School of Graduate Studies

Mathematics, program overview, quick facts.

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Application deadline MSc, PhD:

Fall 2024 entry

Payment deadline: 8-Dec-2023

Supporting document deadline: 15-Dec-2023

MSc, PhD:

Fall 2024 entry

Payment deadline: 8-Dec-2023

Supporting document deadline: 15-Dec-2023

Minimum admission average MSc:

a final-year average of at least mid-B

PhD:

B+

Direct-entry PhD: GPA of 3.7

MSc:

a final-year average of at least mid-B

PhD:

B+

Direct-entry PhD: GPA of 3.7

Direct entry option from bachelor's to PhD? PhD:

Yes

PhD:

Yes

Is a supervisor identified before or after admission? MSc, PhD:

After

MSc, PhD:

After

If a supervisor is identified after admission (as per question above), is admission conditional upon securing a supervisor? MSc, PhD:

No

MSc, PhD:

No

Is a supervisor assigned by the graduate unit or secured by the applicant? MSc, PhD:

Applicant

MSc, PhD:

Applicant

Are any standardized tests required/recommended? MSc, PhD:

N/A

MSc, PhD:

N/A

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Mathematics: mathematics phd.

The PhD is a research-oriented program consisting of coursework, comprehensive examinations, and a thesis embodying the results of original research. Opportunities for graduate study and research are available in most of the main areas of pure and applied mathematics.

Applicants may enter the PhD program via one of two routes: 1) following completion of an appropriate MA or 2) direct entry following completion of a bachelor's degree.

PhD Program

Minimum admission requirements.

Applicants are admitted under the General Regulations of the School of Graduate Studies. Applicants must also satisfy the Department of Mathematics' additional admission requirements stated below.

A master's degree from a recognized university. Students must satisfy the department of their ability to do independent research at an advanced level. They must show evidence of an excellent academic background and mathematical ability.

Completion Requirements

Coursework. Students must successfully complete at least 3.0 full-course equivalents (FCEs) . Out of the following 12 core courses, students must complete 6 courses:

MAT1000H Real Analysis I .

MAT1001H Real Analysis II .

MAT1002H Complex Analysis .

MAT1060H Partial Differential Equations I .

MAT1061H Partial Differential Equations II .

MAT1100H Algebra I .

MAT1101H Algebra II .

MAT1300H Topology I .

MAT1301H Topology II .

MAT1600H Mathematical Probability I .

MAT1601H Mathematical Probability II .

MAT1850H Linear Algebra and Optimization .

Comprehensive examination.

Students must pass a comprehensive examination in basic mathematics before beginning an area of research. This examination is scheduled at the start of the Fall session (usually September) and should be taken no later than the start of the third session.

Students have the option to write the final exam of any core course to obtain core credit. This requires approval of the Graduate Office.

Students who obtain a grade of A– or higher in each of the corresponding core courses for the general areas of mathematics will be exempted from the comprehensive examination requirement in the specific area of study.

Students must pass a qualifying oral examination or give a seminar presentation in their particular area of study before embarking on serious thesis research.

The main requirement of the degree is an acceptable thesis embodying original research of a standard that warrants publication in the research literature.

PhD Program (Direct-Entry)

Exceptionally strong BSc students with a grade point average (GPA) of 3.7 or higher may apply for direct admission to the PhD program. Students must satisfy the department of their ability to do independent research at an advanced level. They must show evidence of an excellent academic background and mathematical ability.

Out of the following 12 core courses, students must complete 6 courses (3.0 FCEs):

Students must also complete 1.0 elective FCE.

Students must complete MAT4000Y Supervised Research Project or its equivalent.

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Graduate School Admissions Requirements

IMPORTANT:  There is a non-refundable $110.00 application charge. Please read through the entire list of requirements before advancing to the application procedures.

Due to the large numbers of applications received in the Department of Mathematics each year, serious consideration will only be given to applicants with a strong background and with first class academic standing. In addition, only a small number of openings is available for international applicants.

Listed below are the minimum admission requirements set by the School of Graduate Studies.

1)    Applicants to a Master's Program at the University of Toronto must hold an appropriate four-year Bachelor's degree with a final year average of at least a mid-B from the University of Toronto, or its equivalent from another recognized university. Applicants to the Ph.D. program must have an appropriate University of Toronto Master's degree, or its equivalent, with an average of at least A-, or demonstrated comparable research competence.  (Direct enry from the bachelor's to the Ph.D. is possible for some eminently qualified applicants - optional ). All applicants must satisfy the admission requirements of the Department, which will take into account the background and accomplishments of the student as well as their academic achievements.

2)    If you are an international applicant, please review the International Degree Equivalency chart. This chart will help you determine if your international degree is considered equivalent.  Qualifications from a number of educational systems around the world are listed and the academic standings indicated are normally accepted as equivalent to a University of Toronto mid-B grade average if the degree obtained has been awarded from an institution which is recognized by the School of Graduate Studies.

4)    Official transcripts of your academic record from each university attended are required for admission. Applicants who attended universities outside North America must provide notarized English translations to accompany all foreign documentation not written in English.  It is the applicant's responsibility to arrange for transcript(s) to be sent directly from their institution to the graduate department.  Academic records must be enclosed in an envelope provided by the institution(s) concerned and sealed or signed across the back of the envelope. Do not open.  Note that faxed records are not considered official and that documents submitted will not be returned to the student.

If academic records are interim pending completion of studies in progress official final academic records indicating that the degree has been conferred must be submitted to the Graduate Department as soon as possible and before admission can be finalized. The School of Graduate Studies includes instructions about clearing these conditions on the Offer of Admission.

6)    A letter of intent or personal statement to be up-loaded on the on-line application form.

7)    It is essential that all incoming graduate students have a good command of English. Facility in the English language must be demonstrated by all applicants educated outside Canada whose primary language is not English. This requirement is a condition of admission and should be met before application. There are four ways to satisfy this requirement:

English Facility Testing

Information on English Facility testing can be obtained by writing directly to the following addresses or by visiting the test websites:

TOEFL/TSE Publications P.O. Box 6151, Princeton, N.J. 08541-6151 U.S.A. Tel: (609) 771-7500 Web: www.toefl.org

IELTS - International English Language Testing Service University of Cambridge Local Examinations Syndicate 1 Hills Rd., Cambride, U.K. CB1 2EU (or contact the nearest British Council Office) Web: www.ielts.org

MELAB - Michigan English Language Assessment Battery English Language Institute, University of Michigan 3020 North University Building, Ann Arbor, Michigan, USA 48109-1057 Web: www.lsa.umich.edu/eli/

COPE P.O. Box 1164, Toronto, Ontario M4T 1K2 E-mail: [email protected] Web: www.copetest.com

To continue, see Application Procedure .

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Mathematics Graduate Program

Thinking of applying to graduate school in mathematics.

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Penn was ranked 8th among all US universities in a leading national study , and our mathematics graduate program was recently highest in a study of graduate programs in arts and sciences at Penn. We have a very active and involved mathematics faculty , diverse course offerings and a broad seminar schedule , with a variety of research projects and strengths in algebra, analysis, geometry-topology, combinatorics, logic, probability, and mathematical physics. We have a supportive atmosphere, with personal attention from the faculty and extensive interaction among graduate students. Our grad students can take courses not only in the Mathematics Department but also elsewhere at Penn, and the wide resources of the university are available. Our former graduate students have gone on to mathematical careers both in academia and in industry.

Our full-time Ph.D. students receive a generous and competitive support package including

  • five years of funding with a combination of  fellowships and teaching assistantships;
  • a stipend and a full tuition scholarship;
  • no teaching responsibilities for at least two years (generally including the first and fourth year);
  • health insurance coverage provided at no cost to the student.

We invite you to learn about our graduate program, our math department, our university and living in Philadelphia, a cosmopolitan city and a true mathematical hub, with easy access to nearby mathematics departments and research institutes.

We are looking for interested, mathematically talented and dedicated students to be a part of our group of excellent future mathematicians. Consider applying to Penn for your graduate education. Questions?

