deformation of Lie Groups and Lie Algebras
• Algebraic Topology: Study of Topological Spaces Using Algebraic Methods
• Homotopy Theory: Study of Continuous Deformations of Spaces
• Homology Theory: Study of Algebraic Invariants of Topological Spaces
• Cohomology Theory: Study of Dual Concepts to Homology Theory
• Singular Homology: Homology Theory Defined Using Simplicial Complexes
• Sheaf Theory: Study of Sheaves and Their Cohomology
• Differential Forms: Study of Multilinear Differential Forms
• De Rham Cohomology: Cohomology Theory Defined Using Differential Forms
• Morse Theory: Study of Critical Points of Smooth Functions
• Symplectic Geometry: Study of Symplectic Manifolds and Their Geometry
• Floer Homology: Study of Symplectic Manifolds Using Pseudoholomorphic Curves
• Gromov-Witten Invariants: Invariants of Symplectic Manifolds Associated with Pseudoholomorphic Curves
• Mirror Symmetry: Duality Between Symplectic and Complex Geometry
• Calabi-Yau Manifolds: Ricci-Flat Complex Manifolds
• Moduli Spaces: Spaces Parameterizing Geometric Objects
• Donaldson-Thomas Invariants: Invariants Counting Sheaves on Calabi-Yau Manifolds
• Algebraic K-Theory: Study of Algebraic Invariants of Rings and Modules
• Homological Algebra: Study of Homology and Cohomology of Algebraic Structures
• Derived Categories: Categories Arising from Homological Algebra
• Stable Homotopy Theory: Homotopy Theory with Stable Homotopy Groups
• Model Categories: Categories with Certain Homotopical Properties
• Higher Category Theory: Study of Higher Categories and Homotopy Theory
• Higher Topos Theory: Study of Higher Categorical Structures
• Higher Algebra: Study of Higher Categorical Structures in Algebra
• Higher Algebraic Geometry: Study of Higher Categorical Structures in Algebraic Geometry
• Higher Representation Theory: Study of Higher Categorical Structures in Representation Theory
• Higher Category Theory: Study of Higher Categorical Structures
• Homotopical Algebra: Study of Algebraic Structures in Homotopy Theory
• Homotopical Groups: Study of Groups with Homotopical Structure
• Homotopical Categories: Study of Categories with Homotopical Structure
• Homotopy Groups: Algebraic Invariants of Topological Spaces
• Homotopy Type Theory: Study of Foundations of Mathematics Using Homotopy Theory

In conclusion, the world of mathematics is vast and multifaceted, offering endless opportunities for exploration and discovery. Whether delving into the abstract realms of pure mathematics or applying mathematical principles to solve real-world problems, mathematicians play a vital role in advancing human knowledge and shaping the future of our world.

By embracing diverse math research topics and interdisciplinary collaborations, we can unlock new possibilities and harness the power of mathematics to address the challenges of today and tomorrow. So, let’s embark on this journey together as we unravel the mysteries of numbers and explore the boundless horizons of mathematical inquiry.

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260 Interesting Math Topics for Essays & Research Papers

Mathematics is the science of numbers and shapes. Writing about it can give you a fresh perspective and help to clarify difficult concepts. You can even use mathematical writing as a tool in problem-solving.

In this article, you will find plenty of interesting math topics. Besides, you will learn about branches of mathematics that you can choose from. And if the thought of letters and numbers makes your head swim, try our custom writing service . Our professionals will craft a paper for you in no time!

And now, let’s proceed to math essay topics and tips.

🔝 Top 10 Interesting Math Topics

✅ branches of mathematics, ✨ fun math topics.

• 🏫 Math Topics for High School
• 🎓 College Math Topics
• 🤔 Advanced Math
• 📚 Math Research
• ✏️ Math Education
• 💵 Business Math

🔍 References

• Number theory in everyday life.
• Logicist definitions of mathematics.
• Multivariable vs. vector calculus.
• 4 conditions of functional analysis.
• Random variable in probability theory.
• How is math used in cryptography?
• The purpose of homological algebra.
• Concave vs. convex in geometry.
• The philosophical problem of foundations.
• Is numerical analysis useful for machine learning?

What exactly is mathematics ? First and foremost, it is very old. Ancient Greeks and Persians were already utilizing mathematical tools. Nowadays, we consider it an interdisciplinary language.

Biologists, linguists, and sociologists alike use math in their work. And not only that, we all deal with it in our daily lives. For instance, it manifests in the measurement of time. We often need it to calculate how much our groceries cost and how much paint we need to buy to cover a wall.

Simply put, mathematics is a universal instrument for problem-solving. We can divide pure math into three branches: geometry, arithmetic, and algebra. Let’s take a closer look:

• Geometry By studying geometry, we try to comprehend our physical surroundings. Geometric shapes can be simple, like a triangle. Or, they can form complicated figures, like a rhombicosidodecahedron.
• Arithmetic Arithmetic deals with numbers and simple operations: subtraction, addition, division, and multiplication.
• Algebra Algebra is used when the exact numbers are unclear. Instead, they are replaced with letters. Businesses often need algebra to predict their sales.

It’s true that most high school students don’t like math. However, that doesn’t mean it can’t be a fun and compelling subject. In the following section, you will find plenty of enthralling mathematical topics for your paper.

If you’re struggling to start working on your essay, we have some fun and cool math topics to offer. They will definitely engage you and make the writing process enjoyable. Besides, fun math topics can show everyone that even math can be entertaining or even a bit silly.

• The link between mathematics and art – analyzing the Golden Ratio in Renaissance-era paintings.
• An evaluation of Georg Cantor’s set theory.
• The best approaches to learning math facts and developing number sense.
• Different approaches to probability as explored through analyzing card tricks. 
• Chess and checkers – the use of mathematics in recreational activities.
• The five types of math used in computer science.
• Real-life applications of the Pythagorean Theorem. 
• A study of the different theories of mathematical logic.
• The use of game theory in social science.
• Mathematical definitions of infinity and how to measure it.
• What is the logic behind unsolvable math problems?
• An explanation of mean, mode, and median using classroom math grades.
• The properties and geometry of a Möbius strip.
• Using truth tables to present the logical validity of a propositional expression.
• The relationship between Pascal’s Triangle and The Binomial Theorem. 
• The use of different number types: the history.
• The application of differential geometry in modern architecture.
• A mathematical approach to the solution of a Rubik’s Cube.
• Comparison of predictive and prescriptive statistical analyses.
• Explaining the iterations of the Koch snowflake.
• The importance of limits in calculus.
• Hexagons as the most balanced shape in the universe.
• The emergence of patterns in chaos theory.
• What were Euclid’s contributions to the field of mathematics?
• The difference between universal algebra and abstract algebra.

🏫 Math Essay Topics for High School

When writing a math paper, you want to demonstrate that you understand a concept. It can be helpful if you need to prepare for an exam. Choose a topic from this section and decide what you want to discuss.

• Explain what we need Pythagoras’ theorem for.
• What is a hyperbola?
• Describe the difference between algebra and arithmetic.
• When is it unnecessary to use a calculator ?
• Find a connection between math and the arts.
• How do you solve a linear equation?
• Discuss how to determine the probability of rolling two dice.
• Is there a link between philosophy and math?
• What types of math do you use in your everyday life?
• What is the numerical data?
• Explain how to use the binomial theorem.
• What is the distributive property of multiplication?
• Discuss the major concepts in ancient Egyptian mathematics. 
• Why do so many students dislike math?
• Should math be required in school?
• How do you do an equivalent transformation?
• Why do we need imaginary numbers?
• How can you calculate the slope of a curve?
• What is the difference between sine, cosine, and tangent?
• How do you define the cross product of two vectors?
• What do we use differential equations for?
• Investigate how to calculate the mean value.
• Define linear growth.
• Give examples of different number types.
• How can you solve a matrix?

🎓 College Math Topics for a Paper

Sometimes you need more than just formulas to explain a complex idea. That’s why knowing how to express yourself is crucial. It is especially true for college-level mathematics. Consider the following ideas for your next research project:

• What do we need n-dimensional spaces for?
• Explain how card counting works.
• Discuss the difference between a discrete and a continuous probability distribution. 
• How does encryption work? 
• Describe extremal problems in discrete geometry.
• What can make a math problem unsolvable?
• Examine the topology of a Möbius strip.

• What is K-theory? 
• Discuss the core problems of computational geometry.
• Explain the use of set theory .
• What do we need Boolean functions for?
• Describe the main topological concepts in modern mathematics.
• Investigate the properties of a rotation matrix.
• Analyze the practical applications of game theory.
• How can you solve a Rubik’s cube mathematically?
• Explain the math behind the Koch snowflake.
• Describe the paradox of Gabriel’s Horn.
• How do fractals form?
• Find a way to solve Sudoku using math.
• Why is the Riemann hypothesis still unsolved?
• Discuss the Millennium Prize Problems.
• How can you divide complex numbers?
• Analyze the degrees in polynomial functions.
• What are the most important concepts in number theory?
• Compare the different types of statistical methods.

🤔 Advanced Topics in Math to Write a Paper on

Once you have passed the trials of basic math, you can move on to the advanced section. This area includes topology, combinatorics, logic, and computational mathematics. Check out the list below for enticing topics to write about:

• What is an abelian group?
• Explain the orbit-stabilizer theorem.
• Discuss what makes the Burnside problem influential.
• What fundamental properties do holomorphic functions have?
• How does Cauchy’s integral theorem lead to Cauchy’s integral formula?
• How do the two Picard theorems relate to each other?
• When is a trigonometric series called a Fourier series?
• Give an example of an algorithm used for machine learning.
• Compare the different types of knapsack problems.
• What is the minimum overlap problem?
• Describe the Bernoulli scheme.
• Give a formal definition of the Chinese restaurant process.
• Discuss the logistic map in relation to chaos.
• What do we need the Feigenbaum constants for?
• Define a difference equation.
• Explain the uses of the Fibonacci sequence.
• What is an oblivious transfer?
• Compare the Riemann and the Ruelle zeta functions.
• How can you use elementary embeddings in model theory?
• Analyze the problem with the wholeness axiom and Kunen’s inconsistency theorem.
• How is Lie algebra used in physics ?
• Define various cases of algebraic cycles.
• Why do we need étale cohomology groups to calculate algebraic curves?
• What does non-Euclidean geometry consist of?
• How can two lines be ultraparallel?

📚 Math Research Topics for a Paper

Choosing the right topic is crucial for a successful research paper in math. It should be hard enough to be compelling, but not exceeding your level of competence. If possible, stick to your area of knowledge. This way your task will become more manageable. Here are some ideas:

• Write about the history of calculus.
• Why are unsolved math problems significant?
• Find reasons for the gender gap in math students.
• What are the toughest mathematical questions asked today?
• Examine the notion of operator spaces.
• How can we design a train schedule for a whole country?
• What makes a number big?

• How can infinities have various sizes?
• What is the best mathematical strategy to win a game of Go?
• Analyze natural occurrences of random walks in biology.
• Explain what kind of mathematics was used in ancient Persia.
• Discuss how the Iwasawa theory relates to modular forms.
• What role do prime numbers play in encryption?
• How did the study of mathematics evolve?
• Investigate the different Tower of Hanoi solutions.
• Research Napier’s bones. How can you use them?
• What is the best mathematical way to find someone who is lost in a maze?
• Examine the Traveling Salesman Problem. Can you find a new strategy?
• Describe how barcodes function.
• Study some real-life examples of chaos theory. How do you define them mathematically?
• Compare the impact of various ground-breaking mathematical equations .
• Research the Seven Bridges of Königsberg. Relate the problem to the city of your choice.
• Discuss Fisher’s fundamental theorem of natural selection.
• How does quantum computing work?
• Pick an unsolved math problem and say what makes it so difficult.

✏️ Math Education Research Topics

For many teachers, the hardest part is to keep the students interested. When it comes to math, it can be especially challenging. It’s crucial to make complicated concepts easy to understand. That’s why we need research on math education.

• Compare traditional methods of teaching math with unconventional ones.
• How can you improve mathematical education in the U.S.?
• Describe ways of encouraging girls to pursue careers in STEM fields.
• Should computer programming be taught in high school?
• Define the goals of mathematics education .
• Research how to make math more accessible to students with learning disabilities. 
• At what age should children begin to practice simple equations?
• Investigate the effectiveness of gamification in algebra classes. 
• What do students gain from taking part in mathematics competitions?
• What are the benefits of moving away from standardized testing ?
• Describe the causes of “ math anxiety .” How can you overcome it?
• Explain the social and political relevance of mathematics education.
• Define the most significant issues in public school math teaching.
• What is the best way to get children interested in geometry?
• How can students hone their mathematical thinking outside the classroom?
• Discuss the benefits of using technology in math class. 
• In what way does culture influence your mathematical education?
• Explore the history of teaching algebra.
• Compare math education in various countries.

• How does dyscalculia affect a student’s daily life?
• Into which school subjects can math be integrated?
• Has a mathematics degree increased in value over the last few years?
• What are the disadvantages of the Common Core Standards?
• What are the advantages of following an integrated curriculum in math?
• Discuss the benefits of Mathcamp.

🧮 Algebra Topics for a Paper

The elegance of algebra stems from its simplicity. It gives us the ability to express complex problems in short equations. The world was changed forever when Einstein wrote down the simple formula E=mc². Now, if your algebra seminar requires you to write a paper, look no further! Here are some brilliant prompts:

• Give an example of an induction proof.
• What are F-algebras used for?
• What are number problems?
• Show the importance of abstract algebraic thinking. 
• Investigate the peculiarities of Fermat’s last theorem.
• What are the essentials of Boolean algebra?
• Explore the relationship between algebra and geometry.
• Compare the differences between commutative and noncommutative algebra.
• Why is Brun’s constant relevant?
• How do you factor quadratics?
• Explain Descartes’ Rule of Signs.
• What is the quadratic formula?
• Compare the four types of sequences and define them.
• Explain how partial fractions work.
• What are logarithms used for?
• Describe the Gaussian elimination.
• What does Cramer’s rule state?
• Explore the difference between eigenvectors and eigenvalues.
• Analyze the Gram-Schmidt process in two dimensions.
• Explain what is meant by “range” and “domain” in algebra.
• What can you do with determinants?
• Learn about the origin of the distance formula.
• Find the best way to solve math word problems.
• Compare the relationships between different systems of equations.
• Explore how the Rubik’s cube relates to group theory.

📏 Geometry Topics for a Research Paper

Shapes and space are the two staples of geometry. Since its appearance in ancient times, it has evolved into a major field of study. Geometry’s most recent addition, topology, explores what happens to an object if you stretch, shrink, and fold it. Things can get pretty crazy from here! The following list contains 25 interesting geometry topics:

• What are the Archimedean solids?
• Find real-life uses for a rhombicosidodecahedron.
• What is studied in projective geometry?
• Compare the most common types of transformations.
• Explain how acute square triangulation works.
• Discuss the Borromean ring configuration.
• Investigate the solutions to Buffon’s needle problem.
• What is unique about right triangles?

