phd in philosophy and mathematics

University of Notre Dame

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MSIM PROGRAM FOR PHILOSOPHY PhD STUDENTS, MAMP PROGRAM FOR MATHEMATICS PhD STUDENTS, AND JOINT MATH/PHILOSOPHY PhD PROGRAM

In collaboration with the Philosophy Department, the Mathematics Department at Notre Dame offers several joint programs for students interested in Mathematical Logic as well as Philosophy. The acronym MSIM stands for Master of Science in Interdisciplinary Mathematics, and this degree is given by the Mathematics Department. The program is available also to students from fields besides Philosophy. See this link: https://math.nd.edu/graduate/msim-degree/ for more information about joint Mathematics/Philosophy graduate degrees at Notre Dame. If you are a PhD student at Notre Dame interested in the MSIM degree with your primary area of interest not in Mathematical logic and Philosophy, the MAMP (Master of the Arts in Mathematical Philosophy) program may be of interest. See https://philosophy.nd.edu/graduate-program/mathematical-philosophy-minor/ for additional information about MAMP. This page gives instructions for how to apply for the MSIM, MAMP, or the joint PhD program in Mathematical Logic and Philosophy. Please contact the Math or Philosophy DGS if you have additional questions.

Admission to either of these degree programs requires the approval of both the Mathematics and Philosophy Departments. Similarly, any extension of the deadlines discussed below need the approval of the Mathematics and Philosophy Departments. Approval by the Philosophy Department requires primary approval by the Logic Group within that department, and final certification by the Philosophy DGS. Approval by the Math department requires approval by the Logic Group within that department in consultation with the Math DGS and if necessary, the graduate committee. As these degrees are additional degrees beyond the student’s Ph.D. program, they are not funded separately. We expect that the students earning these degrees will be exceptional.

A student in the joint PhD program will have to find a Mathematics adviser and a Philosophy adviser. The student will write a single PhD thesis, but it may have separate parts with a Math or Philosophy focus.

Philosophy Primary

An essential criterion for admission to the MSIM or Joint Degree for a Philosophy graduate student by the mathematics department is the approval of a mathematics department faculty member who agrees to oversee the student’s work. This will normally require that the student has become integrated into that faculty member’s research group, and has proposed a viable area for research. It is the student’s responsibility to find their own advisor. Given that, the path towards admission to the MSIM or Joint Degree is as follows:

• Year 1 and 2 (coursework): In addition to Philosophy coursework, the student takes the Mathematics department’s Logic Sequence Math 60510 and Math 60520 in Year 1. The student is also required to take two additional basic courses in mathematics. Basic Algebra I and II is a common choice, but other choices are possible. These courses should be completed in the first two years. S/he also, in this period, plays an active role in some part of the Mathematics department’s on-going research seminars, lectures, etc. 
• Year 2: The student finds a faculty member willing to supervise some advanced work in that faculty member’s area. This might be over the first summer, during the second year, or during the second summer. The student should become well-integrated into the research group of the intended supervisor and take topics courses in Logic.
• Application to the MSIM program is made prior to the start of Year 3, and we encourage applicants interested in continuing to do the joint PhD program to apply well before the start of year 3. The application will include a description of the courses to be taken for the degree, and of the proposed Master’s thesis topic, both of which will have been designed in consultation with the proposed advisor along with letters of support from their advisors.  It is expected that the student’s work in Mathematics classes outside Logic will be above average and similarly with their work in philosophy.  
• If the student is admitted to the MSIM program, s/he will work during Year 3 with the Mathematics advisor on their thesis topic.  
• Students interested in pursuing the joint PhD program, which is called Philosophy and Mathematics, should take the oral exam in Mathematics by the beginning of Year 4. This oral is understood to be similar to the one taken by students pursuing a Ph.D. in Mathematical Logic. Passing this oral exam is required to earn the Joint Ph.D. 
• While working towards the MSIM degree, a student interested in pursuing the joint PhD program must express an intention to apply by the end of May of Year 3 and apply by the beginning  of Year 4. An application consists of a description of the courses to be taken for the degree, a research proposal, hopefully some completed research and letters of support from their advisors. If the decision at that stage is that the student needs further work, then the student may submit a revised application during Year 4.  In any event, if a philosophy student is to be accepted to the joint PhD program, this must happen by the first day of classes in the 5th year.
• If the student in the MSIM program is not admitted to the Joint PhD program, s/he will normally finish the requirements for, and be awarded, the MSIM degree on route to completion of the Philosophy PhD.  In this case we expect the MSIM thesis to be completed by the end of Year 4.  A public defense of the Master’s thesis is expected. The defense should happen by early in Year 5. 
• If the student is admitted to the Joint PhD program in Philosophy and Mathematics, s/he need not complete the requirements for the MSIM degree. Research completed in pursuit of the MSIM thesis might be incorporated into the research for the joint PhD dissertation.  We do expect this degree to be completed within 6 years. 

Mathematics Primary

An essential criterion for admission to the MAMP or Joint PhD for a mathematics graduate student by the Philosophy Department is the recommendation of a Philosophy Department faculty member who agrees to oversee the student’s work. This will normally require that the student has articulated a viable area for research and demonstrated to the satisfaction of the faculty member relevant competence to undertake a research project in the area. It is the student’s responsibility to find their own advisor. The joing PhD program for graduate students in the Department of Mathematics is called the PdD in Mathematics and Philosophy.

• Years 1 and 2: The student should enroll in approximately 1 research seminar in the Philosophy Department each semester. [Generally, four philosophy seminar courses with a heavy writing component are needed for a student applying to the MAMP or joint PhD program.] Knowing that the application to the MAMP includes the submission of a sample of philosophical writing, it is wise to make sure to take seminars with substantial writing components so that by the time of application the student will have experienced several episodes of writing and rewriting in light of instructor feedback. Students should check with the instructor whether the course has a substantial writing component.  Most seminars will fit this description, but some Logic seminars will not. Note that all seminars taken prior to application to the MAMP will be retroactively counted towards fulfillment of the MAMP (and/or Joint PhD.) degree. For students interested in MAMP or the joint PhD program,the Mathematics department can delay two of the required basic courses to the second year to allow students time to complete their philosophy seminars.
• An application to MAMP or the joint PhD program should consist of a transcript, the written work from Philosophy seminars, and a research paper, together with faculty evaluations.
• Year 2 or 3: Application to the MAMP should be made at the end of year 2 or during year 3. Students with a definite expectation to eventually apply to the Joint PhD program are strongly advised to apply before the start of year 3. Students with no plan to apply to the Joint PhD program should in any event apply to the MAMP before the end of their 3rd year of study, so that the commencement of their MAMP thesis research does not disrupt the timely completion of their Mathematics dissertation research.
• Applications for the Joint PhD in Mathematics and Philosophy. will only be considered for students in their first four years of graduate study, and admission to the Joint PhD  must happen before the start of the student’s 5th year. A student applying to the Joint PhD program need not complete their MAMP thesis; in many cases the work going towards that thesis will be further elaborated as the Philosophy component of their PhD dissertation.
• A student who does not apply to the Joint PhD in Mathematics and Philosophy should submit their MAMP thesis by the end of their 4th year.
• A student admitted to the Joint PhD program in Mathematics and Philosophy should have a research plan suited for completion of the degree by the end of their 6th year.

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Mathematics

Doctor of philosophy in mathematics, get your phd in mathematics.

The PhD program places a strong emphasis on preparation for research and teaching.

Students must earn at least 72 semester hours of graduate credit and spend at least three years in residence at a graduate college, including at least one year at the University of Iowa.

They must complete specific courses designated as preparatory for the PhD qualifying examinations; pass the qualifying and comprehensive exams; and write a PhD thesis.

For a complete description of these requirements see the graduate student handbook .

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Create your academic path

You'll find degree overviews, requirements, course lists, academic plans, and more to help you plan your education and explore your possibilities.

Current course list

The MyUI Schedule displays registered courses for a particular session and is available to enrolled students. The list view includes course instructors, time and location, and features to drop courses or change sections.

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

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

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Doctor of Philosophy in Applied and Industrial Mathematics  Unit: College of Arts and Sciences (GA) Department: Mathematics    Program Website   Academic Plan Code(s): MATHPHD

Program Information

The University of Louisville Department of Mathematics is a research-oriented department that prides itself on delivering first-rate graduate instruction. There are a broad range of courses and ample opportunities to interact with faculty. The Department also maintains an active colloquium series with talks given by visiting mathematicians, statisticians and scientists.

The PhD program in Applied and Industrial Mathematics offers a blend of advanced mathematical and statistical knowledge with the experience to apply that knowledge. Students completing the program have a unique perspective from which they can see the whole of mathematics integrated with applied and industrial needs. A broad and rigorous mathematical core combined with customized application electives and an industrial internship prepares students with life-long career skills in teaching, research, and industry.

Prerequisites

Undergraduate coursework equivalent to a major in mathematics from an accredited university. This should include at least a one-year course in either analysis or abstract algebra, equivalent to MATH 501 - MATH 502 and MATH 521 - MATH 522  at the University of Louisville.

Candidates who have not taken both must complete the second in their program.

Dual Degree Program in Applied and Industrial Mathematics (PhD) and Biostatistics (MS)

Dual degrees in Biostatistics and Applied and Industrial Mathematics are offered by the College of Arts and Sciences and the School of Public Health and Information Sciences. Upon completion of the program, students will receive a PhD in Applied and Industrial Mathematics and a Master of Science in Biostatistics.