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Department of Mathematics

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Overview of Graduation Requirements

To graduate with a PhD in Mathematics, a student must satisfy all of the following requirements:

  • 45 credits, including 15 doctoral dissertation research credits/GRAD 6950
  • If you have a Master’s degree in mathematics at UConn, then 30 credits are required, including 15 doctoral dissertation research credits.
  • Pass at least one prelim exam after each semester for the first three semesters of their graduate study.
  • Finish all prelim exam requirements by the beginning of the spring semester in their second year.
  • Finish all core course requirements by the end of their second year of graduate study,
  • Choose a thesis advisor no later than the end of the fall semester of the third year.
  • Form your advisory committee :  Major Advisor and at least two Associate Advisors or Co-Major Advisors and at least one Associate Advisor.
  • Meant to further the student’s education, scholarship and professional development.
  • Material should be in the broad area in which the student intends to write a dissertation, but should not focus on the actual thesis research.  Students present and answer questions about the material they have studied.
  • The exam is normally taken at the end of the third year or beginning of the fourth year.
  • Submit Dissertation Proposal
  • Submit Plan of Study
  • Apply for Graduation in Student Admin by the fourth week of the final semester.
  • Dissertation Specifications under Dissertation Information
  • Thesis templates (for LaTex) are available on our Thesis Formatting page
  • Submit Approval Page – Step 7
  • Complete Survey of Earned Doctorates – Step 7
  • Add Diploma Address in Student Admin and Diploma Info.

Preliminary Examination and Core Course Requirements

Pure Mathematics

  • Math 5111/Measure and Integration
  • Math 5120/Complex Function Theory
  • Math 5210/Abstract Algebra
  • Math 5310/Introduction to Geometry and Topology I
  • Math 5160/Probability Theory and Stochastic Processes I
  • Math 5210/Abstract Algebra I
  • Math 5211/Abstract Algebra II
  • Math 5260/Mathematical Logic I
  • Math 5360/Differential Geometry

Applied Mathematics

  • Math 5410/Introduction to Applied Mathematics I
  • Math 5510/Numerical Analysis and Approximation Theory I
  • Math 5440/Partial Differential Equations
  • Math 5520/Finite Element Solution Methods I

Past Prelim Exams

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PhD Admission Requirements

Please submit your online application for our Doctor of Philosophy (PhD) program through the School of Graduate Studies Online Application Portal between September 22 and November 22  each year.

Successful candidates have a strong background in mathematics, statistics, or a related field. Outstanding performance in their course work, outstanding letters of recommendations and well-thought-out statements of intent are an asset. Prior research experience is also valuable.

You must meet all admissions requirements to be considered for entry into the program. In addition to our admissions requirements for each program, please familiarize yourself with the minimum requirements, rules, and regulations of the School of Graduate School Studies .

Please also review the School of Graduate Studies Admission & Application Requirements .

We receive many outstanding applications, and admission to our program is competitive. Unfortunately, we cannot offer admission to all qualified applicants.

Students can be accepted through one of two routes:

Previous Degree (PhD)

You hold an appropriate master’s degree in statistics from a recognized university with at least a B+ average standing . A standing that is equivalent to at least B+ (U of T 77 ‐ 79% or 3.3/4.0) in the final year of study.

We also consider applicants with graduate degrees in biostatistics, computer science, economics, engineering, mathematics, physics, or any discipline where there is a significant quantitative component.

Previous Degree (Direct-Entry PhD)

You hold a bachelor’s degree in statistics from a recognized university with at least an A- average standing . A standing that is equivalent to at least A- (U of T 80 ‐ 84% or 3.7/4.0) in the final year of study.

For more information on admissions to our PhD program and program requirements, visit the School of Graduate Studies calendar .

Your Application Package

Please note that we do not accept any hard copies of your application or hard copies of supporting documents.

Curriculum Vitae (CV)

Please send a summary of your experiences in education, work, travel, volunteering, and other relevant areas. The maximum length is two pages, single-spaced.

Statement of Intent

As part of your application, please submit a letter of intent or personal statement online outlining your goals for your graduate studies.

Transcripts

Electronic copies of transcripts are required at the time you apply online. Only if you are successful at gaining admissions will we require official copies to be submitted to the department.

Due to COVID we are currently only accepting official e-transcripts. We will notify admitted candidates once the receipt of mail-in paper transcripts will be accepted. International transcripts: Please use International Degree Equivalencies Tool to ensure that you meet the minimum admissions requirements.

We do not require a credential evaluation assessment by a third-party, such as WES.

Letters of Recommendation

You will need three letters of recommendation , to be submitted online by your referees through the online application system prior to the supporting documentation deadline.

Note:  The online application system will automatically email an electronic reference request to each referee  when the application form is submitted. Referees will have until the deadline to upload supporting documentation to submit their reference letter . It is highly recommended that applicants contact their referees ahead of time to inform them of the supporting documents deadline and confirm both their availability and their preferred institutional email address.

English-Language Proficiency Testing (if applicable)

As English is the primary language of instruction and communication at the University of Toronto, applicants must demonstrate an adequate level of proficiency in English, regardless of their citizenship status or country of origin. It is important that these students follow SGS policies on ELP testing requirements and take one of the required tests for admission to a graduate program.

Applicants from universities outside Canada where English is not the primary language of instruction must provide results of an English language proficiency examination as part of their application. Tests must have been taken within the last 24 months at the time of submission of their application.

Please submit official copies of your English proficiency scores (Institution Code: 0982). You can include unofficial copies with your application while waiting for the official ones to arrive.

Learn more about ELP Testing here .

Please do not send the results to our department. Students must arrange for their score to be reported electronically to the University of Toronto (Enrolment Services) by the testing agency. Please check SGS ELP Testing website above for more detail.

Application Fee

The non-refundable application fee is currently CAD $125 per application.

Note: You may apply to more than one program. Each program will require a separate application and application fee. Applicants will not be considered for a program that they did not apply for.

Supervision & MDoc

PhD applicants will be able to select up to three potential supervisors at the time of their application. Supervisors of successful applicants are matched based on research areas of interest.

Learn more about our faculty .

Applicants will also indicate their interest in applying to the Multi-Disciplinary Doctoral Training Program (MDoc) through the cover sheet.

Interested in multi-disciplinary research? Learn more about the MDoc .

Start your application today

Having trouble?

Please review the School of Graduate Studies Admissions Frequently Asked Questions (FAQs) .

Want to know more?

If you have additional questions that have not been answered by the above information, please book an appointment during Prospective Student Office Hours to speak with a member of the Graduate Team or send us an email .

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Natural Sciences and Mathematics

Mathematical sciences.

Doctor of Philosophy in Mathematics

The program offers extensive coursework and intensive research experience in theory, methodology, and applications of mathematics (see  degree requirements ). 

  • Faculty members with broad and diverse research interests are available to supervise doctoral dissertations .
  • Financial support in the form of assistantships, full tuition support, and scholarships and awards are provided. Additional scholarships are available for US citizens and permanent residents.
  • Our students, both domestic and international, have a strong record of starting in full-time jobs right after graduation .
  • Students have opportunities to participate in active seminar series in  Algebra and Combinatorics ;   Computational Science ;  Geometry, Topology and Dynamical Systems ; and  Nonlinear Analysis and Dynamical Systems ; and the departmental  Colloquium  series.
  • To enhance career prospects, students can pursue  Graduate Certificate in Data Science , and possibly use the certificate courses to fulfill the elective requirements.
  • NSM Career Success Center  is available to support professional development and experiential learning of students.  
  • GRE test score is not required for admission.

More than 85% of our 45 Mathematics PhD graduates since 2020, both domestic and international, secured full-time employment within a few months of receiving their degrees. 

Placement of 2022 & 2023 Mathematics PhD Graduates

2023Assistant Professor, Department of Mathematical Sciences, Montana Technological University
2023Postdoctoral Researcher, Department of Biophysics, UT Southwestern Medical Center
2023Postdoctoral Fellow, School of Mathematical and Statistical Sciences, Clemson University
2023Senior Software Engineer, Rotor Inc.
2022Postdoctoral Researcher, Department of Mathematics, Johns Hopkins University
2022Postdoctoral Fellow, Mathematics in Medicine program, Houston Methodist Hospital
2022Postdoctoral Research Associate, National Center for Toxicological Research
2022Assistant Professor, Department of Computer Science and Mathematics, Spring Hill College
2022Instructor, Department of Mathematics, Oregon State University
2022Lecturer, Department of Mathematics, University of Oklahoma
2022Assistant Professor of Instruction, Department of Mathematical Sciences, University of Texas at Dallas
2022Adjunct Professor, Department of Mathematics, Southern Methodist University
2022Actuarial Analyst, Transamerica
2022Systems Engineer, Verizon
2022Data Analyst, Good Faith Energy
2022Senior Data Scientist, Melax Tech

See a more complete list  

Assistantships

Graduate Teaching Assistantships are offered to qualified PhD students on a competitive basis. These assistantships include a monthly stipend (currently set at $2,400) along with a full tuition waiver (covering 9 credit hours per term in the Fall and Spring semesters). The assistantship additionally covers the cost of health insurance purchased through the university and most fees. Graduate Research Assistantships for advanced PhD students are also available on some faculty members’ research grants. Typically, assistantship support is provided for five years and encompasses the Summer semester as well.