• Describe the notion of Dirac manifolds.
• Compare the various relationships between lines.
• What is the Klein bottle?
• How does geometry translate into other disciplines, such as chemistry and physics?
• Explore Riemannian manifolds in Euclidean space.
• How can you prove the angle bisector theorem?
• Do a research on M.C. Escher’s use of geometry.
• Find applications for the golden ratio .
• Describe the importance of circles.
• Investigate what the ancient Greeks knew about geometry.
• What does congruency mean?
• Study the uses of Euler’s formula.
• How do CT scans relate to geometry?
• Why do we need n-dimensional vectors?
• How can you solve Heesch’s problem?
• What are hypercubes?
• Analyze the use of geometry in Picasso’s paintings.

➗ Calculus Topics to Write a Paper on

You can describe calculus as a more complicated algebra. It’s a study of change over time that provides useful insights into everyday problems. Applied calculus is required in a variety of fields such as sociology, engineering, or business. Consult this list of compelling topics on a calculus paper:

• What are the differences between trigonometry, algebra, and calculus?
• Explain the concept of limits.
• Describe the standard formulas needed for derivatives.
• How can you find critical points in a graph?
• Evaluate the application of L’Hôpital’s rule.
• How do you define the area between curves?
• What is the foundation of calculus?

• How does multivariate calculus work?
• Discuss the use of Stokes’ theorem.
• What does Leibniz’s integral rule state?
• What is the Itô stochastic integral?
• Explore the influence of nonstandard analysis on probability theory.
• Research the origins of calculus.
• Who was Maria Gaetana Agnesi?
• Define a continuous function.
• What is the fundamental theorem of calculus?
• How do you calculate the Taylor series of a function?
• Discuss the ways to resolve Runge’s phenomenon.
• Explain the extreme value theorem.
• What do we need predicate calculus for?
• What are linear approximations?
• When does an integral become improper?
• Describe the Ratio and Root Tests.
• How does the method of rings work?
• Where do we apply calculus in real-life situations?

💵 Business Math Topics to Write About

You don’t have to own a company to appreciate business math. Its topics range from credits and loans to insurance, taxes, and investment. Even if you’re not a mathematician, you can use it to handle your finances. Sounds interesting? Then have a look at the following list:

• What are the essential skills needed for business math?
• How do you calculate interest rates?
• Compare business and consumer math.
• What is a discount factor?
• How do you know that an investment is reasonable?
• When does it make sense to pay a loan with another loan?
• Find useful financing techniques that everyone can use.
• How does critical path analysis work?
• Explain how loans work.
• Which areas of work utilize operations research?
• How do businesses use statistics?
• What is the economic lot scheduling problem?
• Compare the uses of different chart types.
• What causes a stock market crash?
• How can you calculate the net present value?
• Explore the history of revenue management.
• When do you use multi-period models?
• Explain the consequences of depreciation.
• Are annuities a good investment?
• Would the U.S. financially benefit from discontinuing the penny?
• What caused the United States housing crash in 2008?
• How do you calculate sales tax?
• Describe the notions of markups and markdowns. 
• Investigate the math behind debt amortization.
• What is the difference between a loan and a mortgage?

With all these ideas, you are perfectly equipped for your next math paper. Good luck!

• What Is Calculus?: Southern State Community College
• What Is Mathematics?: Tennessee Tech University
• What Is Geometry?: University of Waterloo
• What Is Algebra?: BBC
• Ten Simple Rules for Mathematical Writing: Ohio State University
• Practical Algebra Lessons: Purplemath
• Topics in Geometry: Massachusetts Institute of Technology
• The Geometry Junkyard: All Topics: Donald Bren School of Information and Computer Sciences
• Calculus I: Lamar University
• Business Math for Financial Management: The Balance Small Business
• What Is Mathematics: Life Science
• What Is Mathematics Education?: University of California, Berkeley
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100 Interesting Research Paper Topics for High Schoolers

What’s covered:, how to pick the right research topic, elements of a strong research paper.

• Interesting Research Paper Topics

Composing a research paper can be a daunting task for first-time writers. In addition to making sure you’re using concise language and your thoughts are organized clearly, you need to find a topic that draws the reader in.

CollegeVine is here to help you brainstorm creative topics! Below are 100 interesting research paper topics that will help you engage with your project and keep you motivated until you’ve typed the final period. 

A research paper is similar to an academic essay but more lengthy and requires more research. This added length and depth is bittersweet: although a research paper is more work, you can create a more nuanced argument, and learn more about your topic. Research papers are a demonstration of your research ability and your ability to formulate a convincing argument. How well you’re able to engage with the sources and make original contributions will determine the strength of your paper. 

You can’t have a good research paper without a good research paper topic. “Good” is subjective, and different students will find different topics interesting. What’s important is that you find a topic that makes you want to find out more and make a convincing argument. Maybe you’ll be so interested that you’ll want to take it further and investigate some detail in even greater depth!

For example, last year over 4000 students applied for 500 spots in the Lumiere Research Scholar Program , a rigorous research program founded by Harvard researchers. The program pairs high-school students with Ph.D. mentors to work 1-on-1 on an independent research project . The program actually does not require you to have a research topic in mind when you apply, but pro tip: the more specific you can be the more likely you are to get in!

Introduction

The introduction to a research paper serves two critical functions: it conveys the topic of the paper and illustrates how you will address it. A strong introduction will also pique the interest of the reader and make them excited to read more. Selecting a research paper topic that is meaningful, interesting, and fascinates you is an excellent first step toward creating an engaging paper that people will want to read.

Thesis Statement

A thesis statement is technically part of the introduction—generally the last sentence of it—but is so important that it merits a section of its own. The thesis statement is a declarative sentence that tells the reader what the paper is about. A strong thesis statement serves three purposes: present the topic of the paper, deliver a clear opinion on the topic, and summarize the points the paper will cover.

An example of a good thesis statement of diversity in the workforce is:

Diversity in the workplace is not just a moral imperative but also a strategic advantage for businesses, as it fosters innovation, enhances creativity, improves decision-making, and enables companies to better understand and connect with a diverse customer base.

The body is the largest section of a research paper. It’s here where you support your thesis, present your facts and research, and persuade the reader.

Each paragraph in the body of a research paper should have its own idea. The idea is presented, generally in the first sentence of the paragraph, by a topic sentence. The topic sentence acts similarly to the thesis statement, only on a smaller scale, and every sentence in the paragraph with it supports the idea it conveys.

An example of a topic sentence on how diversity in the workplace fosters innovation is:

Diversity in the workplace fosters innovation by bringing together individuals with different backgrounds, perspectives, and experiences, which stimulates creativity, encourages new ideas, and leads to the development of innovative solutions to complex problems.

The body of an engaging research paper flows smoothly from one idea to the next. Create an outline before writing and order your ideas so that each idea logically leads to another.

The conclusion of a research paper should summarize your thesis and reinforce your argument. It’s common to restate the thesis in the conclusion of a research paper.

For example, a conclusion for a paper about diversity in the workforce is:

In conclusion, diversity in the workplace is vital to success in the modern business world. By embracing diversity, companies can tap into the full potential of their workforce, promote creativity and innovation, and better connect with a diverse customer base, ultimately leading to greater success and a more prosperous future for all.

Reference Page

The reference page is normally found at the end of a research paper. It provides proof that you did research using credible sources, properly credits the originators of information, and prevents plagiarism.

There are a number of different formats of reference pages, including APA, MLA, and Chicago. Make sure to format your reference page in your teacher’s preferred style.

• Analyze the benefits of diversity in education.
• Are charter schools useful for the national education system?
• How has modern technology changed teaching?
• Discuss the pros and cons of standardized testing.
• What are the benefits of a gap year between high school and college?
• What funding allocations give the most benefit to students?
• Does homeschooling set students up for success?
• Should universities/high schools require students to be vaccinated?
• What effect does rising college tuition have on high schoolers?
• Do students perform better in same-sex schools?
• Discuss and analyze the impacts of a famous musician on pop music.
• How has pop music evolved over the past decade?
• How has the portrayal of women in music changed in the media over the past decade?
• How does a synthesizer work?
• How has music evolved to feature different instruments/voices?
• How has sound effect technology changed the music industry?
• Analyze the benefits of music education in high schools.
• Are rehabilitation centers more effective than prisons?
• Are congestion taxes useful?
• Does affirmative action help minorities?
• Can a capitalist system effectively reduce inequality?
• Is a three-branch government system effective?
• What causes polarization in today’s politics?
• Is the U.S. government racially unbiased?
• Choose a historical invention and discuss its impact on society today.
• Choose a famous historical leader who lost power—what led to their eventual downfall?
• How has your country evolved over the past century?
• What historical event has had the largest effect on the U.S.?
• Has the government’s response to national disasters improved or declined throughout history?
• Discuss the history of the American occupation of Iraq.
• Explain the history of the Israel-Palestine conflict.
• Is literature relevant in modern society?
• Discuss how fiction can be used for propaganda.
• How does literature teach and inform about society?
• Explain the influence of children’s literature on adulthood.
• How has literature addressed homosexuality?
• Does the media portray minorities realistically?
• Does the media reinforce stereotypes?
• Why have podcasts become so popular?
• Will streaming end traditional television?
• What is a patriot?
• What are the pros and cons of global citizenship?
• What are the causes and effects of bullying?
• Why has the divorce rate in the U.S. been declining in recent years?
• Is it more important to follow social norms or religion?
• What are the responsible limits on abortion, if any?
• How does an MRI machine work?
• Would the U.S. benefit from socialized healthcare?
• Elderly populations
• The education system
• State tax bases
• How do anti-vaxxers affect the health of the country?
• Analyze the costs and benefits of diet culture.
• Should companies allow employees to exercise on company time?
• What is an adequate amount of exercise for an adult per week/per month/per day?
• Discuss the effects of the obesity epidemic on American society.
• Are students smarter since the advent of the internet?
• What departures has the internet made from its original design?
• Has digital downloading helped the music industry?
• Discuss the benefits and costs of stricter internet censorship.
• Analyze the effects of the internet on the paper news industry.
• What would happen if the internet went out?
• How will artificial intelligence (AI) change our lives?
• What are the pros and cons of cryptocurrency?
• How has social media affected the way people relate with each other?
• Should social media have an age restriction?
• Discuss the importance of source software.
• What is more relevant in today’s world: mobile apps or websites?
• How will fully autonomous vehicles change our lives?
• How is text messaging affecting teen literacy?

Mental Health

• What are the benefits of daily exercise?
• How has social media affected people’s mental health?
• What things contribute to poor mental and physical health?
• Analyze how mental health is talked about in pop culture.
• Discuss the pros and cons of more counselors in high schools.
• How does stress affect the body?
• How do emotional support animals help people?
• What are black holes?
• Discuss the biggest successes and failures of the EPA.
• How has the Flint water crisis affected life in Michigan?
• Can science help save endangered species?
• Is the development of an anti-cancer vaccine possible?

Environment

• What are the effects of deforestation on climate change?
• Is climate change reversible?
• How did the COVID-19 pandemic affect global warming and climate change?
• Are carbon credits effective for offsetting emissions or just marketing?
• Is nuclear power a safe alternative to fossil fuels?
• Are hybrid vehicles helping to control pollution in the atmosphere?
• How is plastic waste harming the environment?
• Is entrepreneurism a trait people are born with or something they learn?
• How much more should CEOs make than their average employee?
• Can you start a business without money?
• Should the U.S. raise the minimum wage?
• Discuss how happy employees benefit businesses.
• How important is branding for a business?
• Discuss the ease, or difficulty, of landing a job today.
• What is the economic impact of sporting events?
• Are professional athletes overpaid?
• Should male and female athletes receive equal pay?
• What is a fair and equitable way for transgender athletes to compete in high school sports?
• What are the benefits of playing team sports?
• What is the most corrupt professional sport?

Where to Get More Research Paper Topic Ideas

If you need more help brainstorming topics, especially those that are personalized to your interests, you can use CollegeVine’s free AI tutor, Ivy . Ivy can help you come up with original research topic ideas, and she can also help with the rest of your homework, from math to languages.

Disclaimer: This post includes content sponsored by Lumiere Education.

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100 Research Topics for High School Students

By Eric Eng

High school is such an exciting time for stretching your intellectual muscles. One awesome way to do that is through research projects. But picking the right topic can make all the difference. It should be something you’re passionate about and also practical to tackle. So, we’ve put together a list of engaging research topics for high school students across ten different subjects: physics, math, chemistry, biology, engineering, literature, psychology, political science, economics, and history. Each topic is crafted to spark your curiosity and help you grow those research skills.

Physics Research Topics

Research topics for high school students in physics are an exciting way to enhance your understanding of the universe.

1. Gravitational Waves and Space-Time

How do gravitational waves distort space-time, and what can these distortions tell us about the origins of the universe?

2. Quantum Entanglement Applications

What are the potential technological applications of quantum entanglement, and how can it be harnessed for secure communication?

3. Dark Matter and Galaxy Formation

How does dark matter affect the formation and behavior of galaxies, and what evidence supports its existence?

4. Physics of Renewable Energy

What are the fundamental physical principles behind renewable energy sources, and how do they compare in terms of efficiency?

5. Superconductors in Technology

How are superconductors utilized in modern technology, and what advantages do they offer over traditional materials?

6. Particle Physics at the Large Hadron Collider

What significant discoveries have been made at the Large Hadron Collider, and how do they advance our understanding of particle physics?

7. Microgravity Effects on Organisms

How does microgravity affect the physiological and biological functions of organisms during space travel?

8. Thermodynamics and Engine Efficiency

How do the principles of thermodynamics improve the efficiency and performance of internal combustion engines?

9. Electromagnetism in Wireless Communication

How do principles of electromagnetism enable the functioning of wireless communication systems?

10. Cosmic Radiation and Human Space Travel

What are the effects of cosmic radiation on astronauts, and what measures can be taken to protect them during long-term space missions?

These research topics for high school students are designed to deepen your knowledge and prepare you for advanced studies and innovations in the field of physics.

Math Research Topics

Math research topics for high school students are a fantastic way to explore real-world problems through the lens of mathematical principles .

11. Graph Theory and Social Networks

How can graph theory be applied to identify influential nodes and optimize information flow in social networks?

12. Cryptography and Data Security

What cryptographic techniques are most effective in securing online communications and protecting sensitive data?

13. Mathematical Models in Disease Spread

How do SIR models predict the spread of infectious diseases, and what factors affect their accuracy?

14. Game Theory and Economic Decisions

How does game theory explain the strategic behavior of firms in competitive markets?

15. Calculus in Engineering Design

How is calculus used to optimize the structural integrity and efficiency of engineering designs?

16. Linear Algebra in Computer Graphics

How do matrices and vectors facilitate the creation and manipulation of digital images in computer graphics?

17. Statistical Methods in Public Health

What statistical methods are most effective in analyzing public health data to track disease outbreaks?