Admission Requirements

Interested applicants should have completed undergraduate coursework equivalent to a major in mathematics from an accredited university. This should include at least a one-year course in either analysis or abstract algebra, equivalent to  MATH 501 - MATH 502  and  MATH 521 - MATH 522  at the University of Louisville.

Candidates who have not taken both sequences must complete the second in their program.

Prospective students can apply online . Complete applications require the following:

• Graduate Application form along with paid application fee
• Cover letter to Mathematics department including any information you believe will help process your application. Please indicate in this letter whether you are interested in a GTA position, for example
• Transcripts (an official copy for each undergraduate institution attended. University of Louisville transcripts are automatically submitted)
• At least two letters of recommendation 
• Recent (within three years) GRE scores (only the general exam is required)
• All applicants for whom English is a second language must also submit official TOEFL scores of 79 or higher on the internet-based test, 213 or higher on the computer-based test. English proficiency can also be met by submitting official IELTS scores of at least 6.5 overall band score from the academic module exam or official Duolingo overall score of 105.  Students holding a bachelor's or advanced degree from an accredited institution in the United States may be exempt from this requirement.

For full consideration please submit complete applications by:

Spring admission deadline: November 1 Fall admission deadline: March 1

Late applications will be considered.

Dual Degree Program in Applied and Industrial Mathematics and Biostatistics  Application Procedure

To be admitted to the program, the student is required to apply to and be accepted by both the Department of Mathematics and the Department of Bioinformatics and Biostatistics. A student seeking admission into this program must submit letters to both the Department of Mathematics and the Department of Bioinformatics and Biostatistics stating the intent to take advantage of the dual degree program, as well as their choice of the thesis or non-thesis option for the MS in Biostatistics. Students must submit two recent letters of recommendation with their letter of intent. Applicants will receive written notification stating whether their admission request has been approved or disapproved.

Students currently enrolled in the PhD in Applied and Industrial Mathematics program will need to submit complete application materials to the Department of Bioinformatics and Biostatistics for admission to the MS component of the dual degree, as well as notify his/her advisor in the Department of Mathematics of the intention to enter into the dual degree program. Letters of recommendation for admission to the MS program can be taken from the letters of recommendation written for admission to the PhD program, provided they have been written sufficiently recently.

Program Requirements

Doctor of philosophy in applied and industrial mathematics.

All students admitted to the program must complete the following coursework (or their approved equivalent) and other degree requirements:

Additional Topics and Area of Specialization

In addition to the core, an application area of 18 credit hours will be required. The courses may be in a department outside Mathematics. They will be chosen in consultation with the student's advisory committee.

Qualifying Examinations

Students must pass three written examinations. Two of these will be chosen from the areas of Algebra, Combinatorics and Real Analysis. The third will be chosen from the areas of Mathematical Modeling, Mathematical Statistics and Probability. Normally, these will be taken within a year of completion of the core coursework. These examinations need not be taken together and each may be attempted at most twice.

Industrial Internship

Each student, with prior approval of the Graduate Studies Director, has to complete an internship in an appropriate industrial or governmental setting, or have equivalent experience.

Computing Project

Each student must complete an approved computer project related to the student's area of concentration.

Candidacy Examination

Each student must pass an oral examination in the chosen area of concentration. Usually, at most two attempts at passing this examination will be permitted. Students who wish to make a third attempt must petition the Graduate Studies Committee of the department for permissions to do so.

Dissertation

12 to 18 credit hours: A doctoral dissertation is required of each student.

Required Courses

The required courses for the dual degree program consist of all non-overlapping core courses for both the PhD in Applied and Industrial Mathematics, as well as the course requirements for the MS in Biostatistics. Courses taken to satisfy the Biostatistics component of the dual degree program can be applied to these 18 credit hours of electives which are required for the PhD in Applied and Industrial Mathematics.

Students currently enrolled in the PhD in Applied and Industrial Mathematics program will need to submit complete application materials to the Department of Bioinformatics and Biostatistics for admission to the MS component of the dual degree, as well as notify his/her advisor in the Department of Mathematics of the intention to enter into the dual degree program (see Admissions tab).

Requirements for the PhD in Applied and Industrial Mathematics

Elective/Application Area Courses

18 credit hours of  Application Area courses are chosen in consultation with a student's advisory committee. These courses can be outside of the Department of Mathematics. C ourses taken to satisfy the Biostatistics component of the dual degree program can be approved to satisfy these 18 credit hours.

Each student, with prior approval of the Graduate Studies Director and the Industrial Internship Director, has to complete an internship in an appropriate industrial or governmental setting, or have equivalent experience.  The Industrial Internship required by the Department of Mathematics and the Master's Project or Thesis required for the MS can be satisfied by a single internship and technical report which simultaneously satisfies the requirements for both degrees. Specifically, the internship must both focus on biostatistics so that it satisfies the Project or Thesis, and contain advanced mathematical content so that it satisfies the Industrial Internship. Likewise, the technical report must meet two requirements: it must satisfy the requirements for a Master's Project report or Master's Thesis for the MS degree and it must be written at an advanced mathematical level expected Industrial Internship. Students should enroll in the Master's Project ( PHST 675 ) or Master's Thesis ( PHST 666 ) courses during or shortly after completion of the Industrial Internship to take advantage of the combined Industrial Internship and Master's Project/Thesis.

Dual-degree students will not be permitted to enroll in the Master's Project ( PHST 675 ) or Master's Thesis ( PHST 666 ) courses until at least two qualifying examinations toward the PhD in Applied and Industrial Mathematics have been completed.

Other Requirements

Students must pass qualifying examinations, complete an approved computing project, and pass a candidacy examination as detailed in the catalog entry for the PhD in Applied and Industrial Mathematics.

In order for the student to fulfill the PhD requirements, the student must satisfy both the qualifying examination and dissertation requirements (12-18 credit hours)  for the PhD in Applied and Industrial Mathematics. Failure to complete these requirements will not jeopardize the MS degree if all its requirements have been satisfactorily completed.

MS in Biostatistics

The PHST 661 - PHST 662 / MATH 561 - MATH 562 requirement is waived if the student takes MATH 663 and MATH 667 . The PHST 681 - PHST 682 requirement is waived if the student takes MATH 667 - MATH 668 . Both requirements ( PHST 661 - PHST 662 / MATH 561 - MATH 562 and PHST 681 - PHST 682 ) are waived only if the student completes both the MATH 663 - MATH 664 and MATH 667 - MATH 668 sequences.

Courses taken to satisfy the Biostatistics component of the dual degree program can be applied to the 18 credit hours of electives which are required for the PhD in Applied and Industrial Mathematics.

A course in public health is a requirement for any student graduating with the MS degree from the Department of Bioinformatics and Biostatistics. These credit hours are not applied to the MS degree.

Electives are chosen in consultation with an advisor, typically from PHST 603 , PHST 620 , PHST 640 , PHST 675 , and PHST 682 .

To be completed in accordance with the guidelines written in the catalog entry for the MS in Bioinformatics and Biostatistics Degree.

Combined Industrial Internship, Practicum and Master's Thesis [six - eight (6-8) credit hours]

Special considerations: students who have already completed a master's degree in the department of mathematics.

To preserve the spirit of a dual degree, such students need to complete 36 credit hours of courses as required for the MS in Biostatistics. Six (6) credit hours of the previous master's degree coursework can be applied to this requirement. The remaining credit hours must be chosen from the list of not covered by core courses approved electives for the Department of Bioinformatics and Biostatistics, with preference given to courses in the Departments of Mathematics and Bioinformatics and Biostatistics. Combined Industrial Internship, Practicum and Master's Thesis cannot be replaced by a previous master's thesis. This requirement must be satisfied as previously described, meeting the specifications of both departments.

The University of Louisville is committed to and will provide equality of educational and employment opportunity for all persons regardless of race, sex, age, color, national origin, ethnicity, creed, religion, disability, genetic information, sexual orientation, gender, gender identity and expression, marital status, pregnancy or veteran status.

Every effort has been made to make the catalog accurate as of the date of publication. However, the University of Louisville reserves the right to change programs of study, academic policies, academic requirements, fees, course information, procedures for the confirmation of degrees, or the announced academic calendar and related deadlines without prior notice. Copyright © 2024-2025, University of Louisville. All rights reserved.

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2024-25 Academic Catalog

Doctor of philosophy in mathematics, why study mathematics.

Because mathematics is a framework upon which humanity builds an understanding of the world.

Mission of the Graduate Program:

The mission of the Graduate Program of the Department of Mathematics is to prepare students for leadership roles in meeting the mathematical needs of our society and to produce professional mathematicians for positions in universities, colleges, industry, governmental agencies, and research centers.

Doctor of Philosophy in Mathematics:

The Mathematics Department offers the degree of Doctor of Philosophy (Ph.D.) in Mathematics.  The Ph.D. program provides broad and deep expertise in mathematics, culminating in a dissertation that includes significant original work.  It is intended for students with a strong mathematical background who plan a career in research in academia or industry. A broad range of specialties is possible; research interests of department faculty include algebra, analysis, combinatorics, control theory, dynamical systems, geometry, numerical analysis, partial differential equations, probability, and statistics. There are two tracks: Pure Mathematics and Applied Mathematics. The requirements for each track are listed in the section Degree Requirements. College-wide requirements for graduate students may be found in the  Graduate School Catalog .