All admitted students are considered for assistantships; no separate application is necessary. 

Scholarships, Fellowships & Awards

PhD students are additionally supported through the following awards:

  • NSM McDermott PhD Admission Fellowship  (for highly qualified new students, offered at the time of admission)
  • Dean’s Fellowship  and  EEF Scholarship  (for highly qualified new students who are U.S. citizens and permanent residents, offered at the time of admission)
  • Julia Williams Van Ness Merit Scholarship  and  Mei Lein Fellowship
  • Outstanding Teaching Assistant of the Year Award
  • Dean of Graduate Education Dissertation Research Award
  • Best Dissertation Award ,  David Daniel Thesis Award , and  Outstanding Graduate Student Award

Conference Travel Support

NSM Conference Travel Award  and  Betty and Gifford Johnson Travel Award  are available to provide financial support to PhD students to present their research at professional conferences.

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Ready to start your application?

Before you apply, visit our  How to Apply  page to get familiar with the admission requirements and application process.

[email protected]

Department of Mathematics

Mathematics phd program.

The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both research and student-run seminars.

Questions? Email [email protected]

  • The firm deadline for applications for Autumn 2025, is December 5, 2024.
  • The (general and advanced) GRE tests are no longer accepted. Please do not submit these scores.

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Physical & Mathematical Sciences Admission Category

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Students in physical and mathematical sciences investigate the natural laws and processes of non-living matter. From the high-tech world of quantum optics and biophysics to the intricate problems of black holes and chaotic dynamics, our programs will introduce you to the research and issues that impact the world around us.

Physical & Mathematical Sciences Programs

Why Study Physical & Mathematical Sciences

Physical & Mathematical Sciences Careers

Applying to physical & mathematical sciences, admission requirements.

OUAC Admission Code: TPG (Physical & Mathematical Sciences)

Supplementary Application Form Required: No

Admission Category Prerequisites: English and Calculus

Approximate Admission Range:  Mid to high 80s

Admission Requirements by Curriculum:

  • Ontario High School and Other Canadian Provinces
  • US High School Admission Requirements
  • International Baccalaureate (IB) Admission Requirements
  • British Patterned Admission Requirements
  • Caribbean Advanced Proficiency Examination (CAPE) Admission Requirements
  • Other International School Admission Requirements

It is important to note that in addition to the courses required for admission into the Physical & Mathematical Sciences admission category listed above (English and mathematics/calculus), some programs of study may require you to take additional specific high school subjects in order to take specific courses in first year, or for entry into that program in second year.

For example, if you are interested in astronomy and physics, you will not only need English and mathematics/calculus (which are required for admission into Physical & Mathematical Sciences), but you will also need grade 12 physics or equivalent to be able to enrol in this program.

Transitioning from an admission category to a program of study

Since you are admitted to the general Physical & Mathematical Sciences admission category, during your first year you will not be enrolled in a specific program of study. This means that during your first year, you are able to explore a number of different areas of study. You apply to a program (e.g. major in astronomy and physics) at the end of your first year, and can combine programs outside of your own admission category , excluding programs in Rotman Commerce.

To prepare for admission into your program of study at the end of first year:

Step 1: Search for your desired program of study (e.g. major in astronomy and physics) in the table in the "Physical & Mathematical Sciences (H.B.Sc.)" section below

Step 2: Find the high school subject prerequisites for your desired program of study listed under Subject(s) Required in Addition to English

Step 3:  These prerequisites subjects allow you to enrol in introductory first year courses needed for your program of study selection at the end of first year. You can find these courses listed under Program Area in the Academic Calendar

Program List

Whether you're a math whiz or a science enthusiast – or a little bit of both – discover the program of study that's right for you from the list below.

Physical & Mathematical Sciences (H.B.Sc.)

Bio: Biology; C: Calculus; Ch: Chemistry; Ph: Physics

Rec.: Recommended but not required

Program Subject(s) Required in Addition to English
C
C (Rec. Ph)
C (Rec. Ph)
C, Ph
C, Ch (Rec. Ph)
C, Ch (Rec. Ph)
C
C, Ch (Rec. Ph, Bio)
C
C
C, Ch (Rec. Ph, Bio)
C, Ch, Ph
C, Ch (Rec. Ph, Bio)
C, Bio, Ch, Ph
C
C
C, Ph
C
C
C
C, Ph
C, Ph
C, Ph
C, Ch, Ph
C
C
C
C, Ch (Rec. Ph)

Why Study Physical & Mathematical Sciences at Arts & Science?

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Learn from the Best in Canada

Home to the Fields Institute, an international centre for math research, we have the top mathematics department in Canada. With award-winning faculty like Professor Alison Gibbs, a 3M National Teaching Fellow , you'll be learning from some of the best instructors in Canada.

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Unique Learning Opportunities

Students can gain hands-on experience in our world-class facilities, including our state-of-the-art labs and astronomy observatory . Beyond the classroom, you'll have access to research opportunities inside and beyond the classroom through programs like the Summer Undergraduate Research Program and the Research Opportunities Program . Eligible students will also have the chance to gain 12-20 months of paid work experience and specialized professional development training through the Arts & Science Internship Program .

#1 in Canada for graduate employability — recruiters from top companies have consistently ranked U of T as #1 in Canada and among the best in the world at preparing its students for the workplace. With a science degree from a world-renowned university, you will have a competitive advantage when applying for jobs in fields such as:

  • Actuarial science
  • Conservation
  • Energy sector
  • Financial services
  • Healthcare services
  • Information technology
  • Project management
  • Software development  

Use Career Navigator to explore more careers in the mathematical and physical sciences.

From exploring space to developing innovative tech solutions and medical treatments, Arts & Science alumni are making an impact. Read some of their stories below.

math phd u of t

A&S alumna Fazila Seker launches tool to help surgeons pinpoint breast cancer tumours

math phd u of t

A&S alumnus and mentor Petar Tomic encourages physics students to step outside the box

math phd u of t

A&S alumna Sara Seager: A shortcut through campus revealed her path to the stars

math phd u of t

From Mars exploration to Earth conservation: alumni mentor Julius Lindsay helps physics students navigate career options

math phd u of t

A&S alumna and UN Champion of the Earth Katharine Hayhoe

math phd u of t

Alumna Katie Harris is over the moon for space medicine

You have to understand how things work together, how to communicate them in a way that people can understand and how to get results. That's what you do in physics — you get a problem and use tools to solve it. Where I am today is largely because of my physics background. — Julius Lindsay, BSc 2006
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FACULTY OF ARTS & SCIENCE      

Academic Calendar

About the calendar, courses and programs, new for 2024-25, pdf and archive, course description by course code, mathematics.