18. Differential Equations and Population Dynamics

How do differential equations model the population dynamics of endangered species in varying environments?

19. Probability Theory in Risk Management

How is probability theory applied to assess and mitigate financial risks in investment portfolios?

20. Mathematical Modeling in Climate Change Predictions

How do mathematical models simulate climate change scenarios, and what variables are most critical to their predictions?

These research topics for high school students are designed to spark your curiosity and help you build critical thinking skills and practical knowledge.

Chemistry Research Topics

Chemistry research topics for high school students open up a world of molecular wonders and practical applications.

21. Photosynthesis Chemical Processes

How do the chemical reactions involved in photosynthesis convert light energy into chemical energy in plants?

22. Catalysts and Reaction Rates

How do different catalysts influence the rate of chemical reactions, and what factors affect their efficiency?

23. Environmental Pollutants and Atmospheric Chemistry

How do specific environmental pollutants alter chemical reactions in the atmosphere, and what are the consequences for air quality?

24. Green Chemistry Principles

How can green chemistry practices be applied to reduce chemical waste and promote sustainable industrial processes?

25. Nanotechnology in Drug Delivery

How does nanotechnology improve the targeted delivery and effectiveness of drugs within the human body?

26. Plastic Composition and Environmental Impact

How does the chemical composition of various plastics affect their environmental impact and degradation process?

27. Enzymes in Biochemical Reactions

How do enzymes catalyze biochemical reactions, and what factors influence their activity and specificity?

28. Electrochemistry in Battery Technology

How are electrochemical principles applied to improve the performance and sustainability of modern batteries?

29. Chemical Fertilizers and Soil Health

How do chemical fertilizers impact soil health and agricultural productivity, and what alternatives exist to minimize negative effects?

30. Spectroscopy in Compound Identification

How is spectroscopy used to identify and analyze the composition of chemical compounds in various fields?

These research topics for high school students are designed to enhance your understanding of chemical principles and their real-world applications.

Biology Research Topics

Research topics for high school students in biology open up a fascinating window into the complexities of the living world.

31. Genetic Basis of Inherited Diseases

How do specific genetic mutations cause inherited diseases, and what are the mechanisms behind their transmission?

32. Climate Change and Biodiversity

How does climate change affect biodiversity in different ecosystems, and what species are most at risk?

33. Microbiomes and Human Health

How do microbiomes influence human health, and what roles do they play in disease prevention and treatment?

34. Habitat Destruction and Wildlife

How does habitat destruction impact wildlife populations and their behaviors, and what are the long-term ecological consequences?

35. Genetic Engineering in Agriculture

How can genetic engineering techniques improve crop yields and resistance to pests and diseases?

36. Pollution and Aquatic Ecosystems

How do various pollutants affect aquatic ecosystems, and what are the implications for water quality and marine life?

37. Stem Cells in Regenerative Medicine

How are stem cells used in regenerative medicine to repair and replace damaged tissues and organs?

38. Evolutionary Biology and Species Adaptation

How do evolutionary principles explain the adaptation of species to changing environmental conditions?

39. Diet and Human Health

How do different dietary choices impact human health, and what are the underlying mechanisms?

40. Bioinformatics in Genetic Research

How is bioinformatics used to analyze genetic data, and what insights can it provide into genetic disorders and evolution?

These research topics for high school students are designed to deepen your understanding of life sciences and prepare you for advanced studies and research in the field.

Engineering Research Topics

Engineering research topics give high school students practical insights into designing and creating innovative solutions.

41. 3D Printing in Manufacturing

How does 3D printing technology revolutionize manufacturing processes, and what are its key advantages over traditional methods?

42. Robotics in Modern Industry

How do robotics improve efficiency and productivity in modern industries, and what are some specific applications?

43. Sustainable Building Design

What principles of sustainable building design can be applied to reduce environmental impact and enhance energy efficiency?

44. Artificial Intelligence in Engineering

How is artificial intelligence integrated into engineering solutions to optimize processes and solve complex problems?

45. Renewable Energy Technologies

How do renewable energy technologies, such as solar and wind power, contribute to reducing carbon footprints?

46. Aerodynamics in Vehicle Design

How do aerodynamic principles enhance the performance and fuel efficiency of vehicles?

47. Material Science in Engineering Innovations

How do advancements in material science lead to innovative engineering solutions and improved product performance?

48. Civil Engineering in Urban Development

How does civil engineering contribute to urban development and infrastructure planning in growing cities?

49. Electrical Engineering in Modern Electronics

How are electrical engineering principles applied in the design and development of modern electronic devices?

50. Biomedical Engineering and Medical Devices

How does biomedical engineering contribute to the development of innovative medical devices and healthcare solutions?

These research topics for high school students are designed to broaden your understanding of engineering principles and their real-world applications, preparing you for future innovations and problem-solving in the field.

Literature Research Topics

Literature research topics give high school students the chance to delve into the rich and varied world of written works and their broader implications.

51. Identity in Contemporary Young Adult Fiction

How do contemporary young adult fiction novels explore themes of identity and self-discovery among teenagers?

52. Historical Events and Literary Movements

How have significant historical events influenced and shaped various literary movements, such as Romanticism or Modernism?

53. Symbolism in Classic Literature

How do authors use symbolism in classic literature to convey deeper meanings and themes?

54. Narrative Structure in Modern Storytelling

How do modern authors utilize narrative structures to enhance the storytelling experience and engage readers?

55. Literary Devices in Poetry

How do poets employ literary devices like metaphor, simile, and alliteration to enrich the meaning and emotional impact of their work?

56. Dystopian Themes in Science Fiction

How do science fiction authors use dystopian themes to comment on contemporary social and political issues?

57. Cultural Diversity and Literary Expression

How does cultural diversity influence literary expression and contribute to the richness of global literature?

58. Feminist Theory in Literary Analysis

How is feminist theory applied to analyze and interpret the representation of women and gender roles in literature?

59. Postcolonial Literature Principles

How does postcolonial literature address themes of colonization, identity, and resistance, and what are its key characteristics?

60. Intertextuality in Modern Novels

How do modern novelists use intertextuality to create layers of meaning and connect their works with other literary texts?

These research topics for high school students are designed to deepen your understanding of literary techniques and themes. They prepare you for advanced literary analysis and appreciation.

Psychology Research Topics

Psychology research topics offer high school students a fascinating journey into the complexities of human behavior and mental processes.

61. Social Media and Adolescent Mental Health

How does social media usage affect the mental health and well-being of adolescents, particularly in terms of anxiety and depression?

62. Stress and Cognitive Function

How does chronic stress impact cognitive functions such as memory, attention, and decision-making?

63. Cognitive-Behavioral Therapy and Anxiety Disorders

How effective is cognitive-behavioral therapy (CBT) in treating various anxiety disorders, and what mechanisms underlie its success?

64. Early Childhood Experiences and Personality Development

How do early childhood experiences shape personality traits and influence long-term behavioral patterns?

65. Sleep and Memory Retention

How does the quality and quantity of sleep affect the retention and recall of memories?

66. Neuroplasticity in Brain Recovery

How does neuroplasticity facilitate brain recovery and adaptation following injury or neurological illness?

67. Mindfulness Practices and Emotional Regulation

How do mindfulness practices help individuals regulate their emotions and reduce symptoms of stress and anxiety?

68. Genetic Factors in Mental Health Disorders

How do genetic predispositions contribute to the development of mental health disorders, such as schizophrenia and bipolar disorder?

69. Group Dynamics and Decision-Making

How do group dynamics influence individual decision-making processes and outcomes in collaborative settings?

70. Psychological Assessments in Educational Settings

How are psychological assessments used to support student learning and development in educational environments?

These research topics for high school students are designed to enhance your understanding of mental processes and behavior. They prepare you for advanced studies and practical applications in the field.

Political Science Research Topics

Political science research topics offer high school students an exciting opportunity to dive into the complexities of political systems and their impact on society.

71. Social Media and Political Campaigns

How does social media influence the strategies and outcomes of political campaigns, particularly in terms of voter engagement and misinformation?

72. International Organizations and Global Governance

How do international organizations, such as the United Nations, contribute to global governance and conflict resolution?

73. Political Corruption and Economic Development

How does political corruption affect economic development and stability in different countries?

74. Democracy in Political Systems

How do the principles of democracy vary across different political systems, and what impact do these differences have on governance?

75. Public Opinion and Policy-Making

How does public opinion shape government policy-making processes and legislative decisions?

76. Political Ideology and Government Policies

How do different political ideologies influence the formulation and implementation of government policies?

77. Electoral Systems and Political Representation

How do various electoral systems impact political representation and voter behavior?

78. Political Communication in Media

How do media and communication strategies shape public perception of political issues and candidates?

79. Globalization and National Sovereignty

How does globalization affect national sovereignty and the ability of states to maintain independent policies?

80. Political Theory and Social Movements

How can political theory be used to understand the origins, development, and impact of social movements?

These research topics for high school students are designed to enhance your understanding of political processes and theories. They prepare you for advanced studies and informed civic participation.

Economics Research Topics

Economics research topics give high school students valuable insights into how economic systems and policies shape our world.

81. Minimum Wage Laws and Employment Rates

How do changes in minimum wage laws impact employment rates across different sectors and demographics?

82. Fiscal Policy in Economic Recessions

How do government fiscal policies, such as stimulus packages, help manage and mitigate the effects of economic recessions?

83. Globalization and Local Economies

How does globalization influence local economies, particularly in terms of job creation and market competition?

84. Behavioral Economics and Consumer Decisions

How do psychological factors and cognitive biases affect consumer decision-making and market trends?

85. Trade Policies and International Relations

How do specific trade policies impact international relations and global trade dynamics?

86. Technology in Economic Growth

How do technological advancements drive economic growth and productivity in various industries?

87. Taxation and Income Distribution

How do different taxation policies affect income distribution and economic inequality within a society?

88. Economic Modeling and Market Predictions

How are economic models used to predict market trends, and what are the limitations of these models?

89. Inflation and Purchasing Power

How does inflation impact purchasing power and the cost of living for consumers?

90. Econometrics in Economic Data Analysis

How is econometrics used to analyze and interpret complex economic data, and what insights can it provide?

These research topics for high school students are designed to deepen your understanding of economic principles and their real-world applications, preparing you for further studies and informed decision-making in the field.

History Research Topics

History research topics for high school students offer a deep dive into the past. They help you understand how it shapes our present and future.

91. Industrial Revolution: Causes and Consequences

What were the key factors that led to the Industrial Revolution, and how did it impact society and the economy?

92. Colonialism and Indigenous Populations

How did colonial rule affect the cultural, social, and economic lives of indigenous populations?

93. Women in Historical Social Movements

What roles did women play in various social movements throughout history, and what were their contributions?

94. Historical Revisionism in Modern Historiography

What are the principles and controversies surrounding historical revisionism in contemporary historiography?

95. Technological Advancements and Historical Events

How have technological innovations influenced significant historical events and driven societal changes?

96. Major Wars: Causes and Effects

What were the primary causes, key events, and consequences of major wars in history?

97. Religion in Shaping Historical Narratives

How has religion influenced the crafting and interpretation of historical narratives across different cultures?

98. Historiography and Documenting Events

What methods and principles are used in historiography to accurately record and analyze historical events?

99. Economic Changes and Historical Societies

How have economic shifts impacted social structures and historical developments in various societies?

100. Primary Sources in Historical Research

Why are primary sources important in historical research, and how are they used to ensure accuracy and depth in historical analysis?

These research topics for high school students are designed to deepen your understanding of past events and their significance, preparing you for advanced studies and critical historical inquiry.

How do I pick the right high school research topic?

Choosing the right research topic involves considering your interests, the availability of resources, and the relevance of the topic to current issues. Start by identifying subjects you are passionate about. Then, look for specific questions within those subjects that spark your curiosity. It’s also important to consider the feasibility of the research, including access to necessary materials and data.

What high school research topics are in demand today?

High-demand research topics for high school students today often align with current global challenges and advancements. In science and technology, areas such as renewable energy, artificial intelligence , and genetic engineering are popular. In social sciences, topics like the impact of social media, political polarization, and mental health are highly relevant. Keeping up with current events and scientific journals can help you identify trending topics.

What resources should I use for my high school research?

Effective research requires a mix of resources. Start with your school library and online databases like JSTOR or Google Scholar for academic papers. Utilize books, reputable websites, and expert interviews to gather diverse perspectives. Don’t overlook primary sources, such as historical documents or scientific data, which provide firsthand information. Additionally, consider using software tools for data analysis and project management.

How can I publish or present my high school research?

Publishing and presenting your research can enhance its impact and your academic profile. Consider submitting your work to high school research journals , science fairs , and local or national competitions. You can also present at school or community events, or create a blog or website to share your findings. Networking with teachers and professors can provide guidance and additional opportunities for publication and presentation.

How does high school research enhance my college applications?

High school research demonstrates your ability to undertake independent projects, critical thinking, and problem-solving skills. Colleges value these attributes as they indicate readiness for college-level work. Including research experience in your application can set you apart from other applicants. It shows your commitment to learning and your ability to contribute to academic and extracurricular activities at the college level.

Want to assess your chances of admission? Take our FREE chances calculator today!

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210 Brilliant Math Research Topics and Ideas for Students

Table of Contents

Do you have to submit a math research paper? Are you looking for the best math research topics? Well, in this blog post, we have shared a list of 150+ interesting math research topics to consider for assignments and academic projects. If you are a student who is pursuing a degree in mathematics, then you can very well use the topic ideas suggested here. Also, you can check this blog post and get to know the important steps for writing a brilliant math research paper.

What is Mathematics?

Mathematics is a broad academic discipline that focuses on numbers, structures, spaces, and shapes. This subject contains many analysis and calculation methods. Especially in the real world, math is considered an effective problem-solving tool. By using math, you can find solutions for both simple and complex problems.

Basically, mathematics is an integrated language that is widely used in several fields such as engineering, physics, medicine, finance, computer, business, and biology. Apart from the complex scientific fields, even math plays a vital role in the basic cost and time calculation in our everyday life.

Different Branches of Mathematics

Listed below are some popular branches of mathematics.

Arithmetic: It is a basic branch of math that focuses on numbers and their associated operations such as addition, subtraction, multiplication, and division.

Algebra: When the numbers are unknown, algebra steps in. Generally, along with numbers, algebra uses the letters such as A, B, X, and Y to represent unknown quantities. Mainly, businesses depend on algebra concepts to predict their sales.

Geometry: It is a popular branch of mathematics that deals with shapes, sizes, and figures. The concept commonly revolves around lines, points, solids, angles, and surfaces.

Apart from all these common branches, mathematics also includes more advanced types such as calculus, trigonometry, statistics, topology, probability, etc.

How to Write a Math Research Paper?

In general, a math research paper is an academic paper that is prepared to explain a mathematical concept with proper results. For writing a math research paper, first, you must have a good research topic from any branch of mathematics. As math is a vast discipline, you can easily search and find plenty of research topics from it. But when you have many topics, then it will be more tedious to identify one perfect topic out of them all.