Admission to Graduate Studies

An applicant seeking to pursue graduate study in the College may be admitted as either a degree-seeking or non-degree seeking student. Policies and procedures of Graduate Studies govern the process of Graduate admission. These may be found in the Graduate Studies section of the online catalog.

Please consult the Departments & Programs section of the online catalog for information regarding program-specific admissions criteria and requirements. Special admissions requirements pertain to Interdisciplinary Studies degrees, which may be found in the Graduate Studies section of the online catalog.

Admission to the Ph.D. in Mathematics

The minimum prerequisites for admission are:

• an undergraduate degree from an accredited institution with a program of study in mathematics;
• a record of achievement that shows strong promise of success in graduate school, including a 3.0 cumulative grade-point average in undergraduate studies and a 3.0 grade-point average in mathematics (department requirement);
• course work in abstract algebra, linear algebra, and advanced calculus or introduction to analysis (comparable to KU courses  MATH 500 , MATH 558 , and MATH 590 ).

It is beneficial to have preparation in probability/statistics (comparable to  MATH 627 / MATH 628 ) and/or numerical analysis (comparable to  MATH 581 ). Although not required, it is also helpful to have taken introductory courses in complex analysis ( comparable to  MATH 646 ), partial  differential equations (comparable to  MATH 647 ), geometry (comparable to MATH 660 / MATH 661 ),  and/or topology.

The Mathematics Department currently does not require the general or subject Graduate Record Examination (GRE), although applicants may submit scores if they wish.  International students whose native language is not English must fulfill English language requirements specified by university policies.

Applicants must submit a graduate application online , including the following required materials:

• Transcript from each college or university the applicant has attended (an official transcript must be sent upon acceptance and completion of degree).
• Applicant’s résumé/curriculum vitae.
• A list of the textbooks used in mathematics courses beyond calculus.
• A statement of purpose indicating the applicant’s mathematical preferences and interests.
• 3 letters of reference.
• International applicants must fulfill the University's requirements for English proficiency .

Incomplete applications will not be considered. The minimum admission requirements do not guarantee admission. The Department of Mathematics evaluates candidates and makes recommendations to the Office of Graduate Studies regarding admission. The number of students admitted to the program changes from year to year, and admissions are competitive based on all application materials.

There are no additional application forms for financial support. Students are considered for support based on merit. Most Ph.D. students accepted by the program receive an offer of financial support in the form of a Graduate Teaching Assistantship. The number of GTAs available is limited. Further information about applications and admissions is available from the  Department of Mathematics .

Contact the department:

Michelle Morrison Graduate Program Coordinator Department of Mathematics 433 Snow Hall [email protected]

Ph.D. Degree Requirements

The department requires the student to meet the following requirements before taking the comprehensive examination.

• Pass two written qualifying examinations: one exam in either algebra or analysis and a second exam in either numerical analysis or probability/statistics.  Both qualifying examinations must be completed by the beginning of the student’s fifth semester.
• Complete the required qualifying exam coursework: MATH 727 (Probability), MATH 765 (Analysis I), MATH 781 (Numerical Analysis I), MATH 791 (Abstract Algebra I).  Passing a qualifying exam exempts a student from the corresponding course. This coursework must be completed before the preliminary examination.
• Pass a preliminary examination in an area close to the focus of the eventual doctoral dissertation. The preliminary examination must be completed by the beginning of the student’s eighth semester.
• To meet the Research Skills requirement, students must complete an introductory programming language course approved by the Graduate Committee. The course may have been taken at KU or at another university, either as a graduate or undergraduate. Students may meet the Research Skills requirement by passing EECS 138 or EECS 168 .  Alternatively, students may complete a computing project approved by their advisor and the Graduate Committee demonstrating competence in either a programming language or the use of specialized software that supports the student’s research.
• The Responsible Scholarship requirement must be met by completing the departmental training in responsible scholarship for mathematicians.  The training is offered every spring semester.  Students must have passed the qualifying exams and be working with an advisor in order to participate.
• Complete the course requirements for a track in either Pure Mathematics or Applied Mathematics, as outlined below.

Note:  Contact your department or program for more information about the qualifying exam coursework requirement, the research skills and responsible scholarship, and the current requirements for doctoral students. Current policies on Doctoral Research Skills and Responsible Scholarship are listed in the Graduate Studies section of the online catalog and in the KU Policy Library.

Pure Mathematics

This track requires:

In addition, the pure-track student must complete four additional MATH courses at the 800 level or above before the final examination. MATH 896 , MATH 899 , MATH 993 and MATH 999 may not be used to satisfy this requirement. MATH 990 may be used to satisfy this requirement only with Graduate Committee approval. Courses outside Mathematics may be used to satisfy this requirement only with Graduate Committee approval.

Applied Mathematics

In addition, the applied-track student must complete four additional MATH courses at the 800 level or above before the final examination. MATH 896 , MATH 899 , MATH 993 and MATH 999 may not be used to satisfy this requirement. MATH 990 may be used to satisfy this requirement only with Graduate Committee approval. Courses outside Mathematics may be used to satisfy this requirement only with Graduate Committee approval.

Examination Preparation

Normally the work required to prepare a student for the oral comprehensive examination (and to do research) includes one or more semesters of advanced courses, directed readings, and seminars. In the oral comprehensive examination, a student must show proficiency in the chosen area of mathematics. Precise areas of responsibility on this examination are discussed in detail with the advisory committee (the student’s advisor and two other members of the department’s Graduate Faculty).

In addition to meeting general requirements, the Ph.D. candidate in mathematics must complete a minimum of 28 credit hours of mathematics coursework (this number includes 1 credit hour of MATH 999 ). The minimum amount of credit hours is possible only if a student passes all Ph.D. qualifying exams in lieu of the preparatory coursework ( MATH 727 , MATH 765 , MATH 781 , MATH 791 ). The program routinely takes 12 semesters to complete when factoring in research and milestone exams. A typical student completes 72 or more credit hours when enrolled full-time.

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Doctor of Philosophy Program

Besides satisfying the general regulations of the Graduate School for the degree of Doctor of Philosophy, the student must comply with the requirements briefly outlined below. For complete details about these requirements see section IV of the Graduate Handbook .

Pass four Qualifying Examinations . The exams are based on material that is covered in the courses listed and on material from undergraduate prerequisites. Credit for passing a similar examination at another university cannot be transferred. See sections IV and VI of the Graduate Handbook for more information.

Advanced Topics Examinations. A student becomes eligible to take the Advanced Topics Examination after passing the Qualifying Examinations.

Plan of Study. The plan of study should be submitted electronically to the Graduate School through myPurdue by each student preparing to hold their Advanced Topics. 

Preliminary Examination. The preliminary examination for most students will only require the completion of a form for the Graduate School. An oral or written examination may be required by the student's advisory committee for admission to candidacy. Graduate School regulations require that at least two sessions (including summer sessions) must elapse between the preliminary examination and the thesis defense.

Admission to Candidacy. To be admitted to candidacy for the Ph.D. degree, the student must have fulfilled the requirements above which are detailed in section IV of the Graduate Handbook .

Dissertation. A thesis must be submitted in final form presenting new results of sufficient importance to merit publication.

Recommendation for the Ph.D. Degree. If the requirements are met within the time limits detailed in section IV of the Graduate Handbook , the candidate will be recommended to the faculty to receive the degree of Doctor of Philosophy.

For information about financial support and research in absentia see section IV of the Graduate Handbook .

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Doctor of Philosophy in Mathematics

Program description.

The Mathematics PhD degree curriculum at The University of Texas at Dallas offers extensive coursework and intensive research experience in theory, methodology and applications of mathematics. During their study, PhD students acquire the necessary skills to prepare them for high-level careers in fields requiring mathematical sophistication. The PhD program is designed to accommodate the needs and interests of the students. The student must arrange a course program with the guidance and approval of the graduate advisor. Adjustments can be made as the student’s interests develop and a specific dissertation topic is chosen.

Some of the broad research areas represented in mathematics are as follows: algebraic and complex geometry; analysis and its applications; control theory and optimization; dynamical systems and ordinary differential equations; differential geometry; mathematical physics; mathematical methods in medicine, biology, geosciences and mechanics; numerical analysis and scientific computing; partial differential equations; and topology.

Career Opportunities

Graduates of the program seek positions such as: professor in an academic institution, or professional in industry, government or finance and researcher in public or private sector. Available emphases ensure that candidates can tailor their future career by having targeted their educational background to their research interests.

The jobs of a mathematician consistently appears among the top jobs in the rankings of 200 jobs by CareerCast’s Jobs Rated Almanac based upon factors such as work environment, income, hiring outlook and stress. For more information about careers in mathematics, view the career page of American Mathematical Society.

The  NSM Career Success Center  is an important resource for students pursuing STEM and healthcare careers. Career professionals are available to provide strategies for mastering job interviews, writing professional cover letters and resumes and connecting with campus recruiters, among other services.

Marketable Skills

Review the marketable skills for this academic program.

Application Deadlines and Requirements

The university  application deadlines apply with the exception that, for the upcoming Fall term, all application materials must be received by December 15 for first-round consideration of scholarships and fellowships. See the  Department of Mathematical Sciences graduate programs website  for additional information. 

Visit the  Apply Now  webpage to begin the application process. 