Professor and Chair of the Department  R. Jerrard, MSc, PhD, FRSC

Professor and Associate Chair (Research)  D. Panchenko, BS, MS, PhD

Professor and Associate Chair (Graduate) I. Uriarte-Tuero, BSc, MSc, MPhil, PhD

Professor and Associate Chair (Undergraduate)  S. Yoshinobu, BA, MA, PhD

University Professors J. Friedlander, MA, PhD, FRSC (UTSC)  I.M. Sigal, BA, PhD, FRSC

Professors S. Alexakis, BA, PhD D. Bar-Natan, BSc, PhD E. Bierstone, MA, PhD, FRSC  I. Binder, BSc, MSc, PhD (UTM)  A. Braverman, BSc, PhD  J. Bremer, BSc, BSc, P D (UTSC) A. Burchard, MS, PhD G. Elliott, BSc, PhD, FRSC  M. Gualtieri, BSc, PhD  F. Herzig, BA, PhD  V. Ivrii, MA, PhD, Dr Math, FRSC  L. Jeffrey, AB, PhD, FRSC (UTSC) R. Jerrard, MSc, PhD, FRSC  V. Kapovitch, BSc, PhD  Y. Karshon, BSc, PhD (UTM)  K. Khanin, MSc, PhD (UTM)  B. Khesin, MSc, PhD  A. Khovanskii, MSc, PhD  H. Kim, BSc, PhD  S. Kudla, BA, MA, PhD, FRSC R. McCann, BSc, PhD, FRSC E. Meinrenken, BSc, PhD, FRSC E. Murphy, BS, PhD (UTM)  K. Murty, BSc, PhD, FRSC  A. Nabutovsky, MSc, PhD  A. Nachman, BSc, PhD  D. Panchenko, BSc, MSc, PhD  M. Pugh, BSc, PhD J. Quastel, MSc, PhD, FRSC K. Rafi, BSc, PhD J. Repka, BSc, PhD (U) R. Rotman BA, PhD L. Seco, BA, PhD (UTM)  C. Sulem, MSc, Dr D’Etat, FRSC  S. Todorcevic, BSc, PhD, FRSC J. Tsimerman, BSc, PhD  I. Uriarte-Tuero, BSc, MSc, MPhil, PhD B. Virag, BA, PhD (UTSC)  M. Yampolsky, BSc, PhD (UTM) 

Associate Professors  S. Aretakis, MA, PhD (UTSC) T. Collins, BSc, PhD J. de Simoi, BSc, MSc, PhD (UTM) R. Haslhofer, BSc, MSc, PhD (UTSC) S. Kopparty, BSc, MSc, PhD F. Pusateri, MS, PhD B. Rossman, BA, MA, PhD N. Rozenblyum, PhD S. Saraf, BSc, MSc, PhD A. Shankar (UTM), BSc, PhD A. Stinchombe, BMath, PhD G. Tiozzo, BA, MA, PhD (UTSC) K. Zhang (UTM), BSc, PhD

Associate Professor, Teaching Stream  B. Galvao-Sousa, BSc, MSc, PhD S. Yoshinobu, BA, MA, PhD 

Assistant Professors  N. Bogachev, MSc, PhD (UTSC) D. Dauvergne, PhD (UTM) J. Desjardins, BSc, MSc, MSc, PhD (UTM, CLTA) E. Elmanto BS, PhD (UTSC) M. Groechenig, BSc, DPhil (UTM) A. Kupers, BSc, BSc, MSc, PhD (UTSC) B. Landon, BSc, MSc, PhD J. Lefebvre, BSc, PhD Y. Liokumovich, BSc, MSc, PhD (UTM) D. Litt, BA, PhD M. Mavraki, BSc, MSc, PhD S. Olano, BSc, MSc, PhD (CLTA) W. Pan, BS, PhD V. Papyan, PhD K. Serkh, PhD Y. Shlapentokh-Rothman, PhD (UTM) H. Spink, BA, MA, PhD S. Unger, PhD (UTM) I. Varma, BSc, MSc, PhD W. Yu, PhD (UTSC)

Assistant Professors, Teaching Stream  C. Blois, BSc, MSc, PhD  X. Cui, BSc, MSc, PhD (CLTA) S. Homayouni, BSc, PhD  N. Jung, BA, MSc, PhD  C. Karimian Pour, PhD D. Karslidis, PhD (CLTA) J. Kawach, BSc, MSc, PhD J. Korman, PhD S. Mayes-Tang, Bc, MS, PhD F. Parsch, BSc, MSc, PhD P. Sargent, PhD L. Shorser, BSc, MSc, PhD  J. Siefken, HBS, MS, PhD S. Uppal, BSc, MSc A. Zaman, BSc, MSc, PhD

Lecturers  E.A.P. LeBlanc, MA, PhD 

Professors Emeriti  M.A. Akcoglu, MSc, PhD, FRSC J.G. Arthur, MA, PhD, FRSC, FRS E.J. Barbeau, MA PhD (U)  J. Bland, MSc, PhD  T. Bloom, MA, PhD, FRSC  M. D. Choi, MA, P D, FRSC  H.C. Davis, MA, PhD (N)  E.W. Ellers, Dr Rer Nat  I.R. Graham, BSc, PhD (UTM)  S. Halperin, MSc, PhD, FRSC  V. Jurdjevic, MS, PhD  J.W. Lorimer, MSc, PhD (U)  E. Mendelsohn, MSc, PhD (UTSC) P. Milman, Dipl Maths, P D, FRSC K. Murasugi, MA, DSc, FRSC  F. Murnaghan, MSc, PhD  P. Rosenthal, MA, PhD, LLB P. Selick, BSc, MA, PhD (UTSC)  D.K. Sen, MSc, Dr s Sc  F. D. Tall, AB, PhD (UTM) W.A.R. Weiss, MSc, PhD (UTM) 

Associate Professors Emeriti N.A. Derzko, BSc, PhD  J. Scherk, DPhil (UTSC)  S.M. Tanny, BSc, PhD (UTM) 

Associate Professors Emeriti, Teaching Stream D. Burbulla, BSc, BEd, MA  A. Igelfeld, MSc A. Lam, MSc 

Senior Lecturers Emeriti F. Recio, MSc, PhD

Introduction

Mathematics is the study of shape, quantity, pattern and structure. It serves as a tool for our scientific understanding of the world. Knowledge of mathematics opens gateways to many different professions such as economics, finance, computing, engineering, and the natural sciences. Aside from practical considerations, mathematics can be a highly satisfying intellectual pursuit, with career opportunities in teaching and research.

The department counts many of Canada's leading research mathematicians among its faculty. Our mathematics programs are flexible, allowing students to select courses based on specialization and interest. Contents range from calculus and linear algebra in the non-specialist programs to more advanced topics such as real and complex analysis, ordinary and partial differential equations, differential geometry, topology, commutative algebra, graph theory, mathematical logic, number theory, and functional analysis.

The department offers eight specialist programs in addition to the major and minor programs.

In the Mathematics, Applied Mathematics, Mathematics and Physics, and Mathematics and Philosophy   specialist programs, students acquire an in-depth knowledge and expertise in mathematical reasoning and the language of mathematics, with its emphasis on rigor and precision. These programs are designed for students wishing to pursue graduate studies; most of the graduates of these programs continue on to graduate school with some of them gaining admission to the world’s best graduate schools.

The Mathematical Applications in Economics and Finance specialist program is designed to prepare students for direct entry into the world of finance. It can also serve as a gateway to an MBA or a Master of Finance degree, possibly followed by an eventual doctorate.

The Mathematics and its Applications specialist programs offer three areas of concentration: teaching, physical science, and probability/statistics. These specialist programs are designed as 'enhanced double majors.' The required courses for these concentrations are almost identical for the first two years, but they diverge in the upper years. Students in these programs can also continue on to graduate studies.

The Major   and Minor programs are intended for students who want to combine mathematical skills with work in other subjects. These programs require less coursework than the specialist programs, but still require the completion of some upper year mathematics courses.

Students interested in becoming K-12 teachers should consider applying to the combined degree program --- a six-year program that leads to an Honours Bachelor of Science (HBSc) from the University of Toronto and a Master of Teaching (MT) from the Ontario Institute for Studies in Education (OISE). The HBSc part of this program involves completing a Math Major, a Minor in Education and Society (offered by Victoria College) and a Minor in an area that would lead to a second "teachable" subject.  Please see the Victoria College website for more information.

Arts & Science Internship Program

As of Fall 2021, the new Arts & Science Internship Program (ASIP) stream is available to students who are entering Year 2 or Year 3 of study and enrolled in the Mathematics Specialist, Applied Mathematics Specialist, Mathematics & Physics Specialist, Mathematics & Philosophy Specialist, Mathematical Applications in Economics & Finance Specialist, Mathematics & its Applications Specialist, and Mathematics Major.

Enrolment is limited and requires a supplemental application. Students enrolled in the ASIP stream will be required to complete mandatory Professional Development programming plus a minimum of 12 and maximum of 20 months (Year 2 entry) or a minimum of 12 and maximum of 16 months (Year 3 entry) of paid, full-time work experience. The time to degree completion for students enrolled in ASIP will normally be 5 years. There is an additional cost to participate in the ASIP stream.