Right now, are you searching for a perfect math research topic? Well, then this is what you should do during the topic selection process to spot the right topic.

Topic Selection

Whenever you are asked to come up with a research paper topic on your own, initially, restrict yourself to the research area that you have strong knowledge of and are passionate about. Next, in that research area, explore and identify one great topic that has a broad scope to evaluate and express your ideas.

Remember, the topic you select should be comfortable for you to perform research and write about. Never pick a topic with less or no research scope. The topic should support the research method of your choice. Most importantly, give preference to the topic that has wide research information, references, and evidence. Also, before finalizing the topic, check whether your topic satisfies your instructor’s guidelines.

Research Paper Writing

After you have found a good math research topic, you can proceed to write the research paper. The research paper you write should follow a proper format and structure. So, in the math research paper, make sure to include the following essential sections.

Introduction

Implications.

In the introduction section, you should first give brief background information about your topic to familiarize your readers. Here, mainly you should explain the primary concepts along with the history of its terms. Also, you should state the basic research problem and discuss the symbols and principles that you are going to use in the essay.

The body of your research paper should elaborate on all your findings. Particularly, in the body paragraphs, you should talk about the formulas, theories, and mathematical analysis methods you have used to find solutions for the research problem.

The implication is the last or closing part of your research paper. Here, you should share your research insights with the readers. Also, you should include a brief summary of all the important points that you have discussed in the entire essay.

List of the Best Math Research Topics

Are you struggling to come up with a good math research paper topic for your assignment? No worries! Here we have shared a list of top-rated math research topic ideas on various branches of mathematics.

Explore them all and find a topic that suits you perfectly.

Simple and Easy Math Topics

• Explain the working of Partial fractions.
• Discuss the application of Mathematics in daily life.
• What is the basis of Cramer’s rule?
• How to solve Heesch’s problem?
• Explain the history of calculus .
• What is Euler’s formula?
• Explain the working of Logarithms.
• What are the different types of sequences?
• Explain the different types of Transformations.
• Define Brun’s constant.
• What are the methods of factoring quadratics?
• Examine Archimedean solids.
• Explain Gaussian elimination.
• Write about encryption and prime numbers.
• How does Hypercube work?
• Analyze Pygaoethores Theorem
• Describe the logicist definitions of mathematics
• Describe the purpose of homological algebra
• Compare and contrast Concave and Convex in geometry
• The study and contributions of Blaise Pascal to Probability
• Explain the Fibonacci series briefly
• How the Ancient Greek architecture influenced by mathematics?
• Discuss the ancient Egyptian mathematical applications and accomplishments
• Discuss the easiest ways to memorize algebraic expressions
• Algebra is an exposition on the invariants of matrices – Explain

Basic Math Topics for Middle School Students

• Define the Artin-Wedderburn theorem.
• How to calculate net worth?
• How to identify critical points in graphs?
• What is the role of statistics in business?
• Describe the principles of the Pythagoras theorem.
• What are the applications of finance in math?
• What do limits in math mean?
• Explain the ratio and root test.
• Define Jacobson’s density theorem.
• What are the principles of calculus?

Interesting Math Topics for High School Students

• What are the different number types? Explain with examples.
• Explain the need for imaginary numbers.
• How to calculate the interest rate?
• How to solve a matrix?
• How to prepare a chart of a company’s financial analysis?
• When to use a calculator in class?
• Explain the importance of the Binomial theorem.
• Write about Egyptian mathematics.
• Describe the applications of math in the workplace.
• How to solve linear equations?
• Describe the usage of hyperbola in math.
• Why do so many students hate math?
• What is the difference between algebra and arithmetic?
• How to calculate the mean value?
• What is the numerical data?

Math Research Paper Topics for Undergraduate Students

• Explain the different theories of mathematical logic.
• Discuss the origins of Greek symbols in mathematics.
• Explain the significance of circles.
• Analyze predictive models.
• Explain the emergence of patterns in chaos theory.
• Define abstract algebra.
• What is a continuous stochastic process?
• Write about the history of algebra.
• Analyze Monte Carlo methods for inverse problems.
• What are the goals of standardized testing?
• Define the Pentagonal number theorem.
• Discuss the Lorentz–FitzGerald contraction hypothesis in relativity.
• How to solve simultaneous equations.
• How do supercomputers solve complex mathematical problems?
• What is a parabola in geometry?

Math Research Topics for College Students

• Explain the Fibonacci sequence.
• What are the core problems of computational geometry?
• Discuss the practical applications of game theory.
• What is the Traveling Salesman Problem?
• Describe the Influence of math in biology.
• Analyze the meaning of fractals.
• Discuss the origin and evolution of mathematics.
• What is quantum computing?
• Explain Einstein’s field equation theory.
• What is the influence of math on chemistry?
• How to solve a Rubik’s cube mathematically?
• How to do complex numbers division?
• Explain the use of Boolean functions.
• Analyze the degrees in polynomial functions.
• How to solve Sudoku using mathematics?
• Explain the use of set theory.
• Explain the math behind the Koch snowflake.
• Explore the varieties of the Tower of Hanoi solutions.
• What is the difference between a discrete and a continuous probability distribution?
• How does encryption work?

Applied Math Research Topics

• What is the role of algorithms in probabilistic modeling?
• Explain the significance of step-stress modeling.
• Describe Newton’s laws of motion.
• What dimensions are used to examine fingerprints?
• Analyze statistical signal processing.
• How to do Galilean transformation?
• What is the role of mathematicians in crime data analysis and prevention?
• Explain the uncertainty principle.
• Discuss Liouville’s theorem in Hamiltonian mechanics.
• Analyze the perpendicular axes rule.

Business Math Research Topics

• What is the difference between a loan and a mortgage?
• How to calculate sales tax?
• Explore the math behind debt amortization.
• How do businesses use statistics?
• What is the economic lot scheduling problem?
• Explain how loans work.
• Discuss the significance of business math in real life.
• Define discount factor.
• What are the major causes of a stock market crash?
• Compare the uses of different types of charts.
• Describe the notions of markups and markdowns.
• How does critical path analysis work?
• What are the pros and cons of annuities?
• When to use multi-period models?
• Compare business and consumer math.

Advanced Math Research Paper Topics

• What is an oblivious transfer?
• Compare the Riemann and the Ruelle zeta functions.
• What are the different types of knapsack problems?
• Define an abelian group.
• What are the algorithms used for machine learning?
• Define various cases of algebraic cycles.
• When a trigonometric series is called a Fourier series?
• What is the minimum overlap problem?
• What are the basic properties of holomorphic functions?
• Describe the Bernoulli scheme.

Complex Math Research Topics

• Write about Napier’s bones.
• What makes a number big?
• Examine the notion of operator spaces.
• How do barcodes function?
• Define Fisher’s fundamental theorem of natural selection.
• What are the peculiarities of Borel’s paradox?
• How to design a train schedule for a whole country?
• Describe a hyperboloid in 3D geometry.
• What is an orthodiagonal quadrilateral?
• Explain how the Iwasawa theory relates to modular forms.

Math Research Ideas on Probability and Statistics

• Roll two dice and calculate a probability.
• Write about the Factorial moment in the Theory of Probability.
• Explain the principle of maximum entropy.
• Compare and contrast Cochran’s C test and his Q test.
• Discuss Skorokhod’s representation theorem in random variables
• How to apply the ANOVA method to rank.
• Analyze the De Moivre-Laplace theorem.
• What is the autoregressive conditional duration?
• Explain a negative probability.
• Discuss the practical applications of the Bates distribution.

Algebra Research Topics

• Explain Descartes’ Rule of Signs.
• How to factor quadratics?
• What is the use of F-algebras?
• Discuss the differential equation.
• What is the difference between eigenvectors and eigenvalues?
• What are the properties of a binary operation in algebra?
• What is a commutative ring in algebra?
• Discuss the origin of the distance formula.
• Explain the quadratic formula.
• Analyze the unary operator.
• Define range and domain in algebra.
• Describe the Noetherian ring.
• Discuss the Morita duality in algebraic structures.
• Define the Abel–Ruffini theorem.
• What is the use of determinants?

Math Research Paper Topics on Geometry

• Research the real-life uses of a rhombicosidodecahedron.
• Find out the solutions to Buffon’s needle problem.
• What is unique about right triangles?
• What is the Klein bottle?
• What are the Archimedean solids?
• What does congruency mean?
• Discuss the role of trigonometry in computer graphics.
• What is the need for n-dimensional vectors?
• Explain the Japanese theorem for concyclic polygons.
• Prove the angle bisector theorem.
• Identify the applications for the golden ratio.
• Explain the Heronian tetrahedron.
• Describe the notion of Dirac manifolds.
• What is the use of geometry in Picasso’s paintings?
• How do CT scans relate to geometry?

Calculus Research Topics

• How to calculate the Taylor series of a function?
• What is the role of calculus in real life?
• Discuss the Leibniz integral rule
• Discuss and analyze linear approximations.
• What is the use of predicate calculus?
• What is the foundation of calculus?
• How to calculate the area between curves?
• Describe the standard formulas needed for derivatives.
• Explain the working of multivariate calculus.
• Define the fundamental theorem of calculus.

Outstanding Math Research Topics

• What is a sphericon?
• What is the role of Mathematics in Artificial Intelligence?
• Define De Finetti’s theorem in probability and statistics.
• How to calculate the slope of a curve?
• Discuss the Stern-Brocot tree.
• Explain Pascal’s Triangle.
• Analyze the Georg Cantor set theory.
• How to measure infinity?
• Explain the Scholz conjecture.
• How is geometry used in contemporary architectural designs?
• How to solve the Suslin problem?
• What is a tree automaton?
• Explain the working of the Back-and-forth method.
• What is a Turing machine?
• Discuss the linear speedup theorem.
• Discuss the benefits of using truth tables to present the logical validity of a propositional expression
• Critical analysis of the major concepts in ancient Egyptian mathematics
• Discuss the similarities and differences between a continuous and a discrete probability distribution
• Analysis of the problem with the wholeness axiom and Kunen’s inconsistency theorem
• Develop a study focusing on the Seven Bridges of Königsberg and relate the problem to the city or state of your choice

Latest Math Research Topics

• What does point zero reflect on a graph where the vertical and horizontal lines meet?
• How to recognize adjacent angles easily without any trouble?
• Compare the differential vs. analytic geometry by citing relevant examples.
• Explain how to use a graphics system for solving various types of equations.
• How to divide the feasible and non-feasible regions in linear programming?
• What are confidence intervals and how it helps in statistical math?
• How to differentiate the effect of a magnetic field on a given point of the circle by using appropriate differential formula?
• What are the different types of identities that are used in trigonometric functions?
• Why polynomials are difficult to solve as compared to monomials? Give examples.
• Explain radical expressions and their significance with examples.

Final Words

We hope you have identified an ideal topic from the list of math research topics and ideas recommended above. If you haven’t found a unique research topic or need assistance to complete your math research paper, then contact us.

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166 Extraordinary Math Research Topics For Your Papers

Math research topics cover various genres from which students can choose. Many people think that a research project on a math topic is dull. However, mathematics can be a wonderful and vivid field. Since it’s a universal language, mathematics can describe anything and everything, from galaxies that orbit each other to music. However, the broad nature of this study field also makes selecting a research paper difficult. That’s because learners want to pick interesting topics that will impress educators to award them top scores. This article lists the best math research paper topics. It’s useful because it inspires students to select or customize topics for their academic essays without much struggle.

What Are The Different Types Of Math?

As hinted, math covers several genres. Here are the primary types of mathematics:

Geometry: It’s a math branch that deals with the shapes, size, and relative position of figures. Many people consider geometry a practical math branch because it examines figures, shapes, sizes, and features of various entities, including parts like solids, lines, surfaces, lines, and angles. Algebra: It assists in solving equations and manipulating symbols. This branch helps students represent unknown quantities with alphabets and use them alongside numbers. Calculus: This area is vital in determining rates of change, such as velocity and acceleration. Arithmetic: Arithmetic is the most common and oldest math branch, encompassing basis number operations. These operations include subtraction, addition, divisions, and multiplications, and some schools shorten it as BODMAS. Statistics and Probability: They help analyze numerical data to make predictions. Probability is about chances, while statistics entails handling different data using various techniques. Trigonometry: It assists in calculating angles and distances between points. It mainly deals with triangles’ relationships, sides, and curves.

Now that you understand the types of mathematics, it’s easier to select a suitable research topic. The following are some of the best topic ideas in math. 

 Undergraduate Math Research Topics

Maybe you’re pursuing your undergraduate studies. However, you have challenges comprehending math topics, yet the professor expects you to write a superior paper. In that case, here’s a list of engaging research topics in math to consider for your essays.

• An in-depth comprehension of the meaning of discrete random variables in math and their identification
• Math evolution- Comprehending the Gauss-Markov
• Primary math theorems- Investigating how they work
• Continuous stochastic process- Exploring its role in the math process
• Analyzing the Dempster-Shafer theory
• The application of the transferable belief model
• Exploring the use of math in artificial intelligence
• The application of mathematics in daily life
• Algebra and its history
• Math and culture- What’s the relationship?
• How drawing and painting could help with mathematics
• Ways to boost math interest among learners
• The social and political significance of learning mathematics
• Circles and their relevance in mathematics
• Challenges to math learning in public schools
• Prove the use of F-Algebras
• Understanding the meaning of abstract algebra
• Discuss geometry and algebra
• How acute square triangulation works
• Discuss the essence of right triangles
• Why non-Euclidean geometry should be compulsory for math students
• Investigating number problems
• Discuss the meaning of Dirac manifolds
• How geometry influences chemistry and physics
• Riemannian manifolds’ application in the Euclidean space

These are exciting math topics for undergraduate students. Nevertheless, prepare adequate time and resources to investigate any of these titles to draft a winning essay. You might have to provide theoretical and practical assessments when writing your essay.

Math Research Topics for High School Learners

Maybe your high school teacher asked you to write a research paper. Choosing a familiar topic is an excellent way to get a high grade. Here are some of the best math research paper topics for high school.

• How to draw a chart representing the financial analysis of a prominent company over the last five years
• How to solve a matrix- The vital principles and formulas to embrace
• Exploring various techniques for solving finance and mathematical gaps
• Discount factor- Why it’s crucial for learners and ways to achieve it
• Calculating the interest rate and its essence in the banking industry
• Why imaginary numbers are important
• Investigating the application of math in the workplace
• Explain why learners hate mathematics teachers
• What makes math a complex subject?
• Is making math compulsory in high school a good thing?
• How to solve a dice question from a probability perspective
• Understanding the Binomial theorem and its essence
• Investigating Egyptian mathematics
• Hyperbola- Understanding it and its use in math
• When should students use calculators in class?
• How to solve linear equations
• Is the Pythagoras theorem important in math?
• The interdependence between math and art
• Philosophy’s role in math
• Numerical data overview

High school learners can pick any of these titles and develop them into an essay. Nevertheless, they should prepare to spend some time investigating their topics to write pieces that will impress their educators. Titles that address math history and its influence on education can also suit high school students. However, learners should select titles that fulfil the academic requirements set by the educators.