Contact Information

For more information, contact [email protected]

School of Natural Sciences and Mathematics The University of Texas at Dallas 800 W. Campbell Road Richardson, TX 75080-3021 Phone: 972-883-2416

nsm.utdallas.edu

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Doctorate in Philosophy Mathematics and Statistics

• Degree offered: Doctorate in Philosophy (PhD)
• Registration status option: Full-time
• Language of instruction: English
• with thesis (12 full-time terms; 48 consecutive months)
• Academic units: Faculty of Science , Department of Mathematics and Statistics , Ottawa-Carleton Institute of Mathematics and Statistics (OCIMS) .

Program Description

Ottawa-Carleton Joint Program

The University of Ottawa offers a rich academic environment to study mathematics and statistics under the supervision of professors who have gained an international reputation for their research. Most major fields of research in mathematics and statistics are represented within the Department of Mathematics and Statistics. Moreover, the Department is a participating unit in the master's level collaborative programs in bioinformatics and in biostatistics. Additional information about the Department and its programs is posted on the departmental website at www.mathstat.uottawa.ca.

Since 1984, the graduate programs in mathematics and statistics have been under the umbrella of the Ottawa-Carleton Institute of Mathematics and Statistics (OCIMS). The OCIMS consists of the School of Mathematics and Statistics at Carleton University and the Department of Mathematics and Statistics at the University of Ottawa. The two units have pooled together their resources to offer each year a large selection of graduate courses.

Other Programs Offered Within the Same Discipline or in a Related Area

• Doctorate in Mathematics and Statistics Specialization in in Bioinformatics (PhD)
• Master of Science Mathematics and Statistics Concentration in Mathematics (MSc)
• Master of Science Mathematics and Statistics Concentration in Statistics (MSc)
• Master of Science Mathematics and Statistics Specialization in Bioinformatics (MSc)
• Master of Science Mathematics and Statistics Specialization in Biostatistics (MSc)

Fees and Funding

• Program fees:

The estimated amount for university fees associated with this program are available under the section Finance your studies .

International students enrolled in a French-language program of study may be eligible for a differential tuition fee exemption .

• To learn about possibilities for financing your graduate studies, consult the Awards and financial support section.
• Programs are governed by the general regulations in effect for graduate studies at both universities.
• In accordance with the University of Ottawa regulation, students have the right to complete their assignments, examinations, research papers, and theses in French or in English.
• Research activities can be conducted in English or French or both depending on the language used by the professor and the members of the research group.

Program Contact Information

Graduate studies office, faculty of science, 30 marie-curie street, gendron hall, room 181, ottawa, ontario, canada, tel.: 613-562-5800 x3145, email:  [email protected], twitter | faculty of science, facebook | faculty of science.

For the most accurate and up to date information on application deadlines, language tests and other admission requirements, please visit the  specific requirements  webpage.

To be eligible, candidates must:

• Have a master's degree in mathematics and statistics (or equivalent) with a minimum average of 75% (B+).

Note: International candidates must check the admission equivalencies for the diploma they received in their country of origin.

• Demonstrate a good academic performance in previous studies as shown by official transcripts, research reports, abstracts or any other documents demonstrating research skills.
• Meet the funding requirements.
• We recommend that you contact potential thesis supervisors as soon as possible.
• To register, you need to have been accepted by a thesis supervisor.
• The supervisor’s name is required at the time of application.
• The choice of supervisor will determine the primary campus location of the student. It will also determine which university awards the degree.

Language Requirements

Applicants must be able to understand and fluently speak the language of instruction (French or English) in the program to which they are applying. Proof of linguistic proficiency may be required.

Applicants whose first language is neither French nor English must provide proof of proficiency in the language of instruction.

Note: Candidates are responsible for any fees associated with the language tests.

• The admission requirements listed above are minimum requirements and do not guarantee admission to the program.
• Admissions are governed by the general regulations in effect for graduate studies and by the general regulations of the Ottawa-Carleton Institute of Mathematics and Statistics (OCIMS).

Fast-Track from Master’s to PhD

Students enrolled in the master’s program in mathematics and statistics at the University of Ottawa may be eligible to fast-track directly into the doctoral program without writing a master’s thesis, provided the following conditions are met:

• Completion of two graduate courses (six units) with a grade of A- or better in each.
• Having completed with success one of the basic comprehensive exam.
• Satisfactory progress in the research program.
• Written recommendation by the supervisor and the advisory committee;
• Approval by the graduate studies committee.
• The transfer must take place within sixteen months of initial enrollment in the master’s.
• Following the transfer, all of the requirements of the doctoral program must be met: a total of 18 course units (including the units completed at the master's); the comprehensive exams; and a thesis.

Requirements for this program have been modified. Please consult the  2018-2019 calendars  for the previous requirements.

The Department may require students to take additional courses, depending on their backgrounds.

Students must meet the following requirements:

The optional course units may be selected in related disciplines approved by the Department of Mathematics and Statistics.

A student changing his area of specialization is required to complete the advanced comprehensive examination in the new area within a time period specified by the thesis advisory committee.

Successful completion of all the advanced comprehensive examinations within 20 months from the initial registration.

Presentation and successful defense of a thesis based on an original research carried out under the direct supervision of a faculty member of the Institute.

Students are responsible for ensuring they have met all of the thesis requirements .

Minimum Requirements

The passing grade in all courses is B.

Students who fail two courses (equivalent to 6 units), or the thesis proposal, or the comprehensive exam, or whose research progress is deemed unsatisfactory are required to withdraw.

Research at the University of Ottawa

Located in the heart of Canada’s capital, a few steps away from Parliament Hill, the University of Ottawa ranks among Canada’s top 10 research universities. Our research is founded on excellence, relevance and impact and is conducted in a spirit of equity, diversity and inclusion.

Our research community thrives in four strategic areas:

• Creating a sustainable environment
• Advancing just societies
• Shaping the digital world
• Enabling lifelong health and wellness

From advancing healthcare solutions to tackling global challenges like climate change, the University of Ottawa’s researchers are at the forefront of innovation, making significant contributions to society and beyond.

Research at the Faculty of Science

The Faculty of Science has become a true centre of excellence in research through its world-class professors as well as its programs and infrastructure in Biology, Chemistry, Earth Sciences, Mathematics and Statistics, and Physics.

The research accomplished by its 140 internationally recognized professors, its approximately 400 graduate students and its dozens of postdoctoral researchers and visiting scientists has positioned the Faculty of Science as one of the most research intensive science faculties in Canada. Our professors have received many international and national awards including three NSERC Gerhard Herzberg Gold Medal winners and numerous Fellows of the Royal Society of Canada.

The Faculty of Science, through its strategic use of infrastructure programs, hosts world-class Core Facilities and is at the leading edge for the study of Catalysis, Experimental and Computational Chemistry, Environmental Toxins, Nuclear Magnetic Resonance, Isotope Analysis, Molecular Biology and Genomics, X-Ray Spectrometry/Diffractometry, Geochemistry, Mass Spectrometry, Physiology and Genetics of Aquatic Organisms, and Photonics. The Faculty is also associated with the Fields Institute for research in mathematical science and the Centre de recherche mathématiques (CRM) at the Université de Montréal, providing a unique setting for mathematical research.

For more information, refer to the list of faculty members and their research fields on Uniweb . 

IMPORTANT: Candidates and students looking for professors to supervise their thesis or research project can also consult the website of the faculty or department of their program of choice. Uniweb does not list all professors authorized to supervise research projects at the University of Ottawa.

Not all of the listed courses are given each year. The course is offered in the language in which it is described.

Course codes in parentheses are for Carleton University. A 3-unit course at the University of Ottawa is equivalent to a 0.5-unit course at Carleton University.

MAT 5105 Discrete Applied Mathematics I: Gra. Theory (3 units)

Paths and cycles, trees, connectivity, Euler tours and Hamilton cycles, edge colouring, independent sets and cliques, vertex colouring, planar graphs, directed graphs. Selected topics from one or more of the following areas: algebraic graph theory, topological theory, random graphs. This course is equivalent to MATH 5818 at Carleton University.

Course Component: Lecture

MAT 5106 Combinatorial Optimization (3 units)

Network flow theory and related material. Topics will include shortest paths, minimum spanning trees, maximum flows, minimum cost flows. Optimal matching in bipartite graphs. This course is equivalent to MATH 5808 at Carleton University.

MAT 5107 Discrete Applied Mathematics II: Combinatorial Enumeration (3 units)

Ordinary and exponential generating functions; product formulas; permutations; partitions; rooted trees; cycle index; WZ method. Lagrange Inversions; singularity analysis of generating functions and asymptotics. Selected topics from one or more of the following areas: random graphs, random combinatorial structures, hypergeometric functions. This course is equivalent to MATH 5819 at Carleton University.

MAT 5121 Introduction to Hilbert Space (3 units)

This course is equivalent to MATH 5009 at Carleton University.

MAT 5122 Banach Algebras (3 units)

This course is equivalent to MATH 5003 at Carleton University.

MAT 5125 Real Analysis I (3 units)

General measure and integral, Lebesgue measure and integration on R, Fubini's theorem, Lebesgue-Radon-Nikodym theorem, absolute continuity and differentiation, Lp-Spaces. Selected topics such as Daniell-Stone theory. This course is equivalent to MATH 5007 at Carleton University.

Prerequisites: MAT 3125 (MATH 3001 and MATH 3002).