Students will typically be admitted to the ASIP stream for the Fall term of Year 2 of study, however, in exceptional circumstances students, including transfer students, who enrolled in an eligible program in the Summer after Year 2 can be admitted to the ASIP stream for the Fall of Year 3. Acceptance into an ASIP stream in Year 3 is dependent on space and requires approval of the student’s academic unit and the Faculty of Arts & Science Experiential Learning & Outreach Support (ELOS) Office. Please refer to the ASIP eligibility page for further details.

Further details about ASIP, including eligibility requirements and application procedures, can be found here . Students may also visit the ASIP webpage or contact the ELOS office at [email protected] .

Introductory Courses

The Department of Mathematics offers introductory courses for incoming students to foster the development of mathematics skills.

PUMP Level 1 and PUMP Level 2 (Preparing for University Mathematics Program)

Both programs are non-credit courses that equip students with the necessary background knowledge required to succeed in first year mathematics courses. The content for the courses may be viewed at  https://www.mathematics.utoronto.ca/undergraduate/prospective-students/preparing-university-math-program-pump .

PUMP Level 1 provides a quick math review during the months of July and August, for students who would like to take six weeks prior to the start of the first semester to practice pre-calculus math skills. During other terms, it is scheduled as a longer course, for students who have not taken the appropriate high school mathematics prerequisites for university calculus and linear algebra. This course is recommended for any student who wish to close any existing gap between high school math and University level math courses or anyone who wishes to review high school math before attempting University level math or other science courses.

PUMP Level 2 is an Introduction to Proofs course. The curriculum provides background knowledge that is a preparation for MAT137Y1 , MAT157Y1 , MAT240H1 , MAT247H1 , MAT237Y1 , and other proof-oriented advanced courses. The course covers the reading and comprehension of mathematical statements, analyzing definitions and properties, formulation of arguments, and strategies for proofs. This course is recommended for any student who wish to add to their knowledge by joining the group of students who will commence their preparation for the more challenging concepts in the advance analytical programs, during the months of July and August.

Visit https://www.mathematics.utoronto.ca/undergraduate/prospective-students/PUMP-courses  for up-to-date information on the availability of PUMP Level 1 and PUMP Level 2.

If you have questions about the content of these courses, e-mail [email protected] .

Contact Information

First Year Inquiries: [email protected] Program Inquiries: [email protected]

Bahen Centre, Room 6291

Departmental Office: Bahen Centre, Room 6290 (416-978-3323)

Website:  https://www.mathematics.utoronto.ca/undergraduate






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Graduate Program

Our graduate program is unique from the other top mathematics institutions in the U.S. in that it emphasizes, from the start, independent research. Each year, we have extremely motivated and talented students among our new Ph.D. candidates who, we are proud to say, will become the next generation of leading researchers in their fields. While we urge independent work and research, there exists a real sense of camaraderie among our graduate students. As a result, the atmosphere created is one of excitement and stimulation as well as of mentoring and support. Furthermore, there exists a strong scholarly relationship between the Math Department and the Institute for Advanced Study, located just a short distance from campus, where students can make contact with members there as well as attend the IAS seminar series.  Our program has minimal requirements and maximal research and educational opportunities. We offer a broad variety of advanced research topics courses as well as more introductory level courses in algebra, analysis, and geometry, which help first-year students strengthen their mathematical background and get involved with faculty through basic course work. In addition to the courses, there are several informal seminars specifically geared toward graduate students: (1) Colloquium Lunch Talk, where experts who have been invited to present at the Department Colloquium give introductory talks, which allows graduate students to understand the afternoon colloquium more easily; (2) Graduate Student Seminar (GSS), which is organized and presented by graduate students for graduate students, creating a vibrant mathematical interaction among them; and, (3) What’s Happening in Fine Hall (WHIFH) seminar where faculty give talks in their own research areas specifically geared towards graduate students. Working or reading seminars in various research fields are also organized by graduate students each semester. First-year students are set on the fast track of research by choosing two advanced topics of research, beyond having a strong knowledge of three more general subjects: algebra, and real and complex analysis, as part of the required General Examination. It is the hope that one, or both, of the advanced topics will lead to the further discovery of a thesis problem. Students are expected to write a thesis in four years but will be provided an additional year to complete their work if deemed necessary. Most of our Ph.D.'s are successfully launched into academic positions at premier mathematical institutions as well as in industry .

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Undergraduate Programs

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Mathematics

St. George Campus, Faculty of Arts & Science

Program Information

Degree(s): Honours Bachelor of Science

Program(s): Mathematics (Major, Minor, Specialist)

OUAC Admission Code: TPG (Physical & Mathematical Sciences)

Academic Requirements

Ontario Secondary School Diploma Six 4U/M courses, including:

  • Calculus & Vectors (MCV4U)
  • English (ENG4U)

Find equivalent requirements for Canadian high school systems , US high school system , International Baccalaureate , British-Patterned Education , French-Patterned Education , CAPE , and other international high school systems .

Scarborough Campus

Program(s): Mathematics (Co-op, Major) Mathematics: Comprehensive Stream (Co-op, Specialist) Mathematics: Statistics Stream (Co-op, Specialist) Mathematics: Teaching Stream (Co-op, Specialist)

OUAC Admission Code: TXS (Mathematics)

  • Advanced Functions (MHF4U)

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  • Singler named interim chair of mathematics and statistics at S&T

Posted by news On August 1, 2024

Dr. John Singler has been named interim chair of Missouri S&T’s mathematics and statistics department. His appointment begins Monday, Aug. 12.

math phd u of t

Singler takes over the position from Dr. Xiaoming Wang, the Gary W. Havener Endowed Chair of Mathematics and Statistics at Missouri S&T. Singler previously served as interim chair of the department during the 2021-22 academic year.

Singler is a professor of mathematics and statistics at S&T. In addition to teaching, he researches topics in computational methods for data-driven model order reduction and control of partial differential equations, numerical analysis, applied mathematics, and scientific computing.

“I know that John will do a fantastic job as interim chair and I trust him to keep our students and faculty working in the usual engaged manner,” says Dr. Mehrzad Boroujerdi, vice provost and dean of the College of Arts, Sciences, and Education at S&T. “I look forward to working with John and the whole department as they make this leadership transition and as we turn our attention toward the search for a permanent chair for the department.

“I am also grateful to Xiaoming for his years of service as the department’s first named chair,” says Boroujerdi. “I appreciate all the help and advice he has shared while here and wish him well with his future endeavors as he joins a newly established university in China.”

Singler joined the Missouri S&T faculty as an assistant professor in 2008. He has served as an assistant professor, associate professor and a professor of mathematics and statistics. Prior to joining S&T, Singler was a postdoctoral research associate and instructor at Oregon State University and a joint-appointment postdoctoral researcher for both Oregon State University and Montana State University.

“As an interim chair, my No. 1 goal is to prioritize our students’ success at both the undergraduate and graduate level,” says Singler. “Our department teaches more than 80% of the students at S&T, so we need to make sure that our students receive the best education and research opportunities that we can offer – something that every single one of our mathematics and statistics faculty members work to provide.”

Singler earned a master’s degree and Ph.D. in mathematics from Virginia Tech in 2002 and 2005, respectively. He serves on the editorial board for the SIAM Advances in Design and Control book series, and his research has been funded by the National Science Foundation.

About Missouri S&T

Missouri University of Science and Technology (Missouri S&T) is a STEM-focused research university of over 7,000 students located in Rolla, Missouri. Part of the four-campus University of Missouri System, Missouri S&T offers over 100 degrees in 40 areas of study and is among the nation’s top public universities for salary impact, according to the  Wall Street Journal . For more information about Missouri S&T, visit www.mst.edu .

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OK, but Would 2024 America Beat 2021 Russia?

It’s the question every gymnastics fan must ask. i had to do math to find out..

This is part of Slate’s 2024 Olympics coverage. Read more  here .

For 20 interminable minutes of the women’s gymnastics team final at the Paris Olympics on Tuesday, I wasn’t sure about anything—because Simone Biles hadn’t vaulted yet. It was, after all, on vault in the Tokyo team finals when something made Biles’ brain snap out of sync with her body: the dreaded “ twisties ,” gymnastics’ version of vertigo. But then, in about four seconds of running, springing, blocking, and glorious, glorious twisting flight, it was all going to be golden in 2024. Biles aced the difficult Cheng , and her face, ebullient upon landing, said it all.