Applied Math Research Topics

As a branch, applied math deals with mathematical methods and their real-life applications. These methods are manifest in engineering, finance, medicine, biology, physics, and others. Here are some of the exciting topics in this field.

• Dimensions for examining fingerprints
• Computer tomography and its significance
• Step-stress modelling- What is its importance?
• Explain the essence of data mining- How does it benefit the banking sector?
• A detailed examination of nonlinear models
• How genes discovery helps determine unhealthy and healthy patients
• Algorithms and their role in probabilistic modelling
• Mathematicians and their importance in robots’ development
• Mathematicians’ role in crime prevention and data analysis
• The essence of Law of Motion by Isaac in real life
• The importance of math in energy conservation
• Math and its role in quantum theory
• Analyzing the Lorentz symmetry features
• Evaluating the processing of the statistical signal in detail
• Explain the achievement of Galilean Transformation

These are exciting ideas to explore when writing a research paper in applied math. Nevertheless, take your time to carefully and extensively research your preferred title to write a high-quality essay. Students should also note that some topics in this category require specialized knowledge to write superior papers.

It’s a challenge to write a paper for a high grade. Sometimes every student need a professional help with college paper writing. Therefore, don’t be afraid to hire a writer to complete your assignment. Just write a message “Please, write custom research paper for me” and get time to relax. Contact us today and get a 100% original paper. 

Interesting Math Research Topics

Maybe you’re among the learners that prefer working with exciting ideas. In that case, this category has topics that will interest you.

• The uses of numerical analysis in machine learning
• Foundations and philosophical problems
• Convex versus Concave in geometry
• Homological algebra- What is its purpose?
• Is math useful in cryptography
• Probability theory and random variable
• Functional analysis- What are its four conditions?
• Vector calculus versus multivariable
• Mathematics and logicist definitions
• Ways to apply the number theory in daily life
• Studying complex math equations
• How to calculate mode, median, and mean
• Understanding the meaning of the Scholz conjecture
• The definition of the past correspondence problem
• Computational maths- What are its classes?
• Multiplication table and its importance
• What the Boolean satisfiability problem means for a learner
• Understanding the linear speedup theory in mathematics
• The Turing machine description
• Understanding the Markov algorithm
• Investigating the similarities and differences between Buchi automation and Pushdown automation
• What is the meaning of Tree automation?
• Describing the enclosing sphere method and its use in combinations
• Egyptian pyramids and calculus
• Analyzing De Finetti theorem in statistics and probability
• Examining the congruence meaning in math
• Application and purpose of calculus in the banking industry
• Jean d’Alembert’s most famous works
• Boolean algebra- What are its essential elements
• Isaac Newton- His contribution, life, and time in math
• Understanding the meaning of Sphericon
• What is the purpose of Martingales?
• Gauss times, energy, and contributions to math
• Jakob Bernoulli- Exploring his famous works
• A brief history of math

Some learners think writing a math essay is complex and tedious. However, you can find a topic you will enjoy working with throughout the project. These are exciting ideas to explore in research papers. However, prepare to spend sufficient time investigating your chosen title to write a winning paper, although these are generally relaxing titles for math papers and essays.

Math Research Topics for Middle School

Some middle school students worry about the math topics for their research. However, they can choose unique titles that will impress their teachers. Here are some of these ideas.

• The impacts of standard exam curriculum on math education
• Why is learning math so tricky?
• What is the meaning of the commutative ring in algebra?
• The Artin-Wedderburn theorem and its meaning
• How monopolists and epimorphisms differ
• Understanding the Jacobson density theorem
• How linear approximations work
• Root and ratio test definition
• Statistics role in business
• Economic lot scheduling- What does it mean?
• Causes of the stock market crash
• How many traders contribute to the New York Stock Exchange
• The history of revenue management
• Financial signs of an excellent investment
• Depreciation and its odds
• How a poor currency can benefit a country
• How math helps with debt amortization
• Ways to calculate a person’s net worth
• Distinctions in algebra, trigonometry, and calculus
• Discussing the beginning of calculus
• The essence of stochastic in math
• The meaning of limits in math
• Ways to identify a critical point in a graph
• Nonstandard analysis- What does it mean in the probability theory?
• Continuous function description and meaning
• Calculus- What are its primary principles?
• Pythagoras theorem- What are its central tenets?
• Calculus applications in finance
• Theorem value in math
• The application of linear approximations

This list has some of the best titles for middle school learners. But they also require some research to write superior essays. However, finding information on such topics is relatively easy, making them suitable for middle school students.

Math Research Topics for College Students

Maybe you’re pursuing college studies and need a title for a math research paper. In that case, here are exciting titles to consider for your essay.

• What is the purpose of n-dimensional spaces?
• Card counting- How does it work?
• How continuous probability and discrete distribution differ
• Understanding encryption- How Does it work?
• Extremal problems- Investigating them in discrete geometry
• The Mobius strip- Examining the topology
• Why can a math problem be unsolvable?
• Comparing different statistical methods
• Explain the vital number theory concepts
• Analyzing the polynomial functions’ degrees
• Ways to divide complex numbers
• Describe the prize problems with the millennium
• The reasons for the unsolved Riemann hypothesis
• Methods of solving Sudoku with math
• Explain the fractals formation
• Describe the evolution of math
• Explore different types of Tower of Hanoi solutions
• Discuss the uses of Napier’s bones
• With examples, explain the chaos theory
• Why are mathematical equations important all the time?
• Fisher’s fundamental theorem and natural selection- Why are they important?

College professors expect students to draft papers with relevant and valuable information. These are relevant titles for college students. However, they require extensive research to write winning papers.

Cool Math Topics to Research

Maybe you don’t need a complex topic for your research paper. In that case, consider any of these ideas for your essay. If you have a problem writing even with these topics and you’re thinking: “solve my math for me,” you can always reach out to our service.

• How contemporary architectural designs use geometry
• What makes some math equations complex?
• Ways to solve the Rubik’s cube
• Discuss the meaning of prescriptive statistical and predictive analysis
• Understanding the purpose of the chaos theory
• What limits calculus?- Provide relevant examples
• A comparison of universal and abstract algebra- How do they differ?
• The relationship between probability and card tricks
• Pascal’s Triangle- What does it mean?
• Mobius strip- What are its features in geometry?
• Multiple probability ideas- A brief overview
• Discuss the meaning of the Golden Ration in Renaissance period paintings
• How checkers and chess matter in understanding mathematics
• Ways to measure infinity
• Evaluating the Georg Contor theory
• Are hexagons the most balanced shapes in the world?
• The Koch snowflake- Explain the iterations
• The history of various number types and their use
• Game theory use in social science
• Five math types with significant benefits in computer science

These are some of the most excellent math education research topics. However, they also require extensive research to write high-quality papers.

Enlist the Best College Research Paper Writing Service

Perhaps, you have a topic for your paper but not the time to write a winning piece. Maybe you’re not confident in your research, analytical, and writing skills. Thus, you’re unsure that you can write an essay that will compel your educator to award you the highest grade in your class. Well, you’re not the only one. Many students seek cheap research papers due to varied reasons. Whether it’s limited time and resources or a lack of the necessary skills and experience in academic paper writing, our crew can help you. We offer affordable college paper writing services and help in various math branches. Our experts can assist you if you need help with math research topics for high school students, college, or undergraduates. We are a professional team with a reputation for providing the best-rated academic writing assistance. Whether in university, college, or high school, our crew will offer the service you need to excel academically. Contact us now for cheap and reliable help with your academic essays.

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Recommended research topics for high school student

I am a high school senior and I am interested in doing a math research. I hope someone can recommend areas or topics of research that are challenging, rewarding, and yet do not exceed my capability. (I acknowledge this is quite hard) My math background: a. I have done competition math (Elementary number theory and combinatorics, Euclidean Geometry, and Algebraic manipulation) and I'm fairly comfortable with proofs. b. I had my first courses in Multivariable Calculus, Differential Equation, and Linear Algebra (Familiar with fundamental concepts, basic techniques and motivations) c. I have learned a portion of Abstract Algebra on my own and in summer programs including topics like Lagrange theorem, Vector spaces, Polynomial Rings, and Morphisms. d. I don't have a good background in statistics and probability e. I have been exposed to Knot theory and Chaos theory f. I do have basic programming skills in python and Mathematica, and I can work with LaTeX.

I really appreciate your help!

• soft-question

• $\begingroup$ Have you done anything to do with topology? Dynamical systems might also be an option if you like differential equations, calculus, and programming. $\endgroup$ –  recursive recursion Commented Aug 19, 2014 at 20:50
• $\begingroup$ I second the above recommendations. Also, rigorous analysis if you haven't seen much (my favorite, I must admit). Special relativity? You seem to be more of a pure guy though... Geometry (as in algebraic geometry, etc.) leading on from topology if you've seen some/are going to look at some. $\endgroup$ –  ShakesBeer Commented Aug 19, 2014 at 20:56
• 1 $\begingroup$ Personally, I would recommend solidifying your current knowledge before getting into research. You'll probably learn a lot more by reading and solving problems. Perhaps pick a topic, and learn all you can about it. $\endgroup$ –  Bruno Joyal Commented Aug 19, 2014 at 20:58
• 1 $\begingroup$ I think you should search for one recent journal article that sounds really interesting to you, and seriously read it. This could take weeks, but you will learn a lot, and you will also learn something about the cutting edge of research in that area. It's very hard to find research topics of the sort you describe, but apart from making personal connections with mathematicians, reading new papers is a great way. Perhaps check out www.arXiv.org, and don't be intimidated if it takes you a long time to get through a paper. $\endgroup$ –  Eric Tressler Commented Aug 19, 2014 at 21:13
• $\begingroup$ Please avoid the tags undergraduate-research and research . We are trying to remove them. $\endgroup$ –  Caleb Stanford Commented Jul 24, 2016 at 19:52

Ok, here is my sincere suggestion. First: +1 for your question. Since you have done multi variable calculus and differential equations, how about studying the Laplace Transform? This is (I think) new to you but yet, with your back ground, accessible. It is a cool topic (my opinion) with applications within the framework of calculus you have studied. You can solve (systems of) differential equations with it, as well as certain types of convergent improper integrals. I believe this will be a doable challenge for you!

• $\begingroup$ I have learned the basic computational aspect of Laplace transform like the translation theorems, convolutions, etc. However, now I only know how to calculate and play with the formulas. What would you suggest for me to have a deeper understanding on this subject?Those integral transforms seem really cool! In addition, in what way can I find things to research that can really did out my originality? I don't wish to do a exploratory project, but rather make up something new. I know it's bold for me to say this, yet that's my end goal. $\endgroup$ –  Bohan Lu Commented Aug 19, 2014 at 23:43
• $\begingroup$ @BohanLu Here is one: math.stackexchange.com/questions/376945/… But when I searched the internet, I could not find much of examples. It seems like calculating convergent improper integrals with Laplace is not a common thing. Mostly Laplace is used for Diff Eq related problems. When I did this stuff, I got very intrigued by the fact that a whole class of improper integrals could be evaluated this way, I made my own study out of it. And so I developed categories of integrals that work that way. Anybody else has a suggestion here??? $\endgroup$ –  imranfat Commented Aug 20, 2014 at 15:19

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High School Research

Advanced high school math students interested in research and mathematics can undertake research projects during the academic year as well as the summer. The two programs available to high school students are:

• RSI - Research Science Institute
• PRIMES - Program for Research In Mathematics, Engineering, and Science

Please visit each section for more information.

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Department members engage in cutting-edge research on a wide variety of topics in mathematics and its applications. Topics continually evolve to reflect emerging interests and developments, but can roughly grouped into the following areas.

Algebra, Combinatorics, and Geometry

Algebra, combinatorics, and geometry are areas of very active research at the University of Pittsburgh.

Analysis and Partial Differential Equations

The research of the analysis group covers functional analysis, harmonic analysis, several complex variables, partial differential equations, and analysis on metric and Carnot-Caratheodory spaces.

Applied Analysis

The department is a leader in the analysis of systems of nonlinear differential equations and dynamical systems  that arise in modeling a variety of physical phenomena. They include problems in biology, chemistry, phase transitions, fluid flow, flame propagation, diffusion processes, and pattern formation in nonlinear stochastic partial differential equations.

Mathematical Biology

The biological world stands as the next great frontier for mathematical modeling and analysis. This group studies complex systems and dynamics arising in various biological phenomena.

Mathematical Finance

A rapidly growing area of mathematical finance is Quantitative Behavioral Finance. The high-tech boom and bust of the late 1990s followed by the housing and financial upheavals of 2008 have made a convincing case for the necessity of adopting broader assumptions in finance.

Numerical Analysis and Scientific Computing

The diversity of this group is reflected in its research interests: numerical analysis of partial differential equations , adaptive methods for scientific computing, computational methods of fluid dynamics and turbulence, numerical solution of nonlinear problems arising from porous media flow and transport, optimal control, and simulation of stochastic reaction diffusion systems.

100+ Amazing Algebra Topics for Research Papers

Many students seek algebra topics when writing research papers in this mathematical field. Algebra is the study field that entails studying mathematical symbols and rules for their manipulation. Algebra is the unifying thread for most mathematics, including solving elementary equations to learning abstractions like rings, groups, and fields.

In most cases, people use algebra when unsure about the exact numbers. Therefore, they replace those numbers with letters. In business, algebra helps with sales prediction. While many students dislike mathematics, avoiding algebra research paper topics is almost impossible at an advanced study level.

Therefore, this article lists topics to consider when writing a research paper in this academic field. It’s helpful because many learners struggle to find suitable topics when writing research papers in this field.

How to Write Theses on Advanced Algebra Topics

A thesis on an algebra topic is an individual project that the learner writes after investigating and studying a specific idea. Here’s a step-by-step guide for writing a thesis on an algebra topic.

Pick a topic: Start by selecting a title for your algebra thesis. Your topic should relate to your research interests and your supervisor’s guidelines. Investigate your topic: Once you’ve chosen a topic, research it extensively to know the relevant theories, formulas, and texts. Your thesis should be an extension of a particular topic’s analysis and a report on your research. Write the thesis: Once you’ve explored the topic extensively, start writing your paper. Your dissertation should have an abstract, an introduction, the body, and a conclusion.

The abstract should summarise your thesis’ aims, scope, and conclusions. The introduction should introduce the topic, size, and significance while providing relevant literature and outlining the logical structure. The body should have several chapters with details and proofs of numerical implementations, while the conclusion should restate your main arguments and tell readers the effects. Also, it should suggest future work.

College Algebra Topics

You may need topics to consider if you’re in college and want to write an algebra research paper. Here’s a list of titles worth considering for your essay.