MAT 5126 Real Analysis II (3 units)

Banach and Hilbert spaces, bounded linear operators, dual spaces. Topics selected from: weak- and weak-topologies, Alaoglu's theorem, compact operators, differential calculus in Banach spaces, Riesz representation theorems. This course is equivalent to MATH 5008 at Carleton University.

Prerequisite: MAT 5125 (MATH 5007).

MAT 5127 Complex Analysis (3 units)

This course is equivalent to MATH 5005 at Carleton University.

MAT 5131 Ordinary Differential Equations I (3 units)

One or two specialized Linear systems, fundamental solution. Nonlinear systems, existence and uniqueness, flow. Equilibria, periodic solutions, stability.Invariant manifolds and hyperbolic theory. topics taken from, but not limited to: perturbation and asymptotic methods, normal forms and bifurcations, global dynamics.This course is equivalent to MATH 5405 at Carleton University.

MAT 5133 Partial Differential Equations I (3 units)

First-order equations, characteristics method, classification of second-order equations, separation of variables, Green's functions. Lp and Soboloev spaces, distributions, variational formulation and weak solutions, Lax-Milgram theorem, Galerkin approximation. Parabolic PDes. Wave equations, hyperbolic systems, nonlinear PDes, reaction diffusion equations, infinite-dimensional dynamical systems, regularity. This course is equivalent to MATH 5406 at Carleton University.

Permission of the Department is required.

MAT 5134 Topics in Differential Equations (3 units)

This course is equivalent to MATH 5407 at Carleton University.

MAT 5141 Algebra I: Rings and Modules (3 units)

Noetherian and artinian modules and rings. Algebraic sets, vanishing ideals, Hilbert Basis Theorem, radical ideals, Hilbert Nullstellensatz. Localization of rings and modules. Tensor product of modules and algebras. Semisimple rings and modules, Schur's lemma, Jacobson Density Theorem, Artin-Wedderburn Theorem. Short exact sequences, free modules, projective modules, injective modules, flat modules. This course is equivalent to MATH 5107 at Carleton University.

MAT 5142 Algebra II: Groups and Galois Theory (3 units)

Group actions, class equation, Sylow theorems, central, composition and derived series, Jordan-Holder theorem, field extensions and minimal polynomials, algebraic closure, separable extensions, integral ring extensions, Galois groups, fundamental theorem of Galois theory, finite fields, cyclotomic field extensions, fundamental theorem of algebra, transcendental extensions. This course is equivalent to MATH 5109 at Carleton University.

MAT 5143 Lie Algebras (3 units)

This course is equivalent to MATH 5104 at Carleton University.

MAT 5144 Commutative Algebra (3 units)

Prime spectrum of a commutative ring (as a topological space); localization of rings and modules; tensor product of modules and algebras; Hilbert's Nullstellensatz and consequences for finitely generated algebras; Krull dimension of a ring; integral dependence, going-up, going-down; Noether Normalization Lemma and dimension theory for finitely generated algebras over a field; noetherian rings and Hilbert Basis Theorem; introduction to affine algebraic varieties and their morphisms. This course is equivalent to MATH 5001 at Carleton University.

MAT 5145 Group Theory (3 units)

This course is equivalent to MATH 5106 at Carleton University.

MAT 5146 Rings and Modules (3 units)

This course is equivalent to MATH 5103 at Carleton University.

MAT 5147 Homological Algebra and Category Theory (3 units)

This course is equivalent to MATH 5108 at Carleton University.

MAT 5148 Groups Representations and Applications (3 units)

This course is equivalent to MATH 5102 at Carleton University.

MAT 5149 Algebraic Geometry (3 units)

Brief overview of commutative algebra, Hilbert's Nullstellensatz, algebraic sets, and Zariski topology. Affine and projective varieties over algebraically closed fields. Regular functions and rational maps. Additional topics chosen from: the relation of varieties over complex numbers to complex analytic manifolds, genus, divisors, line bundles, Riemann-Roch Theorem, Bézout's Theorem. This course is equivalent to MATH 5002 at Carleton University.

MAT 5150 Topics in Geometry (3 units)

This course is equivalent to MATH 5201 at Carleton University.

MAT 5151 Topology I (3 units)

Topological spaces, product and identification topologies, countability and separation axioms, compactness, connectedness, homotopy, fundamental group, net and filter convergence. This course is equivalent to MATH 5205 at Carleton University.

MAT 5152 Topology II (3 units)

Covering spaces, homology via the Eilenberg-Steenrod axioms, applications, construction of a homology functor. This course is equivalent to MATH 5206 at Carleton University.

Prerequisites: MAT 3143 and MAT 5151 (MATH 3100 and MATH 5205).

MAT 5155 Differentiable Manifolds (3 units)

This course is equivalent to MATH 5208 at Carleton University.

MAT 5158 Lie Groups (3 units)

This course is equivalent to MATH 6104 at Carleton University.

MAT 5160 Mathematical Cryptography (3 units)

Analysis of cryptographic methods used in authentication and data protection, with particular attention to the underlying mathematics, e.g. Algebraic Geometry, Number Theory, and Finite Fields. Advanced topics on Public-Key Cryptography: RSA and integer factorization, Diffie-Hellman, discrete logarithms, elliptic curves. Topics in current research. This course is equivalent to MATH 5300 at Carleton University.

Prerequisite: undergraduate honours algebra, including group theory and finite fields.

MAT 5161 Mathematical Logic (3 units)

A basic graduate course in mathematical logic. Propositional and Predicate logic, Proof theory, Gentzen's Cut-Elimination, Completeness, Compactness, Henkin models, model theory, arithmetic and undecidability. Special Topics (time permitting) depending on interests of instructor and audience. This course is equivalent to MATH 5301 at Carleton University.

Prerequisite: Honours undergraduate algebra, analysis and topology (or permission of the instructor).

MAT 5162 Mathematical Foundations of Computer Science (3 units)

Foundations of functional languages, lambda calculi (typed, polymorphically typed, untyped), Curry-Howard Isomorphism, proofs-as-programs, normalization and rewriting theory, operational semantics, type assignment, introduction to denotational semantics of programs, fixed-point programming. Topics chosen from: denotational semantics for lambda calculi, models of programming languages, complexity theory and logic of computation, models of concurrent and distributed systems, etc. This course is equivalent to MATH 6807 at Carleton University.

Prerequisite: Honours undergraduate algebra and either topology or analysis. Some acquaintance with Logic useful.

MAT 5163 Analytic Number Theory (3 units)

This course is equivalent to MATH 5305 at Carleton University.

MAT 5164 Algebraic Number Theory (3 units)

This course is equivalent to MATH 5306 at Carleton University.

MAT 5165 Theory of Automata (3 units)

This course is equivalent to MATH 5605 at Carleton University.

MAT 5167 Formal Language and Syntax Analysis (3 units)

This course is equivalent to MATH/COMP 5807 at Carleton University.

MAT 5168 Homology Theory (3 units)

This course is equivalent to MATH 5202 at Carleton University.

MAT 5169 Foundations of Geometry (3 units)

This course is equivalent to MATH 5207 at Carleton University.

MAT 5170 Probability Theory I (3 units)

Probability spaces, random variables, expected values as integrals, joint distributions, independence and product measures, cumulative distribution functions and extensions of probability measures, Borel- Cantelli lemmas, convergence concepts, independent identically distributed sequences of random variables. This course is equivalent to STAT 5709 at Carleton University.

Prerequisites: MAT 3125 and MAT 3172 .

MAT 5171 Probability Theory II (3 units)

Laws of large numbers, characteristic functions, central limit theorem, conditional probabilities and expectation, basic properties and convergence theorems for martingales, introduction to Brownian motion. This course is equivalent to STAT 5709 at Carleton University.

Prerequisite: MAT 5170 .

MAT 5172 Topics in Stochastic Processes (3 units)

This course is equivalent to STAT 5508 at Carleton University.

MAT 5173 Stochastic Analysis (3 units)

Brownian motion, continuous martingales and stochastic integration. This course is equivalent to STAT 5604 at Carleton University.

MAT 5174 Network Performance (3 units)

The course will focus on advanced techniques in performance evaluation of large complex networks. Topics may include classical queueing theory and simulation analysis; models of packet networks; loss and delay systems; blocking probabilities. This course is equivalent to STAT 5704 at Carleton University.

Prerequisite: Some familiarity with probability and stochastic processes and queueing, or permission of the instructor.

MAT 5175 Robust Statistical Inference (3 units)

This course is equivalent to STAT 5506 at Carleton University.

MAT 5176 Advanced Statistical Inference (3 units)

Pure significance tests; uniformly most powerful unbiased and invariant tests; asymptotic comparison of tests; confidence intervals; large sample theory of likelihood ratio and chi-square tests; likelihood inference; Bayesian inference. Topics such as empirical Bayes inference, fiducial and structural inference, resampling methods. This course is equivalent to STAT 5507 at Carleton University.

MAT 5177 Multivariate Normal Theory (3 units)

This course is equivalent to STAT 5500 at Carleton University.

MAT 5180 Numerical Analysis for Differential Equations (3 units)

Floating pointing arithmetic; numerical solution of ordinary differential equations; finite difference methods for partial differential equations; stability, consistency and convergence: von Neumann analysis, Courant-Friedrichs-Lewy condition, Lax theorem; finite element methods: boundary value problems and elliptic partial differential equations; spectral and Pseudo-spectral methods. This course is equivalent to MATH 5806 at Carleton University.