There would be no GOAT emergency, and with the team’s star intact, it was no longer a matter of if the U.S. would run away with the gold medal on its “ redemption tour .” It was a matter of how many—points, that is, full entire points that the team would win by, in a sport often decided by tenths. Indeed, the meet’s most thrilling contest turned out to be for bronze, which was decided by less than three-tenths . That hair-thin difference came between fourth-place finishers Great Britain and, yes, Olympic team bronze medalists Brazil ! Hooray! Brazil’s historic achievement—the first Olympic team medal by a program from South America—was, I grant, possible largely with generous assists from other squads’ falls all over the place. Brazil didn’t have its best meet, but a lot of other teams had even worse meets. (I feel especially sad on behalf of 2008 gold medalists China, who finished sixth.)

When it all shook out, the answer to that margin-of-victory question was more than 5 full points separating the U.S. from historic silver medalists Italy. ( Congratulazioni! ) Biles, Jordan Chiles, Jade Carey, and Suni Lee (Hezly Rivera was effectively on reserve after a shaky qualifications) could have absorbed five additional falls between them and still walked out draped in gold. By the time Biles took to the floor exercise to cap the meet, she could have replaced half her routine with the Barbaras Rhabarberbar TikTok dance, and the U.S. still would have won. It was, frankly, a blowout.

So: Does this mean that the U.S. is the most unstoppable gymnastics program in the history of humanity?

In a word: nyet . Because as much as I am currently soaring on the wings of a giant imaginary bald eagle over an imaginary NASCAR race between extra-polluting gas cars encrusted in Flamin’ Hot Cheetos, something is nagging at me: Would this be the case if You-Know-Who were in Paris? Would a healthy, happy, mentally stable U.S. 2024 squad, if it were able to go back in time as part of this redemption tour, kick Diet Rite Russia’s asses? I personally think silver was and remains a resplendent color for the 2021 American squad—but it was clear to me that if this year’s Olympic Village had a DeLorean, these women would take a do-over of the Tokyo Games. But how would the do-over go ?

I need to know this so badly that I did math.

At the end of team finals in 2021, the “Russian Olympic Committee” bested a mostly Simone-less USA, 169.528 to 166.096. The 2024 American squad ended Tuesday , on the other hand, with a badass 171.296, meaning, in simplest terms, yes: Trader Josef’s Private Label Russia, facing off head-to-head back in 2021 with today’s American squad (transported back in time!), would end the meet metaphorically squirming for its life on the floor like Johnny Lawrence in the original Karate Kid . So, this settles it, right?

I wish. As you know from the literal preschool-style colors and shapes the television has to put next to scores to let you know if they’re good , gymnastics scoring is deeply complex. If you get sucked into the vast recesses of the “gymternet,” fans exchanging comparisons of “DV” and “CV” seem to be speaking another language. This is because gymnastics’ fearsome Code of Points not only assigns different “difficulty values” to every skill gymnasts complete, and numbers to every deduction that gymnasts can receive, but also has the nerve to be revised every quadrennial. This means that putting today’s American scores directly toe-to-toe with Green Text Bubble Russia’s three years ago isn’t quite fair.

It also gets complicated when we examine the nature of the code’s changes since Tokyo, especially on the events of balance beam and floor exercise. Today’s U.S. team, for example, received a handful-of-tenths bonus for its beam dismounts , an advantage it wouldn’t have in 2021. So does this mean that, in the interest of fairness, I should dock those tenths from my imaginary Hunt for Red October sequel, to put today’s scores more in line with the 2021 Code of Points? Well, not so fast. On both beam and floor, the International Gymnastics Federation (or FIG; it’s fronch !) added a litany of new “artistry” deductions after Tokyo. If there’s one thing the post–Perfect 10 Code does, it takes every single deduction imaginable , so it is safe to assume that every gymnast in Paris’ Bercy Arena probably sustained some sort of artistry penalty that 2021 gymnasts didn’t, which I think would even things out. As a result, I am going to call the imaginary balance beam contest between the 2021 ROC and do-over USA a wash.

The same goes for floor, which now offers gymnasts a “dismount bonus” but also provides judges the option of taking up to 2 entire points off for artistry—in an attempt to even the playing field between gymnasts who excel at dance and those who are better at tumbling. (From what I can see in these Games, however, this has in practice mostly meant that it’s damn hard for anyone to crack 14 on floor.)

Where the score comparisons between the two Olympic gold-medal teams are far more cut-and-dried, however, are on uneven bars and vault.

Both Chiles and Lee compete skills on bars that have lost some value in 2024, but Chiles, Lee, and Biles have gained the “dismount bonus” that more than cancels the loss out. To spare you the math I spent more time doing than I will ever admit, I’ll just say that with everything factored in, going back in time with today’s exact routines would convert today’s U.S. score to 170.896 at this point, i.e., still enough to beat the 2021 ROC. These colors don’t run! (Please don’t email me to say that they are, technically, the same colors as Russia’s.)

Now all that’s left is vault. In an effort to create parity between vault-heavy teams (that’s USA) and bars/beam-heavy ones (like China), the FIG slashed start-value scores for all the big-gun vaults a gymnast can do by 0.4 points. In 2021 everyone’s favorite villain MyKayla Skinner competed a Cheng vault that was start-valued at a 6.0, but on Tuesday, it was vaulted incredibly by Brazil’s Rebeca Andrade with a start value of just 5.6. So the final thing we need to do when going back in time for a magical mano a mano would be to credit the members of 2024 Team USA with 1.2 more points, which means that they would absolutely obliterate Aldi Russia by more than 2 points! This is the most patriotic I have ever been! (I should also take this moment to mention that I have nothing, personally , against any of the young women on the 2021 team from You-Know-Where. They were incredible in Tokyo and absolutely earned their gold.)

There are so many more permutations that I could, technically, run (maybe, even, I did run them but decided they were too picayune for Slate Magazine!). Is it fair to count great vaulter Jade Carey from today, for example, when she went to Tokyo as an individual specialist and wasn’t able to compete in team finals at all back then? (Because if we’re talking do-overs, it’s possible that that might have shaken out differently too.) Also, the members of the ROC actually had a bad meet (for them!) in team finals, and the U.S. still had a worse one! How would Russia’s best possible day match up against—no. Listen, time travel is fake, and we have to stop somewhere. I cannot not think about this matchup, but somewhere the counterfactual imagination needs to turn off and I need to touch grass.

In the end, in most feasible scenarios, the answer is, however, clear: Today’s American team on this exact day would have beaten Tokyo’s “unaffiliated team full of Russians” on that exact day. That’s enough for me, but it does bring up one final sticking point. The biggest difference between today and Tokyo’s team finals is glaringly obvious. It is 4-foot-8, has five eponymous skills, and is named Simone.

Biles is great enough that she does offer Team USA a large amount of that 5-point cushion without any form of Russia, and a 1-to-2-point cushion with them. She was in 2021, and would be now, a large portion of the U.S. margin of error . Our program is good. It’s great! But if Biles retires after Paris, barring true freak occurrences, you will not be seeing a 5-point margin of victory anytime in the conceivable future.

Now, I would never go so far as to say “The U.S. team is great only because Biles is on it” because, first of all, do you hear what that sounds like? The ’96 Bulls were good only because of Jordan. Yes, greatests of all time tend to do that for a team. That’s how sports work! But just as Scottie Pippen was no slouch, the rest of Team USA had a great meet, and Lee and Chiles are currently the third- and fourth-best all-around gymnasts in the entire world. We’re good! We’re No. 1! We did it! We are “redeemed” (though I, personally, did not need to see a gold medal for this to happen). But how good the American program remains in a post-Biles era? Especially if, Bog forbid, Russia is allowed to do sports again? Not even my genius mathematical brain can manage to compute this feat. We are going to need an actual time machine for that.

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Program Requirements — PhD

Length of program.