• Exploring the relationship between Rubik’s cube and the group theory
• Comparing the relationship between various equation systems
• Finding the most appropriate way to solve mathematical word problems
• Investigating the distance formula and its origin
• Exploring the things you can achieve with determinants
• Explaining what “domain” and “range” mean in algebra
• A two-dimension analysis of the Gram-Schmidt process
• Exploring the differences between eigenvalues and eigenvectors
• What the Cramer’s rule states, and why does it matter
• Describing the Gaussian elimination
• Provide an induction-proof example
• Describe the uses of F-algebras
• Understanding the number problems in algebra
• What’s the essence of abstract algebra?
• Investigating Fermat’s last theorem peculiarities
• Exploring the algebra essentials
• Investigating the relationship between geometry and algebra

These are exciting topics in college algebra. However, writing a winning paper about any of them requires careful research and analysis. Therefore, prepare to spend sufficient time working on any of these titles.

Cool Topics in Algebra

Perhaps, you want to write about an excellent topic in this mathematical field. If so, consider the following ideas for your algebra paper.

• Discussing a differential equation with illustrations
• Describing and analysing the Noetherian ring
• Explain the commutative ring from an algebra viewpoint
• Describe the Artin-Weddderburn theorem
• Studying the Jacobson density theorem
• Describe the four properties of any binary operation from an algebra viewpoint
• A detailed analysis of the unary operator
• Analysing the Abel-Ruffini theorem
• Monomorphisms versus Epimorphisms: Contrast and comparison
• Discus Morita duality with algebraic structures in mind
• Nilpotent versus Idempotent in Ring theory

Pick any idea from this list and develop it into a research topic. Your educator will love your paper and award you a good grade if you research it and write an informative essay.

Linear Algebra Topics

Linear algebra covers vector spaces and the linear mapping between them. Linear equation systems have unknowns, and mathematicians use vectors and matrices to represent them. Here are exciting topics in linear algebra to consider for your research paper.

• Decomposition of singular value
• Investigating linear independence and dependence
• Exploring projections in linear algebra
• What are linear transformations in linear algebra?
• Describe positive definite matrices
• What are orthogonal matrices?
• Describe Euclidean vector spaces with examples
• Explain how you can solve equation systems with matrices
• Determinants versus matrix inverses
• Describe mathematical operations using matrices
• Functional analysis of linear algebra
• Exploring linear algebra and its fundamentals

These are some of the exciting project topics in linear algebra. Nevertheless, prepare sufficient resources and time to investigate any of these titles to write a winning paper.

Pre Algebra Topics

Are you interested in a pre-algebra research topic? If so, this category has some of the most exciting ideas to explore.

• Investigating the importance of pre-algebra
• The best way to start pre-algebra for a beginner
• Pre-algebra and algebra- Which is the hardest and why?
• Core lessons in pre-algebra
• What follows pre-algebra?
• The first things to learn in pre-algebra
• Investigating the standard form in pre-algebra
• Provide pre-algebra examples using the basic rules to evaluate expressions
• Differentiate pre-algebra and algebra
• Describe five pre-algebra formulas

Consider exploring any of these ideas if you’re interested in pre-algebra. Nevertheless, choose a title you’re comfortable with to develop a winning paper.

Intermediate Algebra Topics for Research

Perhaps, you’re interested in intermediate algebra. If so, consider any of these ideas for your research paper.

• Reviewing absolute value and real numbers
• Investigating real numbers’ operations
• Exploring the cube and square roots of real numbers
• Analysing algebraic formulas and expressions
• What are the rules of scientific notation and exponents?
• How to solve a linear inequality with a single variable
• Exploring relations, functions, and graphics from an algebraic viewpoint
• Investigating linear systems with two variables and solutions
• How to solve a linear system with two variables
• Exploring linear systems applications with two variables
• How to solve a linear system with three variables
• Gaussian elimination and matrices
• How to simplify a radical expression
• How to add and subtract a radical expression
• How to multiply and divide a radical expression
• How to extract a square root and complete the square
• Investigating quadratic functions and graphs
• How to solve a polynomial and rational inequality
• How to solve logarithmic and exponential equations
• Exploring arithmetic series and sequences

These are exciting topics in intermediate algebra to consider for research papers. Nevertheless, learners should prepare to solve equations in their work.

Algebra Topics High School Students Can Explore

Are you in high school and want to explore algebra? If yes, consider these topics for your research, they could be a great coursework help to you.

• Crucial principles and formulas to embrace when solving a matrix
• Ways to create charts on a firm’s financial analysis for the past five years
• How to find solutions to finance and mathematical gaps
• Ways to solve linear equations
• What is a linear equation- Provide examples
• Describe the substitution and elimination methods for solving equations
• How to solve logarithmic equations
• What are partial fractions?
• Describe linear inequalities with examples
• How to solve a quadratic equation by factoring
• How to solve a quadratic equation by formula
• How to solve a quadratic equation with a square completion method
• How to frame a worksheet for a quadratic equation
• Explain the relationship between roots and coefficients
• Describe rational expressions and ways to simplify them
• Describe a cubic equation roots
• What is the greatest common factor- Provide examples
• What is the least common multiple- Provide examples
• Describe the remainder theorem with examples

Explore any of these titles for your high school paper. However, pick a title you’re comfortable working with from the beginning to the end to make your work easier.

Advanced Topics in Algebra and Geometry

Maybe you want to explore something more advanced in your paper. In that case, the following list has advanced topics in geometry and algebra worth considering.

• Arithmetical structures and their algorithmic aspects
• Fractional thermoentropy spaces in topological quantum fields
• Fractional thermoentripy spaces in large-scale systems
• Eigenpoints configurations
• Investigating the higher dimension aperiodic domino problem
• Exploring math anxiety, executive functions, and math performance
• Coherent quantiles and lifting elements
• Absolute values extension on two subfields
• Reviewing the laws of form and Majorana fermions
• Studying the specialisation and rational maps degree
• Investigating mathematical-pedagogical knowledge of prospective teachers in ECD programs
• The adeles I model theory
• Exploring logarithmic vector fields, arrangements, and divisors’ freeness
• How to reconstruct curves from Hodge classes
• Investigating Eigen points configuration

These are advanced topics in algebra and geometry worth investigating. However, please prepare to explore your topic extensively to write a strong essay.

Abstract Algebra Topics

Most people study abstract algebra in college. If you’re interested in research in this area, consider these topics for your project.

• Describe abstract algebra applications
• Why is abstract algebra essential?
• Describe ring theory and its application
• What is group theory, and why does it matter?
• Describe the critical conceptual algebra levels
• Describe the fundamental theorem of the finite Abelian groups
• Describe Sylow’s theorems
• What is Polya counting?
• Describe the RSA algorithm
• What are the homomorphisms and ideals of Rings?
• Describe integral domains and factorisation
• Describe Boolean algebra and its importance
• State and explain Cauchy’s Theorem- Why is it important?

This algebra topics list is not exhaustive. You can find more ideas worth exploring in your project. Nevertheless, pick an idea you will work with comfortably to deliver a winning paper.

Get Professional Math Homework Help!

Perhaps, you don’t have the time to find accurate algebra homework solutions. Maybe you need math thesis help from an expert. If so, you’ve no reason to search further. Our thesis writing services in USA can help you write a winning assignment. We offer custom help with math assignments at cheap prices.

If you want to get a quality algebra dissertation without sweating, place an order with us. We’re an online team providing homework help to students across educational levels. We guarantee you a top-notch service once you approach us, saying, “Please do my math assignment.” We’re fast and can beat even a tight deadline without compromising quality. And whether you’re in high school, university, or college, we will write a paper that will compel your teacher to award you the best grade in your class. Contact us now!

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“Teachers should teach math in a way that encourages students to engage in sense-making and not merely to memorize or internalize exactly what the teacher says or does,” says Jon R. Star.

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One way is the wrong way to do math. Here’s the right way.

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Research by Ed School psychologist reinforces case for stressing multiple problem-solving paths over memorization

There’s never just one way to solve a math problem, says Jon R. Star , a psychologist and professor of education at the Harvard Graduate School of Education. With researchers from Vanderbilt University, Star found that teaching students multiple ways to solve math problems instead of using a single method improves teaching and learning. In an interview with the Gazette, Star, a former math teacher, outlined the research and explained how anyone, with the right instruction, can develop a knack for numbers.

Jon R. Star

GAZETTE: What is the most common misconception about math learning?

STAR: That you’re either a math person or you’re not a math person — that some people are just born with math smarts, and they can do math, and other people are just not, and there’s not much you can do about it.

GAZETTE: What does science say about the process of learning math?

STAR: One thing we know from psychology about the learning process is that the act of reaching into your brain, grabbing some knowledge, pulling it out, chewing on it, talking about it, and putting it back helps you learn. Psychologists call this elaborative encoding. The more times you can do that process — putting knowledge in, getting it out, elaborating on it, putting it back in — the more you will have learned, remembered, and understood the material. We’re trying to get math teachers to help students engage in that process of elaborative encoding.

GAZETTE: How did you learn math yourself?

STAR: Learning math should involve some sense-making. It’s necessary that we listen to what our teacher tells us about the math and try to make sense of it in our minds. Math learning is not about pouring the words directly from the teacher’s mouth into the students’ ears and brains. That’s not the way it works. I think that’s how I learned math. But that’s not how I hope students learn math and that’s not how I hope teachers think about the teaching of math. Teachers should teach math in a way that encourages students to engage in sense-making and not merely to memorize or internalize exactly what the teacher says or does.

GAZETTE: Tell us about the teaching method described in the research.

STAR: One of the strategies that some teachers may use when teaching math is to show students how to solve problems and expect that the student is going to end up using the same method that the teacher showed. But there are many ways to solve math problems; there’s never just one way.

The strategy we developed asks that teachers compare two ways for solving a problem, side by side, and that they follow an instructional routine to lead a discussion to help students understand the difference between the two methods. That discussion is really the heart of this routine because it is fundamentally about sharing reasoning: Teachers ask students to explain why a strategy works, and students must dig into their heads and try to say what they understand. And listening to other people’s reasoning reinforces the process of learning.

GAZETTE: Why is this strategy an improvement over just learning a single method?

STAR: We think that learning multiple strategies for solving problems deepens students’ understanding of the content. There is a direct benefit to learning through comparing multiple methods, but there are also other types of benefits to students’ motivation. In this process, students come to see math a little differently — not just as a set of problems, each of which has exactly one way to solve it that you must memorize, but rather, as a terrain where there are always decisions to be made and multiple strategies that one might need to justify or debate. Because that is what math is.

For teachers, this can also be empowering because they are interested in increasing their students’ understanding, and we’ve given them a set of tools that can help them do that and potentially make the class more interesting as well. It’s important to note, too, that this approach is not something that we invented. In this case, what we’re asking teachers to do is something that they do a little bit of already. Every high school math teacher, for certain topics, is teaching students multiple strategies. It’s built into the curriculum. All that we’re saying is, first, you should do it more because it’s a good thing, and second, when you do it, this is a certain way that we found to be especially effective, both in terms of the visual materials and the pedagogy. It’s not a big stretch for most teachers. Conversations around ways to teach math for the past 30 or 40 years, and perhaps longer, have been emphasizing the use of multiple strategies.

GAZETTE: What are the potential challenges for math teachers to put this in practice?

STAR: If we want teachers to introduce students to multiple ways to solve problems, we must recognize that that is a lot of information for students and teachers. There is a concern that there could be information overload, and that’s very legitimate. Also, a well-intentioned teacher might take our strategy too far. A teacher might say something like, “Well, if comparing two strategies is good, then why don’t I compare three or four or five?” Not that that’s impossible to do well. But the visual materials you would have to design to help students manage that information overload are quite challenging. We don’t recommend that.

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all the numbers are changing, but what doesn't change is the relationship between x and y: y is always one more than twice x. That is, y=2x+1. Finding what doesn't change "tames" the situation. So, you have tamed this problem! Yay. And if you want a fancy mathematical name for things that don’t vary, we call these things "invariants." The number of messed-up recruits is invariant, even though they are all wiggling back and forth, trying to figure out which way is right!

3) Encourage generalizations

So, of course, the next question that comes to my mind is how to generalize what you’ve already discovered: there are 15 ways that 2 mistakes can be arranged in a line of 6 recruits. What about a different number of mistakes? Or a different number of recruits? Is there some way to predict? Or, alternatively, is there some way to predict how these 15 ways of making mistakes will play out as the recruits try to settle themselves down? Which direction interests you?

4) Inquire about reasoning and rigor

The students were looking at the number of ways the recruits could line up with 2 out of n faced the wrong way: Anyway, I had a question of my own. It looks like the number of possibilities increases pretty fast, as the number of recruits increases. For example, I counted 15 possibilities in your last set (the line of six). What I wonder is this: when the numbers get that large, how you can possibly know that you've found all the possibilities? (For example, I noticed that >>>><< is missing.) The question "How do I know I've counted 'em all?" is actually quite a big deal in mathematics, as mathematicians are often called upon to find ways of counting things that nobody has ever listed (exactly like the example you are working on).

The students responded by finding a pattern for generating the lineups in a meaningful order: The way that we can prove that we have all the possibilities is that we can just add the number of places that the second wrong person could be in. For example, if 2 are wrong in a line of 6, then the first one doesn’t move and you count the space in which the second one can move in. So for the line of six, it would be 5+4+3+2+1=15. That is the way to make sure that we have all the ways. Thanks so much for giving challenges. We enjoyed thinking!

5) Work towards proof

a) The group wrote the following: When we found out that 6 recruits had 15 different starting arrangements, we needed more information. We needed to figure out how many starting positions are there for a different number of recruits.

By drawing out the arrangements for 5 recruits and 7 recruits we found out that the number of starting arrangements for the recruit number before plus that recruit number before it would equal the number of starting arrangements for that number of recruits.

We also found out that if you divide the starting arrangements by the number of recruits there is a pattern.

To which the mentor replied: Wow! I don't think (in all the years I've been hanging around mathematics) I've ever seen anyone describe this particular pattern before! Really nice! If you already knew me, you'd be able to predict what I'm about to ask, but you don't, so I have to ask it: "But why?" That is, why is this pattern (the 6, 10, 15, 21, 28…) the pattern that you find for this circumstance (two recruits wrong in lines of lengths, 4, 5, 6, 7, 8…)? Answering that—explaining why you should get those numbers and why the pattern must continue for longer lines—is doing the kind of thing that mathematics is really about.

b) Responding to students studying a circular variation of raw recruits that never settled down: This is a really interesting conclusion! How can you show that it will always continue forever and that it doesn’t matter what the original arrangement was? Have you got a reason or did you try all the cases or…? I look forward to hearing more from you.