MAT 5181 Data Mining I (3 units)

Visualization and knowledge discovery in massive datasets; unsupervised learning: clustering algorithms; dimension reduction; supervised learning: pattern recognition, smoothing techniques, classification. Computer software will be used. This course is equivalent to STAT 5703 at Carleton University.

MAT 5182 Modern Applied and Computational Statistics (3 units)

Resampling and computer intensive methods: bootstrap, jackknife with applications to bias estimation, variance estimation, confidence intervals, and regression analysis. Smoothing methods in curve estimation; statistical classification and pattern recognition: error counting methods, optimal classifiers, bootstrap estimates of the bias of the misclassification error. This course is equivalent to STAT 5702 at Carleton University.

MAT 5185 Asymptotic Methods of Applied Mathematics (3 units)

Asymptotic series: properties, matching, application to linear and nonlinear differential equations. Asymptotic expansion of integrals: elementary methods, methods of Laplace, Stationary Phase and Steepest Descent, Watson's Lemma, Riemann-Lebesgue Lemma. Perturbation methods: regular and singular perturbation for differential equations, multiple scale analysis, boundary layer theory, WKB theory. This course is equivalent to MATH 5408 at Carleton University.

MAT 5187 Topics in Applied Mathematics (3 units)

This course is equivalent to MATH 5403 at Carleton University.

MAT 5190 Mathematical Statistics I (3 units)

Statistical decision theory; likelihood functions; sufficiency; factorization theorem; exponential families; UMVU estimators; Fisher's information; Cramer-Rao lower bound; maximum likelihood and moment estimation; invariant and robust point estimation; asymptotic properties; Bayesian point estimation. This course is equivalent to STAT 5600 at Carleton University.

Prerequisites: MAT 3172 , MAT 3375 . The courses MAT 5190 , MAT 5375 cannot be combined for credits.

MAT 5191 Mathematical Statistics II (3 units)

Confidence intervals and pivotals; Bayesian intervals; optimal tests and Neyman-Pearson theory; likelihood ratio and score tests; significance tests; goodness-of-fit tests; large sample theory and applications to maximum likelihood and robust estimation. This course is equivalent to STAT 5501 at Carleton University.

Prerequisite: MAT 5190 .

MAT 5192 Sampling Theory and Methods (3 units)

Unequal probability sampling with and without replacement; unified theory of standard errors; prediction approach; ratio and regression estimation; stratification and optimal designs; multistage cluster sampling; double sampling; domains of study; post-stratification; non-response; measurement errors. Related topics. This course is equivalent to STAT 5502 at Carleton University.

MAT 5193 Linear Models (3 units)

Theory of non-full-rank linear models: estimable functions, best linear unbiased estimators, hypothesis testing, confidence regions; multi-way classification; analysis of covariance; variance component models: maximum likelihood estimation, MINQUE, ANOVA methods. Miscellaneous topics. This course is equivalent to STAT 5503 at Carleton University.

Prerequisite: MAT 4175 (MATH 4500) or MAT 5190 (STAT 5600).

MAT 5194 Stochastic Processes and Times Series Analysis (3 units)

This course is equivalent to STAT 5504 at Carleton University.

MAT 5195 Design of Experiments (3 units)

Overview of linear model theory; orthogonality; randomized block and split plot designs; Latin square designs; randomization theory; incomplete block designs; factorial experiments; confounding and fractional replication; response surface methodology. Miscellaneous topics. This course is equivalent to STAT 5505 at Carleton University.

Prerequisites: MAT 3375 and MAT 3376 or MAT 5190 (STAT 3505 and STAT 4500 or STAT 5600).

MAT 5196 Multivariate Analysis (3 units)

This course is equivalent to STAT 5509 at Carleton University.

MAT 5197 Stochastic Optimization (3 units)

Topics chosen from stochastic dynamic programming, Markov decision processes, search theory, optimal stopping. This course is equivalent to STAT 5601 at Carleton University.

Prerequisite: STAT 3506 or MAT 4371 .

MAT 5198 Stochastic Models (3 units)

Markov systems, stochastic networks, queuing networks, spatial processes, approximation methods in stochastic processes and queuing theory. Applications to the modelling and analysis of computer-communications systems and other distributed networks. This course is equivalent to MATH 5701 at Carleton University.

MAT 5301 Topics in Combinatorial Mathematics (3 units)

This course is equivalent to MATH 5609 at Carleton University.

MAT 5303 Linear Optimization (3 units)

This course is equivalent to MATH 5801 at Carleton University.

MAT 5304 Nonlinear Optimization (3 units)

This course is equivalent to MATH 5803 at Carleton University.

MAT 5307 Topics in Operations Research (3 units)

This course is equivalent to MATH 5804 at Carleton University.

MAT 5308 Topics in Algorithm Design (3 units)

This course is equivalent to MATH 5805 at Carleton University.

MAT 5309 Harmonic Analysis on Groups (3 units)

This course is equivalent to MATH 6002 at Carleton University.

MAT 5312 Topics in Topology (3 units)

This course is equivalent to MATH 6201 at Carleton University.

MAT 5313 Topics in Probability and Statistics (3 units)

This course is equivalent to MATH 6507 at Carleton University.

MAT 5314 Topics in Probability and Statistics (3 units)

This course is equivalent to STAT 6508 at Carleton University.

MAT 5315 Advanced Design of Surveys (3 units)

MAT 5317 Analysis of Categorical Data (3 units)

Analysis of one-way and two-way tables of nominal date; multi-dimensional contingency tables, log-linear models; tests of symmetry, marginal homogeneity in square tables; incomplete tables; tables with ordered categories; fixed margins, logistic models with binary response; measures of association and agreement; biological applications. This course is equivalent to STAT 5602 at Carleton University.

MAT 5318 Reliability and Survival Analysis (3 units)

This course is equivalent to STAT 5603 at Carleton University.

MAT 5319 Topics in Probability and Statistics (3 units)

MAT 5324 Game Theory (3 units)

This course is equivalent to MATH 5607 at Carleton University.

MAT 5325 Topics in Information and Systems Science (3 units)

This course is equivalent to MATH 5802 at Carleton University.

MAT 5326 Topics in Analysis (3 units)

This course is equivalent to MATH 6008 at Carleton University.

MAT 5327 Topics in Algebra (3 units)

This course is equivalent to MATH 6101 at Carleton University.

MAT 5328 Topics in Analysis (3 units)

MAT 5329 Topics in Analysis (3 units)

This course is equivalent to MATH 6009 at Carleton University.

MAT 5330 Topics in Algebra (3 units)

This course is equivalent to MATH 6102 at Carleton University.

MAT 5331 Topics in Algebra (3 units)

This course is equivalent to MATH 6103 at Carleton University.

MAT 5341 Quantum Computing (3 units)

Space of quantum bits; entanglement. Observables in quantum mechanics. Density matrix and Schmidt decomposition. Quantum cryptography. Classical and quantum logic gates. Quantum Fourier transform. Shor's quantum algorithm for factorization of integers. This course is equivalent to MATH 5821 at Carleton University.

MAT 5343 Mathematical Aspects of Wavelets and Digital Signal Processing (3 units)

Lossless compression methods. Discrete Fourier transform and Fourier-based compression methods. JPEG and MPEG. Wavelet analysis. Digital filters and discrete wavelet transform. Daubechies wavelets. Wavelet compression. This course is equivalent to MATH 5822 at Carleton University.

Prerequisites: Linear algebra and Fourier series

MAT 5361 Topics in Mathematical Logic (3 units)

This course is equivalent to MATH 6806 at Carleton University.

MAT 5375 Introduction to Mathematical Statistics (3 units)

Limit theorems; sampling distributions; parametric estimation; concepts of sufficiency and efficiency; Neyman-Pearson paradigm, likelihood ratio tests; parametric and non-parametric methods for two-sample comparisons; notions of experimental design, categorical data analysis, the general linear model, decision theory and Bayesian inference. This course is essential for students in applied statistics. This course is equivalent to STAT 5610 at Carleton University.

The courses MAT 5190 , MAT 5375 cannot be combined for credits.

MAT 5505 Mathématiques discrètes appliquées I : Théorie des graphes (3 crédits)

Chemins et cycles, arbres, connexité, parcours eulériens et cycles hamiltoniens, coloration des arêtes, ensembles indépendants et cliques, coloration des sommets, graphes planaires, graphes orientés. Sujets choisis parmi les thèmes suivants : théorie algébrique des graphes, théorie topologique des graphes, graphes aléatoires. Ce cours est équivalent à MATH 5818 à la Carleton University.

Volet : Cours magistral

MAT 5506 Optimisation combinatoire (3 crédits)

Théorie des flots et thèmes voisins. On traitera parmi d'autres les sujets suivants : chemins minimaux, arbres générateurs de coût minimal, flots de coût maximal, flots de coût minimal. Couplage optimal dans les graphes bipartis. Ce cours est équivalent à MATH 5808 à la Carleton University.

MAT 5507 Mathématiques discrètes appliquées II : Énumération combinatoire (3 crédits)

Fonctions génératrices ordinaires et exponentielles; formules de produit; permutations; partitions; arborescences; indice de cycle; méthode WZ. Inversion de Lagrange; analyse des singularités des fonctions génératrices et leur comportement asymptotique. Sujets choisis parmi les thèmes suivants : graphes aléatoires, structures combinatoires aléatoires, fonctions hypergéométriques. Ce cours est équivalent à MATH 5819 à la Carleton University.