The PhD Program normally takes four years of full-time study beyond the Master's level to complete. A Master's degree is a prerequisite. Expected progress is outlined in the following table:

Year 1 Course work (6 courses on your transcript); Pass atleast three comprehensive exams; Select a thesis advisor.
Year 2 Supervisory committee selected by student and the thesis advisor; First annual supervisory committee progress report due. 
Year 3 Presenation of preliminary thesis result to supervisory committee; Achieve PhD candidacy
Year 4 Thesis content seminar; Departmental PhD thesis examination; Final PhD thesis examination at the School of Graduate Studies.
Year 4 — October Student interested in academic employment after the PhD must have a major thesis results ready.

Degree Requirements

1) Coursework for PhD (4-year program): 

Completion of at least 6 half-courses (or the equivalent combination of half and full-year courses). Normally, 6 half-courses are taken in the first year of study (3 half courses in the fall term and 3 in the spring term). It is strongly recommended that student take some additional courses in later years. 

2) Comprehensive Examination: 

The student is required to pass six core courses with an A- grade before beginning an area of specialization. A single "pass/fail" examination in the six general areas (analysis (real and complex), algebra, topology, partial differential equations, linear algebra & optimization and probability) is offered over a 2-day period in early or late September. Passing the comprehensive exam will fulfill the core course requirement. Students have the option to write the final exam of any core course and obtain core credit.

The main requirement of the degree is an acceptable thesis. This will embody an individual contribution to original research of a stand that warrants publication in the research literature. It must be written under the supervision of one or more members of the department. 

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4) Departmental Academia / Student Advancement 

Students are expected to become extensively involved in departmental life (seminars, colloquia, and related activities).

Core Courses

The following is a list and description of the core courses offered to graduate students during the academic year. These are the basic beginning graduate courses. They are designed to help the student broaden and strengthen his/ her general background in mathematics prior to specializing towards a thesis. A student with a strong background in the area of any of the core courses should not take that particular course: 

MAT1000H F  MAT457H1 F Real Analysis 
MAT1001H S MAT458H1 S Real Analysis II 
MAT1002H S MAT454H1 S Complex Analysis 
MAT1060H F   Partial Differential Equations I
MAT1061H S   Partial Differential Equations II
MAT1100H F   Algebra I
MAT1101H S   Algebra II 
MAT1300H F   Topology I
MAT1301H S   Topology II
MAT1600H F   Mathematical Probability I
MAT1601H S   Mathematical Probability II
MAT1850H F   Linear Algebra and Optimization

Program Requirements — PhD Direct-Entry

Length of program — direct-entry.

The PhD Direct-Entry program normally takes five years of full-time study to complete. Expected progress in the program is outlined in the following table: 

Year 1 6 courses of which four half-course credits in core material. Completion of a summer Supervised Research Project
Year 2 Course work; Pass at leat 3 comprehensive exams; Select a thesis advisor. 
Year 3 Supervisory committee selected by the supervisor and the student; First annual supervisory committee progress report due.
Year 4 Presentation of preliminary thesis results to supervisory committee; Achieve PhD candidacy.
Year 5 Thesis Content Seminar; Departmental PhD Thesis Examination; Final P PhD Thesis Examination at the School of Graduate Studies
Year 5 — October Students interested in academic employment after the PhD must have major thesis results ready.

Program Requirements — Direct-Entry

1) Coursework for PhD (Direct-Entry program): 

Completion of at least 8 half courses (or the equivalent combination of half- and full-year courses). Normally 6 half courses are taken in the first year of study (3 half-courses in the fall term and 3 in the spring term) and 2 half-courses in the second year. It is strongly recommended that the student do a Supervised Reading Project (MAT1900Y, MAT1950Y) in the summer between Year 1 and 2 and take some additional courses in other years. Students must achieve an A- grade in each core course.

4) Departmental Academia  / Student Advancement 

Core Courses — Direct-Entry

The following is a list and description of the core courses offered to graduate students during the academic year. These are the basic beginning graduate courses. They are designed to help the student broaden and strengthen his/ her general background in mathematics prior to specializing towards a thesis. A student with a strong background in the area of any of the core courses should not take that particular course:  

Our Courses 

Please have a look at our graduate course listings to see what we are currently offering. 

Graduate Student Handbook 

Questions .

If you have any questions about requirements for our graduate programs, please email us at  [email protected]

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N.C. A&T Secures More than $100M in Contracts, Grants for Second Straight Year

By Todd Simmons / 07/30/2024 Research

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EAST GREENSBORO, N.C. (July 30, 2024) – Researchers at North Carolina Agricultural and Technical State University have secured more than $100 million in research and sponsored program contracts and grants for the second consecutive year, underscoring the university’s continued growth as a leading doctoral research institution.

N.C. A&T faculty and student researchers brought in more than $102 million in FY2024, raising to nearly $250 million the amount of research funding earned over the past two fiscal years. Researchers brought in three major projects in FY23 totaling $50 million that pushed last year’s total to $147.4 million.

Over the past five years, contract and grant funding has grown to $485 million, cementing A&T’s status as one of North Carolina’s top three public research universities and the nation’s leading public, historically Black research institution. With new faculty joining A&T this fall, research expanding in recently established centers of excellence and additional doctoral degree programs coming online, the university projects continued growth in 2024-25.

“North Carolina A&T faculty continue to build on their success as outstanding scientific researchers and grow the reputation of our university as a place where important science is being done,” said Melissa Hodge-Penn, Ed.D., A&T’s interim vice chancellor for Research. “We’re developing awareness of our major focus areas, such as autonomous vehicles, bioengineering, health care delivery and a wide range of significant issues for African Americans. It’s exciting to witness our continued ascent.”

Among the projects showcasing the university’s growth:

  • The National Institutes of Health awarded $5.8 million over a five-year period to establish the Genomics Research and Data Science Center for Computation and Cloud Computing (GRADS-4C) led by Joseph L. Graves Jr., Ph.D., in the College of Science and Technology and Kristen Rhinehardt, Ph.D., in the College of Engineering. GRADS-4C’s mission is to “develop an educational and hands-on research training network with resources in computational genomics, data sciences, and cloud computing to investigate and improve human health, as well as develop the future workforce, particularly among underserved populations.”
  • The National Science Foundation (NSF) awarded a 10-year grant worth up to $160 million to establish an NSF Regional Innovation Engines in the Piedmont Triad, one of 10 such engines across the nation. The Piedmont Triad Regenerative Medicine Engine is a collaborative effort led by Wake Forest University, with N.C. A&T, Winston-Salem State University, Forsyth Technical Community College and industry partners ReMDO and Axiom Space as core team members. A&T’s contributions include development of biomaterials and bioengineering development and expertise in adult education that will support “an innovation ecosystem to stimulate workforce development, job creation, and economic growth through the development of technologies that benefit the emerging regenerative medicine industry.” A&T received $931,814 in FY24.

Additional support and collaborations include:

  • The College of Engineering established a partnership with two regional innovation hubs that received funding from the Department of Defense as part of the CHIPS and Science Act of 2022 to “promote economic growth as they develop the physical, digital and human infrastructure to support success in microelectronics research.” The CLAWS regional hub, led by North Carolina State University, focuses on bandgap semiconductors and also partners with industry giants like Wolfspeed. The University of Southern California leads the CA DREAMS hub, creating a coalition including The Boeing Co., HRL Laboratories and Lockheed Martin.
  • Leila Hashemi-Beni, Ph.D., and applied science and technology doctoral student Tewodros Syum Gebre, received support from Microsoft under the company’s “Accelerating Foundation Models Research” (AFMR) collaboration. The pilot project they conducted used “models available through Microsoft’s Azure Open AI Service to develop a system that will lead to advancements in traffic management using physic informed deep learning.”

Media Contact Information: [email protected]

Latest News

Head shots of Brandon L. Daye, left, and Bryan L. Daye

Foundation to Honor A&T Students for Promoting Civic Leadership among Youth

07/30/2024 in College of Agriculture and Environmental Sciences , College of Business and Economics

This is a photo of researchers in a lab.

07/30/2024 in Research

This is a photo of an actor in the production, "Seven Guitars"

N.C. A&T Theatre Arts Program to Perform “Seven Guitars” at International Black Theatre Festival

07/29/2024 in College of Arts, Humanities and Social Sciences

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COMMENTS

  1. Graduate Program

    Program Requirements. Tuition & Funding. PhD Program Completion. Curriculum & Courses. Course Listings: 2023-24. Course Descriptions 2023-24. Course Descriptions: 2024-25. Learn about graduate (master's and doctoral programs) at the Department of Mathematics. Includes admissions, courses and more.