6) Distinguish between examples and reasons

a) You have very thoroughly dealt with finding the answer to the problem you posed—it really does seem, as you put it, "safe to say" how many there will be. Is there a way that you can show that that pattern must continue? I guess I’d look for some reason why adding the new recruit adds exactly the number of additional cases that you predict. If you could say how the addition of one new recruit depends on how long the line already is, you’d have a complete proof. Want to give that a try?

b) A student, working on Amida Kuji and having provided an example, wrote the following as part of a proof: In like manner, to be given each relationship of objects in an arrangement, you can generate the arrangement itself, for no two different arrangements can have the same object relationships. The mentor response points out the gap and offers ways to structure the process of extrapolating from the specific to the general: This statement is the same as your conjecture, but this is not a proof. You repeat your claim and suggest that the example serves as a model for a proof. If that is so, it is up to you to make the connections explicit. How might you prove that a set of ordered pairs, one per pair of objects forces a unique arrangement for the entire list? Try thinking about a given object (e.g., C) and what each of its ordered pairs tells us? Try to generalize from your example. What must be true for the set of ordered pairs? Are all sets of n C2 ordered pairs legal? How many sets of n C2 ordered pairs are there? Do they all lead to a particular arrangement? Your answers to these questions should help you work toward a proof of your conjecture.

9) Encourage extensions

What you’ve done—finding the pattern, but far more important, finding the explanation (and stating it so clearly)—is really great! (Perhaps I should say "finding and stating explanations like this is real mathematics"!) Yet it almost sounded as if you put it down at the very end, when you concluded "making our project mostly an interesting coincidence." This is a truly nice piece of work!

The question, now, is "What next?" You really have completely solved the problem you set out to solve: found the answer, and proved that you’re right!

I began looking back at the examples you gave, and noticed patterns in them that I had never seen before. At first, I started coloring parts red, because they just "stuck out" as noticeable and I wanted to see them better. Then, it occurred to me that I was coloring the recruits that were back-to-back, and that maybe I should be paying attention to the ones who were facing each other, as they were "where the action was," so I started coloring them pink. (In one case, I recopied your example to do the pinks.) To be honest, I’m not sure what I’m looking for, but there was such a clear pattern of the "action spot" moving around that I thought it might tell me something new. Anything come to your minds?

10) Build a Mathematical Community

I just went back to another paper and then came back to yours to look again. There's another pattern in the table. Add the recruits and the corresponding starting arrangements (for example, add 6 and 15) and you get the next number of starting arrangements. I don't know whether this, or your 1.5, 2, 2.5, 3, 3.5… pattern will help you find out why 6, 10, 15… make sense as answers, but they might. Maybe you can work with [your classmates] who made the other observation to try to develop a complete understanding of the problem.

11) Highlight Connections

Your rule—the (n-1)+(n-2)+(n-3)+… +3+2+1 part—is interesting all by itself, as it counts the number of dots in a triangle of dots. See how?

12) Wrap Up

This is really a very nice and complete piece of work: you've stated a problem, found a solution, and given a proof (complete explanation of why that solution must be correct). To wrap it up and give it the polish of a good piece of mathematical research, I'd suggest two things.

The first thing is to extend the idea to account for all but two mistakes and the (slightly trivial) one mistake and all but one mistake. (If you felt like looking at 3 and all but 3, that'd be nice, too, but it's more work—though not a ton—and the ones that I suggested are really not more work.)

The second thing I'd suggest is to write it all up in a way that would be understandable by someone who did not know the problem or your class: clear statement of the problem, the solution, what you did to get the solution, and the proof.

I look forward to seeing your masterpiece!

Advice for Keeping a Formal Mathematics Research Logbook

As part of your mathematics research experience, you will keep a mathematics research logbook. In this logbook, keep a record of everything you do and everything you read that relates to this work. Write down questions that you have as you are reading or working on the project. Experiment. Make conjectures. Try to prove your conjectures. Your journal will become a record of your entire mathematics research experience. Don’t worry if your writing is not always perfect. Often journal pages look rough, with notes to yourself, false starts, and partial solutions. However, be sure that you can read your own notes later and try to organize your writing in ways that will facilitate your thinking. Your logbook will serve as a record of where you are in your work at any moment and will be an invaluable tool when you write reports about your research.

Ideally, your mathematics research logbook should have pre-numbered pages. You can often find numbered graph paper science logs at office supply stores. If you can not find a notebook that has the pages already numbered, then the first thing you should do is go through the entire book putting numbers on each page using pen.

• Date each entry.

• Work in pen.

• Don’t erase or white out mistakes. Instead, draw a single line through what you would like ignored. There are many reasons for using this approach:

– Your notebook will look a lot nicer if it doesn’t have scribbled messes in it.

– You can still see what you wrote at a later date if you decide that it wasn’t a mistake after all.

– It is sometimes useful to be able to go back and see where you ran into difficulties.

– You’ll be able to go back and see if you already tried something so you won’t spend time trying that same approach again if it didn’t work.

• When you do research using existing sources, be sure to list the bibliographic information at the start of each section of notes you take. It is a lot easier to write down the citation while it is in front of you than it is to try to find it at a later date.

• Never tear a page out of your notebook. The idea is to keep a record of everything you have done. One reason for pre-numbering the pages is to show that nothing has been removed.

• If you find an interesting article or picture that you would like to include in your notebook, you can staple or tape it onto a page.

Advice for Keeping a Loose-Leaf Mathematics Research Logbook

Get yourself a good loose-leaf binder, some lined paper for notes, some graph paper for graphs and some blank paper for pictures and diagrams. Be sure to keep everything that is related to your project in your binder.

– Your notebook will look a lot nicer if it does not have scribbled messes in it.

• Be sure to keep everything related to your project. The idea is to keep a record of everything you have done.

• If you find an interesting article or picture that you would like to include in your notebook, punch holes in it and insert it in an appropriate section in your binder.

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Ideas for high school pure maths projects

I am thinking of giving my high school students some pure maths projects to do. It is a lot easier to think of some interesting stats projects but not in pure maths. The students' maths background are weak, they might not really understand the relationship between integration and area finding. I am planning of giving a short project that could be done in 1-2 weeks time (for 1-2 pages long) that emphasises on conceptual understanding but if possible exciting and upon completing the projects students should feel more confident tackling more problems.

From my experience when I studied maths back then in high school, I preferred to understand the concepts first before trying to do any problems. But nowadays, I think it is a common phenomenon that students tend to jump straight into doing problems without bothering the purposes, motives, and relationships from one concept to the other. In other words, students are not interested in connecting the dots, they just want to do and pass the tests.

The topics that we are discussing now are: differential and integral calculus of trigonometric and logarithmic functions.

Here are some ideas that I have in mind: 1. Summarise different interpretations of derivatives (for example: geometric interpretation, algebraic interpretation, physical interpretation, etc) 2. Relate the idea of (definite) integration (continuous) and summation (discrete) and give some properties or equations which are very similar in both cases. 3. Summarise common trig identities and prove them. For example, $sin^2\theta+cos^2\theta=1$ can be proved using Pythagoras.

I would really appreciate if anyone could share some other ideas or examples which might be helpful in enhancing students' understanding of concepts, I have a very limited knowledge on the current research, maybe there are some exciting research topics which do not require tons of advanced maths. Many thanks!

• secondary-education

• $\begingroup$ Can basic elementary number theory be handled by them? $\endgroup$ –  Git Gud Commented Mar 30, 2014 at 11:55
• $\begingroup$ @Git Gud: Some really basics stuff yeah I think, like divisibility, prime factorisation, gcd, etc.. But we don't want to go to far to something like Fermat's Little Theorem, Chinese Remainder Theorem etc. But I would like to know some ideas in elementary number theory which might be useful in some other occasions. Thanks! :) $\endgroup$ –  user71346 Commented Mar 30, 2014 at 12:03
• 1 $\begingroup$ You've made your issues clear, but not in the form of a question. Putting it into a question, with a question mark, focuses the post and makes it easier for people to answer well. $\endgroup$ –  user173 Commented Mar 30, 2014 at 12:47
• 1 $\begingroup$ Would something like asking them to provide primality certificates of some given prime numbers be feasible (i.e. I'm not asking about this particular question, but its character)? $\endgroup$ –  dtldarek Commented Mar 30, 2014 at 13:29
• 2 $\begingroup$ ams.org/programs/students/high-school/emp-student-research $\endgroup$ –  David Ebert Commented Jun 4, 2014 at 6:14

13 Answers 13

Joseph Malkevitch , based out of CUNY York College but also a visiting professor at Columbia University Teachers College, has a fair bit on his website about (high school) student research.

Depending on the student's mathematical level, one could point to Malkevitch's pages on Mathematics Research Projects or a couple other pages directed at undergraduate students (1) (2) .

Other helpful links and pieces of writing can be found on his main site (click his linked name above).

• 3 $\begingroup$ Very good, substantive answer. A good standard to set. :) $\endgroup$ –  paul garrett Commented Mar 30, 2014 at 23:13

Just a list of some cool things:

• Recurrent relations There are a lot of different ways to find solutions for recurrent relations. Logistic maps are also very neat way to illustrate what's going on.
• Bernoulli numbers This is what I gave a short presentation on. It may be a bit boring for highschoolers sinec there is not really a cool way to explain or illustrate what you're doing, but maybe for the students who are more interested in pure math.
• Linear algebra
• Complex numbers Some very basic complex analysis can be suited for high-schoolers (of course, formal proofs for all the theorems that are commonly used is way too much, but maybe some arguments or some informal proofs would be feasible).
• Infinite series There was an excellent pdf on this, which presented the difference between the different types on convergence for infinite series, together with some convergence tests, all in a very intuitive way very suited for highschoolers, but unfortunately I can't find it now.
• Cardano's formula for solving (some) cubic equations this can be done geometrically like the quadratic formula, but probably requires guidance.
• Fourier theory An illustrated approach could be really cool, together wth an explanation of some of the basic concepts of Fourier analysis.
• Calculus some semi-rigorous proofs using limits and limits of summations can probably made by high school students and can be very interesting.
• Trigonometric identities like cos and sin addition and multiplication formulas
• Platonian solids There is a very nice proof that there are only 5 platonian solids, and there are some nice properties for 3-dimensional solids as well (F + V = E + 2), and some basic linear algebra for calculating areas, volumes and angles would be appropriate.
• Ramsey theory This can be explained quite nicely by using the analogy of people in a group who are either friends or not. Also, the proofs have a nice graphical representation. Graph theory in general has some really cool topics for high school students, so there are definitely more topics here.
• Programming an AI for a simple game It's always fun to play a game against a computer, and it's impressive when you can program a computer in such a way that it performs better in a game then most humans can.
• Maps and projections Things like the Mercator projection and stuff. I don't know the specifics, but I know a guy who did this as his high school project.
• Non-euclidian geometry I don't know too much about this, so this may be too hard, but this is a really cool demonstration of how axiomatic systems work and a fun mind-experiment that, suprisingly, can be embedded in a picture.
• Game theory Game theory provides a lot of interesting question. For example, I was just playing that 2048 game, and I found myself repeating: right, down, right, down, ... until i got stuck, then I did left or up, and started over again. Provided you have the probabilities of the new blocks appearing (else you could estimate them or just create your own variant in which the probabilities are known) you can, for example, try to analyze the average score. Then you could also try to find a pattern that ends the game as quickly as possible, or one that ends the game with the lowest average score (and are these patterns the same?). The nice thing is that even when a mathematical analysis is not feasible, you can just let your computer play for a day and come up with a very good estimate.

I've taken some subjects that I found interesting myself, and some others from a course where everybody had to give a presentation on a mathematical subject. Some of these subjects may be too hard or maybe too specialized to write a 100-page paper about, but I'll let you be the judge of that.

I've mainly focussed on things that have either a nice geometric representation (because a picture usually makes things more interesting and easier to understand) or some nice things that are not to hard to understand but still are considered interesting and/or nontrivial. I think all but the first three have elements that allow for a nice graphical explanation.

That being said, the students probably require a considerable amount of guidance. Most of the material they'll find is not suited for them, so the teacher either needs to have some material that is appropriate, or help out in another way that allows the students to do the research relatively independent.

• 2 $\begingroup$ Note that this is one of the theorems mentioned in my link above. The specific site is york.cuny.edu/~malk/high-school-research/… and includes as recommended reading: O'Rourke, Joseph, Art Gallery Theorems and Algorithms, Oxford U. Press, Oxford, 1987. $\endgroup$ –  Benjamin Dickman Commented Mar 31, 2014 at 18:42
• 3 $\begingroup$ My Art Gallery book is online at this link . $\endgroup$ –  Joseph O'Rourke Commented Jun 4, 2014 at 20:03

Here are a few projects done at my high school:

1) Given a quadratic in the form $y=ax^2+bx+c$, determine what changing $a$, $b$ and $c$ does to the turning point (vertex) of the parabola and prove your answer. Most students are able to figure out $a$ and $c$ relatively quickly, and they are good practice for $b$, which turns out to be much harder.

2) Prove that 7 congruent circles form 12 points of tangency as shown in the diagram below. Challenge students to prove this at least two ways using separate branches of maths.

3) Taxicab Geometry . Resources and questions abound online. This is one example of a good guiding worksheet. I haven't done Taxicab Geometry with my students, but I think it's an interesting way to challenge students to rethink all of their basic geometry definitions and axioms.

4) Have students revisit every maths theorem and formula used in high school. Have them summarise the theorem in their own words and give two examples of how it is used. (This project was given to the "bottom set" of students, with the feeling that they needed more practice, whereas the top students were more prepared for an extension.)

• $\begingroup$ For (2) it looks like 12 points of tangency, how do you count 18? $\endgroup$ –  JTP - Apologise to Monica Commented Jun 4, 2014 at 2:59
• $\begingroup$ @JoeTaxpayer Oops. You're right. $\endgroup$ –  David Ebert Commented Jun 4, 2014 at 6:15

Solving quadratic and cubic equations. At least for cubics, this really does require that your students have seen complex numbers.

Solving the quadratic by completing the square is simple, clever, and you may not have ever shown them the proof in class.

For the ambitious, Cardano's method for solving the cubic is quite straight forward, based on the lemma that for any two numbers $S$ and $P$, there are two (possibly complex) numbers whose sum is $S$ and whose product is $P$.

Staying within the realm of algebra, some basic things about complex numbers could make for a decent two-page project. Students could prove the basic geometrical facts about complex numbers:

• Addition corresponds to vector addition on an Argand diagram.
• Multiplication correponds to multiplying the lengths and adding the angles.

Proving those facts could be page 1. Page 2 could be using them to prove another geometrical fact about complex numbers:

• There are exactly $n$ $n$-th roots of $1$, and they form the vertices of an $n$-gon centered at $0$. From this you can deduce that there are exactly $n$ $n$-th roots of any number.
• You can use complex numbers to prove certain trig identities.

As a professional mathematician, I certainly appreciate the projects listed above, and this might not be exactly the kind of answer you're looking for. The projects below will definitely help students understand a particular concept (dimension and proof-writing, respectively) but will not directly help them solve any problems.