MAT 5521 Introduction aux espaces hilbertiens (3 crédits)

Ce cours est équivalent à MATH 5009 à la Carleton University.

MAT 5522 Algèbres de banach (3 crédits)

Ce cours est équivalent à MATH 5003 à la Carleton University.

MAT 5525 Analyse réelle I (3 crédits)

Mesure et intégration, mesure de Lebesgue et intégration sur R, théorème de Fubini, théorème de Lebesgue-Radon-Nikodym, continuité absolue et dérivation, espaces Lp. Chapitres choisis comme par exemple la théorie de Stone-Daniell. Ce cours est équivalent à MATH 5007 à la Carleton University.

Préalables : MAT 3525 (MATH 3001 and MATH 3002).

MAT 5526 Analyse réelle II (3 crédits)

Espaces de Banach et de Hilbert, opérateurs linéaires bornés, espaces duals. Chapitres choisis parmi les suivants : topologies faibles, théorème d'Alaoglu, opérateurs compacts, calcul différentiel dans les espaces de Banach, théorèmes de représentation de Riesz. Ce cours est équivalent à MATH 5008 à la Carleton University.

Prerequisite for MAT 5526

MAT 5527 Analyse complexe (3 crédits)

Ce cours est équivalent à MATH 5005 à la Carleton University.

MAT 5531 Équations différentielles ordinaires I (3 crédits)

Ce cours est équivalent à MATH 5405 à la Carleton University.

MAT 5533 Équations aux dérivées partielles I (3 crédits)

Ce cours est équivalent à MATH 5406 à la Carleton University.

Prerequisite: An intermediate level course on Ordinary Differential Equations such as MAT 3130 Dynamical Systems or equivalent, or the permission of the School or Department.

MAT 5534 Équations différentielles : Chapitres choisis (3 crédits)

Ce cours est équivalent à MATH 5407 à la Carleton University.

MAT 5541 Algèbre I: Anneaux et modules (3 crédits)

Modules et anneaux noethériens et artiniens. Ensembles algébriques, leurs idéaux, théorème de base de Hilbert, idéaux radicaux, Hilbert Nullstellensatz. Localisation des anneaux et des modules. Produit tensoriel des modules et des algèbres. Anneaux et modules semi-simples, le lemme de Schur, le théorème de densité de Jacobson, le théorème d'Artin-Wedderburn. Suites exactes courtes, modules libres, modules projectifs, modules injectifs, modules plats. Ce cours est équivalent à MATH 5107 à la Carleton University.

MAT 5542 Algèbre II: Groupes et la théorie de Galois (3 crédits)

Actions de groupes, formule des classes, théorèmes de Sylow, séries centrales, de composition et dérivées, théorème de Jordan-Holder, extensions de corps et polynômes minimaux, fermeture algébrique, extensions séparables, intégralité, groupes de Galois, théorème fondamental de la théorie de Galois, corps finis, extensions cyclotomiques, théorème fondamental de l'algèbre, extensions transcendantes. Ce cours est équivalent à MATH 5109 à la Carleton University.

MAT 5543 Algèbre de lie (3 crédits)

Ce cours est équivalent à MATH 5104 à la Carleton University.

MAT 5544 Algèbre commutative (3 crédits)

Spectre premier d'un anneau commutatif (comme espace topologique); localisation des anneaux et des modules; produit tensoriel des modules et algèbres; théorème des zéros de Hilbert et conséquences pour les algèbres de type fini sur un corps; dimension de Krull d'un anneau; dépendance intégrale, théorèmes de « going-up » et « going-down »; lemme de normalisation de Noether et théorie de la dimension dans les algèbres de type fini sur un corps; anneaux noethériens et théorème « de la base » de Hilbert; introduction aux variétés algébriques affines et à leurs morphismes.

MAT 5545 Théorie des groupes (3 crédits)

Ce cours est équivalent à MATH 5106 à la Carleton University.

MAT 5546 Anneaux et modules (3 crédits)

Ce cours est équivalent à MATH 5103 à la Carleton University.

MAT 5547 Algèbre homologique et théorie des catégories (3 crédits)

Ce cours est équivalent à MATH 5108 à la Carleton University.

MAT 5548 Représentation de groupes et applications (3 crédits)

MAT 5549 Géométrie algébrique (3 crédits)

Quelques notions d'algèbre commutative, théorème des zéros de Hilbert, ensembles algébriques, topologie de Zariski. Variétés affines et projectives sur un corps algébriquement clos. Fonctions régulières et applications rationnelles. Sujets choisis parmi : la relation entre les variétés algébriques complexes et les variétés analytiques complexes; genres; diviseurs; fibrés en droites; Théorèmes de Riemann-Roch et de Bézout.

Prerequisite: MAT 3143

MAT 5551 Topologie I (3 crédits)

Espaces topologiques; topologie produit et topologie quotient; axiomes de dénombrabilité et axiomes de séparation; espaces compacts, connexes; homotopie, groupe fondamental; convergence des filtres et des suites généralisées. Ce cours est équivalent à MATH 5205 à la Carleton University.

Prerequisite: MAT 3153 (MATH 3001).

MAT 5552 Topologie II (3 crédits)

Revêtements, homologie (axiomes d'Eilenberg-Steenrod), applications, construction d'une théorie de l'homologie. Ce cours est équivalent à MATH 5206 à la Carleton University.

MAT 5555 Variétés différentielles (3 crédits)

Ce cours est équivalent à MATH 5208 à la Carleton University.

MAT 5558 Groupes de Lie I (3 crédits)

Ce cours est équivalent à MATH 6104 à la Carleton University.

MAT 5565 Théorie des automates I (3 crédits)

Ce cours est équivalent à MATH 5605 à la Carleton University.

MAT 5567 Langages formels et analyse syntactique (3 crédits)

Ce cours est équivalent à MATH/COMP 5807 à la Carleton University.

MAT 5568 Homologie (3 crédits)

Ce cours est équivalent à MATH 5202 à la Carleton University.

MAT 5570 Théorie des probabilités I (3 crédits)

Espaces probabilisés, variables aléatoires, l'espérance mathématique définie comme une intégrale, lois conjointes, indépendance et mesure produit, répartitions et extensions de mesures de probabilité, lemmes de Borel-Cantelli, notions de convergence, suites de variables aléatoires indépendantes et équidistribuées. Ce cours est équivalent à STAT 5708 à la Carleton University.

Prerequisites: MAT 3125 and MAT 3172 (MATH 3001, MATH 3002 and MATH 3500).

MAT 5571 Théorie des probabilités II (3 crédits)

Lois des grands nombres, fonctions caractéristiques, théorème-limite central, probabilité et espérance conditionnelles, propriétés élémentaires et théorèmes de convergence des martingales, introduction au mouvement brownien. Ce cours est équivalent à MATH 5709 à la Carleton University.

Prerequisite: MAT 5170 (STAT 5708).

MAT 5572 Processus stochastique : Chapitres choisis (3 crédits)

Ce cours est équivalent à STAT 5508 à la Carleton University.

MAT 5576 Inférence statistique (3 crédits)

Tests de signification pure; tests uniformément les plus puissants sans biais et sans variance; comparaison asymptotique des tests; intervalles de confiance; théorie des grands échantillons et tests du carré chi; inférence de la vraisemblance; inférence de Bayes; inférence empirique de Bayes; induction fiduciaire et structurale; méthodes de répétition de l'échantillonnage. Ce cours est équivalent à STAT 5507 à la Carleton University.

Préalables : MAT 4170 ou l'équivalent, et MAT 5191 .

MAT 5577 Analyse multivariée normale (3 crédits)

Ce cours est équivalent à STAT 5500 à la Carleton University.

MAT 5580 Analyse numérique I pour les équations différentielles (3 crédits)

Arithmétique des nombres à virgule flottante; solution numérique des équations différentielles ordinaires; méthode des différences finies pour les équations aux dérivées partielles; stabilité, consistance et convergence : analyse de von Neumann, condition de Courant-Friedrichs-Lewy, théorème de Lax; méthode des éléments finis : problèmes aux limites et équations aux dérivées partielles elliptiques; méthodes Spectrale et Pseudo-Spectrale.

MAT 5590 Statistique mathématiques I (3 crédits)

Théorie de la décision statistique; fonctions de vraisemblance; suffisance; théorème de factorisation; familles exponentielles; Estimateurs UMVU; Fonction d'information de Fisher; Limite inférieure de Cramer-Rao; maximum de vraisemblance et estimation du moment; estimation ponctuelle invariante et robuste; propriétés asymptotiques; Estimation ponctuelle bayésienne. Ce cours est équivalent au cours STAT 5600 à l’Université Carleton.

Préalables : MAT 3172 , MAT 3375 . Les cours MAT 5775 , MAT 5190 ne peuvent être combinés pour l'obtention de crédits.

MAT 5591 Statistique mathématiques II (3 crédits)

Intervalles de confiance et pivots; Intervalles bayésiens; tests optimaux et théorie de Neyman-Pearson; tests de vraisemblance et de Rao score; tests de signification; tests d'adéquation; théorie basée sur de grands échantillons et applications au maximum de vraisemblance et estimation robuste. Ce cours est équivalent à STAT 5501 à la Carleton University.

Préalable : MAT 5590 .