  2. PhD Admission Information

    Graduate Office. Department of Mathematics. University of Toronto. Bahen Centre for Information Technology, Room 6166. 40 St. George Street. Toronto, Ontario, Canada M5S 2E4. Telephone: (416) 978-7894. Fax: (416) 978-4107. PhD Admission Requirements Previous Degree.

  3. Mathematics

    Program Overview. The Department of Mathematics offers opportunities for research—leading to the Master of Science and Doctor of Philosophy degrees—in the fields of pure mathematics and applied mathematics. Faculty areas of research include, but are not limited to, real and complex analysis, ordinary and partial differential equations ...

  4. Admissions Requirements & Procedures

    Applications to the Department of Mathematics must be submitted to the School of Graduate Studies (SGS) using an online application which is housed on a secure server at the University of Toronto.. The online application allows applicants to manage and submit biographical and educational information as well as a Statement of Intent immediately to the University.

  5. Mathematics: Mathematics PhD

    Applicants are admitted under the General Regulations of the School of Graduate Studies. Applicants must also satisfy the Department of Mathematics' additional admission requirements stated below. Exceptionally strong BSc students with a grade point average (GPA) of 3.7 or higher may apply for direct admission to the PhD program.

  6. Graduate School Admissions: Mathematics

    The U of T School of Continuing Studies Academic Preparation Course (600 level), minimum grade of B English Facility Testing. Information on English Facility testing can be obtained by writing directly to the following addresses or by visiting the test websites: TOEFL/TSE Publications P.O. Box 6151, Princeton, N.J. 08541-6151 U.S.A. Tel: (609 ...

  7. Mathematics Major, PhD

    Graduate School. 111 Student Services Building, Knoxville, TN 37996. Phone: 865-974-2475. Email: [email protected]. The University of Tennessee, Knoxville. Knoxville, Tennessee 37996. 865-974-1000. The flagship campus of the University of Tennessee System and partner in the Tennessee Transfer Pathway .

  8. Department of Mathematics, University of Texas at Austin

    Department of Mathematics The University of Texas at Austin 2515 Speedway, PMA 8.100 Austin, TX 78712. Login. Quick Links for UT Math. Help

  9. Mathematics Graduate Program

    Our grad students can take courses not only in the Mathematics Department but also elsewhere at Penn, and the wide resources of the university are available. Our former graduate students have gone on to mathematical careers both in academia and in industry. Our full-time Ph.D. students receive a generous and competitive support package including.

  10. Mathematics and Philosophy

    Statement of Land Acknowledgement. We wish to acknowledge this land on which the University of Toronto operates. For thousands of years it has been the traditional land of the Huron-Wendat, the Seneca, and the Mississaugas of the Credit.

  11. Ph.D. in Mathematics

    To graduate with a PhD in Mathematics, a student must satisfy all of the following requirements: Course Credits : 45 credits, including 15 doctoral dissertation research credits/GRAD 6950. If you have a Master's degree in mathematics at UConn, then 30 credits are required, including 15 doctoral dissertation research credits.

  12. Mathematics Programs at UT

    The program requires 30 hours of graduate coursework, and it is normally possible to finish the degree in two years. Many students earn an MS as they make progress towards a PhD. The department's unique Master of Mathematics (M.M.) degree is an online professional program primarily intended for working high school teachers.

  13. PhD Admission Requirements

    A standing that is equivalent to at least A- (U of T 80 ‐ 84% or 3.7/4.0) in the final year of study. We also consider applicants with graduate degrees in biostatistics, computer science, economics, engineering, mathematics, physics, or any discipline where there is a significant quantitative component.

  14. Doctor of Philosophy in Mathematics

    The program offers extensive coursework and intensive research experience in theory, methodology, and applications of mathematics (see degree requirements ). Faculty members with broad and diverse research interests are available to supervise doctoral dissertations. Financial support in the form of assistantships, full tuition support, and ...

  15. Mathematics PhD Program

    The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both ...

  16. Physical & Mathematical Sciences Admission Category

    Physical & Mathematical Sciences Careers #1 in Canada for graduate employability — recruiters from top companies have consistently ranked U of T as #1 in Canada and among the best in the world at preparing its students for the workplace. With a science degree from a world-renowned university, you will have a competitive advantage when applying for jobs in fields such as:

  17. Mathematics

    This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program. Students are encouraged to take their introductory analysis, algebra, and physics in their first year of study ( MAT157Y1, MAT240H1, MAT247H1, PHY151H1, PHY152H1). Arts & Science Internship Program

  18. About our Graduate Program

    About our Graduate Program. Mathematics has been taught at the University of Toronto since 1827. Since the first Canadian PhD degree in mathematics was conferred to Samuel Beatty (under the supervision of John Charles Fields) in 1915, more than 400 PhD degrees and 950 master's degrees have been awarded in this University.

  19. Graduate Program

    Our graduate program is unique from the other top mathematics institutions in the U.S. in that it emphasizes, from the start, independent research. Each year, we have extremely motivated and talented students among our new Ph.D. candidates who, we are proud to say, will become the next generation of leading researchers in their fields. While we ...

  20. U of T math students US PhD program admission success : r/UofT

    3. UofT is a top 20 worldwide math institution (for research). Most of the professors here are also quite good lecturers, but the class sizes are quite large and you'll need to be pretty active in finding opportunities yourself to do research/reading courses, etc. The class sizes gets better in third and fourth year. 4.

  21. Mathematics

    Six 4U/M courses, including: Calculus & Vectors (MCV4U) English (ENG4U) Find equivalent requirements for Canadian high school systems, US high school system, International Baccalaureate, British-Patterned Education, French-Patterned Education, CAPE, and other international high school systems. Learn more about Mathematics in the Faculty of Arts ...

  22. Singler named interim chair of mathematics and statistics at S&T

    Missouri University of Science and Technology (Missouri S&T) is a STEM-focused research university of over 7,000 students located in Rolla, Missouri. Part of the four-campus University of Missouri System, Missouri S&T offers over 100 degrees in 40 areas of study and is among the nation's top public universities for salary impact, according to ...

  23. Foundation to Honor A&T Students for Promoting Civic Leadership among

    EAST GREENSBORO, N.C. (July 30, 2024) - The Andrew Goodman Foundation (AGF) will honor North Carolina Agricultural and Technical State University students and twin brothers, Brandon L. Daye and Bryan L. Daye of Burlington, North Carolina, as it commemorates the 60 th anniversary of Freedom Summer 1964. Brandon Daye, who is working toward a B.S. in agribusiness, B.S. in supply chain ...

  24. Olympics women's gymnastics: Team USA's gold medal left one question

    I need to know this so badly that I did math. Advertisement At the end of team finals in 2021, the "Russian Olympic Committee" bested a mostly Simone-less USA, 169.528 to 166.096.

  25. Department of Mathematics

    Department of Mathematics, University of Toronto . Bahen Centre, Room 6290 40 St. George St., Toronto, ON, M5S 2E4; 416-978-3323; Email Us

  26. Admission requirements

    The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg, and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River.

  27. Course Descriptions 2023-24

    This course will develop advanced methods in linear algebra and introduce the theory of optimization. On the linear algebra side, we will study important matrix factorizations (e.g. LU, QR, SVD), matrix approximations (both deterministic and randomized), convergence of iterative methods, and spectral theorems.

  28. Program Requirements

    Degree Requirements. Completion of at least 6 half-courses (or the equivalent combination of half and full-year courses). Normally, 6 half-courses are taken in the first year of study (3 half courses in the fall term and 3 in the spring term). It is strongly recommended that student take some additional courses in later years.

  29. School of Science, Technology, Engineering, and Mathematics

    Gain the skills you need to be a leader in a STEM field. Join a diverse community committed to understanding, appreciating, and caring for God's creation and addressing the challenges of our day.At the Calvin School of STEM, no matter what academic path you choose, you'll gain a deep literacy in modern science and technology. Through internships, research opportunities, and access to top ...

  30. N.C. A&T Secures More than $100M in Contracts, Grants for Second

    EAST GREENSBORO, N.C. (July 30, 2024) - Researchers at North Carolina Agricultural and Technical State University have secured more than $100 million in research and sponsored program contracts and grants for the second consecutive year, underscoring the university's continued growth as a leading doctoral research institution.