When I used to teach high school, I would usually try to develop projects that connected mathematics to other disciplines. I would focus especially on the humanities and arts, since students whose interests leaned in those disciplines were often the most challenging to motivate and engage. Two projects with which I had some success:

• In a geometry class, I had students read Flatland and then asked that they come up with a creative project based on what they read. One student turned it into an analysis of women's rights in Victorian England; another painted, on a thin strip of wood, what an inhabitant of Flatland might see; another made the argument that cubist paintings were a 2-d rendering of what a 4-d person might see looking at a 3-d person and then made some paintings in that style.
• Also in the same geometry class, I tried to make an analogy between proof-writing (even though this was only ten years ago, we were still teaching proofs at this school) and editorial writing. What are your givens/the editorial writer's biases and assumptions? What are you trying to prove/the editorial writer trying to say? Can you/the editorial writer justify each step in your argument? I then had the students take an editorial in a local newspaper and attempt to decompose it into a two column proof.

At my daughters high school, last year every student must do a project of student research. They can choose the subject themselves (my daughter choose biology). Some math projects which have been done: -Fractals, programming fractals. -determinants and the eight-queen-problem

• 1 $\begingroup$ Can you maybe add some details about how deep the projects have been studied? $\endgroup$ –  Markus Klein Commented Mar 31, 2014 at 11:33
• 1 $\begingroup$ surpringly deep! The expectation is that should be used >100hr,and final report about 100 pages. My daughters project was studying birds during winter months in a park nearby our house, detailing which species visited, how many, etc, what they were eating, writing detailed observation protocol. The maths project I found surpringly deep! for the age. $\endgroup$ –  kjetil b halvorsen Commented Mar 31, 2014 at 11:38

If you understand some French, you can go to the site of Math en Jeans and look at the subjects other people have worked at with high school students.

Continued fractions can produce a vast range of good projects, which you can give at any age from (willing) middle school to (reluctant) high school students. One simple way to motivate the concept is to ask students to discover approximations to pi that were in wide use in ancient world . Sure, everybody knows $\pi \approx 22/7$, but can you do better than that? How do you proceed from $22/7$ to the next approximation? How do you convert continued fractions to "regular" ones, and vice versa? What if you allow not only the fractions like $1/a_n$, but also $2/a_n$, $3/a_n$, etc? E.g., if your first approximation is $\pi \approx 3.14 = 157/50 = 3 + 7/50$, how can you improve it using the continued fractions approach? Has anybody discovered this approximation? Can you produce a reasonably looking approximation that is not listed on Wikipedia?

You might also want to read Euclidlab - http://euclidlab.org/unsolved . They have many interesting projects, which should appeal to high-schoolers (I am a high-schooler myself and am thus speaking from ``experience''). In fact, I am planning on joining Camp Euclid, which other high-school students might find interesting (it costs a lot, though).

COMAP (The Consortium for Mathematics and Its Applications) publishes a newsletter for its members called Consortium. The current issue of Consortium can be downloaded for free from the web page below (which also includes other free COMAP materials) until the next issue appears, at which time the "current" issue goes behind a firewall.

https://www.comap.com/Free/

Consortium has many articles that can inspire student research (middle school to graduate school) research, In particular, the last couple of issues of Consortium have featured a "new column" that I edit, that discusses research problems specifically designed for (but not limited to) pre-college students. There problems appear under the title: "Student Research Corner." If you use the COMAP search feature you can find the titles of these research problems which are quick starting but all are geometrical questions nearly all involving graph theory and polyhedra.

Ask them to show that the following procedure constructs all rhombuses (rhombi?) of a fixed side length: take two circles of the same radius. Let them be placed to intersect at two distinct points. Now the two centres and the intersection points together form vertices of a rhombus. Now 'pull the circles apart' slightly or push them closer and obtain more of them.

Maybe something with 3D point groups (not all the details of the group theory, but describing the types of them (mirror plane, rotation, etc.) and classifying some common objects. (E.g. it is interesting that octahedron and cube have same symmetry. also, 2-D tiling patterns (but not 3d space groups...too complicated).

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News from Brown

Rhode island high schoolers embrace stem lessons at icerm’s girls get math program.

The five-day camp at Brown’s Institute for Computational and Experimental Research in Mathematics engages students in hands-on math activities and advanced computational labs, guided by experts.

Girls Get Math is designed to cultivate interest, inspire confidence and instill a sense of belonging for young students exploring math and science fields. Photo by Halle Bryant

PROVIDENCE, R.I. [Brown University] — No cabins, canoes or campfires, for a week at least — this summer, a group of Rhode Island high schoolers swapped s'mores and singalongs for STEM topics at GirlsGetMath@ICERM , a five-day math camp at Brown University.

Hosted by Brown’s Institute for Computational and Experimental Research in Mathematics , the annual camp is designed to cultivate interest, inspire confidence and instill a sense of belonging for young students exploring math and science fields. It introduces concepts not often included in traditional high school curricula through activities, games, lectures and computer labs.

This year's program welcomed 23 rising 10th and 11th graders from across Rhode Island, who engaged in a range of interactive activities, hands-on labs and thought-provoking discussions where students could explore the beauty and utility of mathematics. Each morning, for instance, the Girls Get Math students tackled a question of the day, with topics ranging from whimsical musings like “What color is math?” to technical queries such as “What’s your favorite trig function?” The questions served as icebreakers, sparking discussions that made mathematics approachable and engaging, students said.

"The best part was meeting girls my age who love the same things I do and love math,” said Briella Weimer, a junior at Barrington High School.

One highlight was a visit to the Harris Lab at Brown's School of Engineering, where students were introduced to fluid dynamics, impact dynamics, materials science and structural optimization. Under the guidance of Brown graduate students, participants explored the principles of fluid viscosity by injecting bubbles into different materials, a hands-on experiment that tied physics concepts like friction and gravity to real-world applications.

Visiting a lab in Brown's School of Engineering, students explored the principles of fluid viscosity by injecting bubbles into different materials. Photo by Halle Bryant

This year's program welcomed 23 rising 10th and 11th graders from across Rhode Island. Photo by Halle Bryant

At ICERM, students got an introduction to MATLAB, a mathematical programming language widely used in academic research. Photo by Halle Bryant

Back at ICERM — one of just seven federally funded mathematics institutes across the nation — the students dove into computation-based labs, including an introduction to MATLAB, a mathematical programming language widely used in research. They also explored topics such as epidemic modeling, image processing, and the creation of digital filters and effects, gaining valuable skills that are typically introduced in college-level courses.

"It was exciting to see the questions the students were asking throughout the week and how deep and interesting those questions were,” said Amalia Culiuc, a lecturer in applied mathematics, who leads the program with Anarina Murillo, an assistant professor of biostatistics at Brown. “Every year we are really impressed by how quickly students go from playing with math to really being serious about it and doing really serious math with just a little bit of background.”

This year’s program included funding from grants and gifts from the American Mathematical Society, Math for America, MathWorks and Rhode Island Energy.

Related news:

Brain-computer interface allows man with als to ‘speak’ again, new study unveils 16,000 years of climate history in the tropical andes, isabel tribe: examining ancient sediment to predict earth’s future.

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Feasible Topics for Senior High School student (STEM related, better if it's math related too)?

I know it's probably too early for a highschooler to do original research or anything of the sort, nothing too complicated either, but my school is requiring us to do one for our last year in SHS. I'm interested in most math topics (Linear algebra, Calculus, Trigonometry), and I've been trying to think of math related research, but most of the comparative studies, derivations and all that is still undergrad research. Looking at the past year batches' papers, most of them were just biology and experimentations on plants. Perhaps linear regression on multiplication rate of single-celled organisms? But I worry it won't be that feasible. If anyone can provide insights on some topics suitable for high school students, I'd really appreciate it. Thanks in advance

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Kennesaw State physics major pursues life-changing research

KENNESAW, Ga. | Aug 19, 2024

The rising junior from Smyrna said classes in astronomy and physics taught her how physical forces effect everything around her, and she wanted to immerse herself in them. So, she came to Kennesaw State University for the opportunity to conduct research right away as a freshman.

“ Honestly, the research opportunities drew me to KSU,” said Manqueros, who is pursuing a bachelor’s degree in physics in Kennesaw State’s College of Science and Mathematics . “Other colleges mainly take graduate students for their research, and I knew that at KSU I could do meaningful research even if I was an undergraduate student.”

That desire for meaningful research drew her to the lab of associate professor Kisa Ranasinghe, who creates bioactive glass that can transport nanoparticles that treat various ailments. Manqueros approached Ranasinghe at an early-semester meeting for physics majors after hearing the professor discuss her work; Manqueros was hooked, and Ranasinghe was impressed.

“When someone stops me to say they’re interested in my research and want to learn more, that’s an indicator, right?” Ranasinghe said. “For a freshman to take that initiative and show that amount of enthusiasm is truly impressive. Very quickly I found out she has great potential.”

From that day forward, Manqueros poured herself into the life-changing research into bioglass, which isn’t really glass but a conduit that acts like glass to bring therapeutic nanoparticles into the body. Manqueros said cerium oxide nanoparticles within the bioglass can interact to treat Alzheimer’s disease, cancer, diabetes, and other physical and neurological conditions. The first part of her explanation, though, involves demystifying the idea of glass in the body.

“A lot of times when we say we're doing research on glass that we can put into your body, people freak out because they imagine the glass breaking—it’s not like that,” she explained. “The simple fact that we work with glass to better people's health—that's something that I really want to get across to people. What we do from the physics point of view is study those nanoparticles and how they interact within the glass.”

Manqueros will investigate these problems as a Birla Carbon Scholar this summer. She has also been the lead author on an abstract for a poster presentation that published earlier this year in the Georgia Journal of Science, and she presented findings at the Georgia Academy of Science conference in March, where she won first prize for undergraduate oral presentations in the division that covers physics, mathematics, computer science, and engineering.

Ranasinghe said Manqueros’ future is wide-open, though Manqueros said the future will involve more physics, either a master’s degree or a doctorate while continuing the research into bioglass. Life-changing research with societal impact will keep her engaged for a long time to come, she said.

“I actually enjoy what I do,” she said. “Oftentimes when you're doing work as a physicist, people don't see the meaning in what you do because they wonder why we need to study this. This research is impacting anyone who has some sort of disease or wants to improve their health or their body. I like that I have a direct impact on people's lives through the research that I do here at KSU.”

– Story by Dave Shelles

Photos by Matt Yung

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For Others, With Others

Using nutrition survey data to understand the impact of school meals on children’s health

• # Master’s (Doctoral) Program in Economics
• # Department of Economics
• # Graduate School of Economics
• # Faculty of Economics

Sayaka Nakamura Professor Department of Economics Faculty of Economics

• bookmark#toggle keyup.enter->bookmark#toggle onBookmarkItemUpdate@window->bookmark#handleUpdate">

Compared to health issues faced by the elderly, there is insufficient research regarding the health of women and children. Professor Sayaka Nakamura from the Faculty of Economics talks about undertaking empirical research on these often overlooked problems, and her desire to spur policy discussions.

In Japan, where the population is aging rapidly, research related to health issues faced by the elderly is gaining attention. In contrast, there appears to be less focus on research about children’s health—such as the impact of women’s employment on the diets and health of children. Awareness of this issue serves as the starting point of my research.

Recently, I published a working paper about the impact of a Japanese school lunch program on the weight of junior high school students. Using the National Health and Nutrition Survey conducted by the Ministry of Health, Labour and Welfare, I used data analysis to verify how the school lunch programs affected the weight of students.

The results showed that school lunch programs significantly reduce obesity in children from households with financial struggles, and that this effect continues for several years after graduating. Besides directly reducing obesity through healthy meals, school lunch programs contribute toward reducing obesity in the long term by encouraging healthy diets.

Aiding international policy discussions regarding improvement in quality of school lunch programs

Research about the impact of school lunch programs on body weight is also being conducted in Europe and the United States. However, in the United States and the United Kingdom, participation in school lunch programs is optional, and subsidies for school lunch programs are limited to children from low-income households. Therefore, it is difficult to examine the impact of school lunch programs on children without bias, and research findings are also mixed.

In principle, the Japanese school lunch program mandates all students at schools participating in the program to eat the provided lunch. This makes it easier to discern the impact of the program on children’s health.

Our findings do not simply back the excellent food education effects of Japanese school lunch programs. As evidence of the positive impact that high quality school lunch programs have on children’s health, the results also have meaning in encouraging international policy discussions.

I also used data—such as from the Ministry of Health, Labour and Welfare’s National Health and Nutrition Survey—to conduct research on the changes in body mass index (BMI). Since the mid-1950s, the BMI of Japanese men across all generations has steadily increased. Conversely, the BMI of women across has steadily decreased.

Outside Japan, in the vast majority of countries BMI keeps increasing for both men and women. Why is it that, in Japan, only the BMI of women continues to decrease? This is a theme that had been neglected in the past.

We find that the gap in BMI trend between men and women in Japan was due to a larger decrease in physical activity level in men than in women. Our findings suggest that this is driven by the decrease in men’s physical labor due to economic development and the weakening occupational gender gap.

Using public data to make clear the issues faced by Japan

In conducting empirical research, it is necessary to have many ordinary people participate in studies without any selection bias. However, this incurs huge costs, and there is also the issue of personal information protection. The standard approach is to use existing data, but in Japan, it is difficult to use public administrative records, and often, survey data—collected by having subjects answer questions—is used.

The use of survey data comes with issues, such as people refusing to participate or answer specific questions, inaccurate responses, and difficulties in conducting follow-up surveys for the same persons. Because some countries allow researchers to use administrative records and others provide better survey data, some Japanese researchers use overseas data. However, this does not divulge the issues faced by Japan.

Economics emphasizes positive analysis that throws light on facts. To thoroughly unravel what is happening now, it is necessary to plan out research methods in detail. Furthermore, presenting previously unknown information as proper research results will lead to more constructive policy discussions. This is the significance of empirical research and its real charm.

The book I recommend

“The Testaments” by Margaret Atwood, Japanese translation by Yukiko Konosu, Hayakawa Publishing Corporation

This is the sequel to “The Handmaid’s Tale,” a book that depicts women robbed of their rights in a totalitarian state ruled by a cultist group. To escape from control, women collected and analyzed information and sought to convey it to people. Their stance is also applicable to my thoughts about empirical research.

Sayaka Nakamura

• Professor Department of Economics Faculty of Economics

Graduated in 1998 from the Social Sciences division of the Faculty of Liberal Arts, International Christian University, completed the master’s program of the Graduate School of Economics, the University of Tokyo in 2000, and obtained her Ph.D. in Economics in 2006 from Northwestern University. Took on several positions—such as Sid Richardson Scholar in Health Economics, Baker Institute for Public Policy, Rice University as well as associate professor at Yokohama City University’s International College of Arts and Sciences and associate professor at Nagoya University’s School of Economics—before assuming her current position in 2022. Specializes in applied microeconometrics and health economics.

Interviewed: October 2023

• # The Knot- Nexus of Knowledge by Sophia Professors

The Knot- Nexus of Knowledge by Sophia Professors

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