MAT 5593 Modèles linéaires (3 crédits)

Théorie des modèles linéaires des rangs non-exhaustifs : fonctions estimables, meilleurs estimateurs linéaires sans biais, vérification des hypothèses, régions de confiance; classification multidimensionnelle; analyse de la covariance; modèles de composantes de variance; méthode du maximum de vraisemblance; méthode MINQUE, ANOVA; sujets divers. Ce cours est équivalent à STAT 5503 à la Carleton University.

Prerequisite for MAT 5593

MAT 5595 Plan d'expériences (3 crédits)

Aperçu de la théorie du modèle linéaire; orthogonalité; blocs complets avec randomisation totale, plans split plot; plans de carré latin; théorie du caractère aléatoire; plans de blocs incomplets; expériences factorielles; la théorie de la randomisation; les effets confondus et la replication fractionelle; méthodologie de la surface de réponse; sujets divers.

MAT 5596 Analyse multivariée (3 crédits)

Cours visant à donner à l'étudiant la possibilité d'entreprendre de la recherche mathématique dans le contexte d'un projet en collaboration avec un organisme parrain des secteurs public ou privé. Inclut des séminaires sur des sujets pertinents au projet de l'étudiant. Note finale de S (satisfaisant) ou NS (non satisfaisant) décidée par le professeur responsable du cours en consultation avec le superviseur du stage, fondée sur le contenu mathématique et sur la présentation orale et écrite des résultats. Ce cours est équivalent à STAT 5509 à la Carleton University.

Préalable : Permission de l'Institut.

MAT 5597 Optimisation stochastique (3 crédits)

Ce cours est équivalent à STAT 5601 à la Carleton University.

MAT 5598 Modèles stochastiques (3 crédits)

Ce cours est équivalent à MATH 5701 à la Carleton University.

MAT 5709 Analyse harmonique sur les groupes (3 crédits)

Ce cours est équivalent à MATH 6002 à la Carleton University.

MAT 5712 Topologie : Chapitres choisis (3 crédits)

Ce cours est équivalent à MATH 6201 à la Carleton University.

MAT 5713 Topics in Probability and Statistics (3 crédits)

Ce cours est équivalent à MATH 6507 à la Carleton University.

MAT 5714 Théories problèmes et statistique (3 crédits)

Ce cours est équivalent à MATH 6508 à la Carleton University.

MAT 5715 Planification des sondages (3 crédits)

MAT 5726 Analyse : Chapitres choisis (3 crédits)

Ce cours est équivalent à MATH 6008 à la Carleton University.

MAT 5727 Algèbre - chapitres choisis : Introduction à la géométrie algébrique (3 crédits)

Ce cours est équivalent à MATH 6101 à la Carleton University.

MAT 5728 Analyse : Chapitres choisis (3 crédits)

MAT 5729 Analyse : Chapitres choisis (3 crédits)

Ce cours est équivalent à MATH 6009 à la Carleton University.

MAT 5730 Analyse : Chapitres choisis (3 crédits)

Ce cours est équivalent à MATH 6102 à la Carleton University.

MAT 5731 Analyse : Chapitres choisis (3 crédits)

Ce cours est équivalent à MATH 6103 à la Carleton University.

MAT 5761 Logique mathématique : Chapitres choisis (3 crédits)

Ce cours est équivalent à MATH 6806 à la Carleton University.

MAT 5775 Introduction à la statistique mathématique (3 crédits)

L'inférence statistique; distributions des statistiques classiques et les théorèmes central limites qui s'y rapportent; estimation paramétrique; statistique suffisante; estimateur efficace; paradigme Neyman-Pearson, tests de rapport de vraisemblance; méthodes paramétrique et non paramétrique pour la comparaison de deux échantillons; planification des expériences, analyse des données catégoriques, modèles linéaires généralisés, théorie de la décision et inférence Baysienne. Ce cours est essentiel au étudiant(e)s en statistique appliquée. Ce cours est équivalent au cours STAT 5610 à l'Université Carleton.

Les cours MAT 5775 , MAT 5590 ne peuvent être combinés pour l'obtention de crédits.

MAT 5990 Séminaire / Seminar (3 crédits / 3 units)

Ce cours est équivalent à MATH 5900 à la Carleton University. / This course is equivalent to MATH 5900 at Carleton University.

Volet / Course Component: Cours magistral / Lecture

MAT 5990S M.Sc. Séminaire / Seminar M.A. (3 crédits / 3 units)

MAT 5990T Séminaire / Seminar (3 crédits / 3 units)

MAT 5991 Travaux dirigés / Directed Studies (3 crédits / 3 units)

Ce cours est équivalent à MATH 5901 à la Carleton University. / This course is equivalent to MATH 5901 at Carleton University.

Volet / Course Component: Recherche / Research

MAT 5992 Seminar in Biostatistics (3 crédits / 3 units)

Students work in teams on the analysis of experimental data or experimental plans. The participation of experimenters in these teams is encouraged. Student teams present their results in the seminar, and prepare a brief written report on their work.

MAT 5996 Stage de recherche / Research Internship (3 crédits / 3 units)

Cours visant à donner à l'étudiant la possibilité d'entreprendre de la recherche mathématique dans le contexte d'un projet en collaboration avec un organisme parrain des secteurs public ou privé. Inclut des séminaires sur des sujets pertinents au projet de l'étudiant. Note finale S (satisfaisant) ou NS (non satisfaisant), à décider par le professeur responsable du cours en consultation avec le superviseur du stage, fondée sur le contenu mathématique et sur la présentation orale et écrite des résultats. / Project-oriented course affording students the opportunity to undertake research in applied mathematics as a cooperative project with governmental or industrial sponsors. Project work and seminars on related topics. Grade S (Satisfactory) or NS (Not satisfactory) to be assigned based upon the mathematical content as well as upon the oral and written presentation of results, and to be determined by the professor in charge of the course in consultation with the internship supervisor.

MAT 6990 Séminaire / Seminar (3 crédits / 3 units)

Ce cours est équivalent à MATH 6900 à la Carleton University. / This course is equivalent to MATH 6900 at Carleton University.

MAT 6991 Travaux dirigés / Directed Studies (3 crédits / 3 units)

Ce cours est équivalent à MATH 6901 à la Carleton University. / This course is equivalent to MATH 6901 at Carleton University.

MAT 6997 Projet en mathématiques et statistique / Project in Mathematics and Statistics (6 crédits / 6 units)

Projet en mathématiques et statistique dirigé par un professeur approuvé par le directeur des études supérieures et donnant lieu à la rédaction d'un rapport approfondi (30-40 pages approx). Noté S (satisfaisant) ou NS (non satisfaisant) par le directeur du projet et un autre professeur nommé par le directeur des études supérieures en mathématiques et statistique. Le projet est normalement complété en une session. Ce cours est équivalent à MATH 5910 à la Carleton University. / Project in mathematics and statistics supervised by a professor approved by the director of graduate studies and leading to the writing of an in-depth report (approx. 30-40 pages). Graded S (Satisfactory) or NS (Not satisfactory) by the supervisor and by another professor appointed by the director of graduate studies in mathematics and statistics. The project will normally be completed in one session. This course is equivalent to MATH 5910 at Carleton University.

MAT 9900 Examen de synthèse: Analyse réelle I / Comprehensive Exam: Real Analysis 1

Cet examen porte sur le contenu du cours MAT 5525 . Cet examen est l'examen final du cours et est corrigé par les professeurs qui enseignent MAT 5525 et MAT 5526 dans l'année académique. Noté S (satisfaisant) ou NS (non satisfaisant). / This exam covers the content of the course MAT 5125 . This exam is the final exam of the course and is graded by the professors who teach MAT 5125 and MAT 5126 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9901 Examen de synthèse: Analyse réelle II / Comprehensive Exam: Real Analysis II

Cet examen porte sur le contenu du cours MAT 5526 . Cet examen est l'examen final du cours et est corrigé par les professeurs qui enseignent MAT 5525 et MAT 5526 dans l'année académique. Noté S (satisfaisant) ou NS (non satisfaisant). / This exam covers the content of the course MAT 5126 . This exam is the final exam of the course and is graded by the professors who teach MAT 5125 and MAT 5126 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9902 Examen de synthèse: Algèbre I / Comprehensive Exam: Algebra I

Cet examen porte sur le contenu du cours MAT 5541 . Cet examen est l'examen final du cours et est corrigé par les professeurs qui enseignent MAT 5541 et MAT 5542 dans l'année académique. Noté S (satisfaisant) ou NS (non satisfaisant). / This exam covers the content of the course MAT 5141 . This exam is the final exam of the course and is graded by the professors who teach MAT 5141 and MAT 5142 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9903 Examen de synthèse: Algèbre II / Comprehensive Exam: Algebra II

Cet examen porte sur le contenu du cours MAT 5542 . Cet examen est l'examen final de ce cours et est corrigé par les professeurs qui enseignent MAT 5541 et MAT 5542 dans l'année académique. Noté S (satisfaisant) ou NS (non satisfaisant). / This exam covers the content of the course MAT 5142 . This exam is the final exam of the course and is graded by the professors who teach MAT 5141 and MAT 5142 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9904 Examen de synthèse: Topologie I / Comprehensive Exam: Topology I

Cet examen porte sur le contenu du cours MAT 5551 . Cet examenn est l'examen final du cours et est corrigé par les professeurs qui enseignent MAT 5551 et MAT 5552 dans l'année académique. Noté S (satisfaisant) ou NS (non satisfaisant) / This exam covers the content of the course MAT 5151 . This exam is the final exam of the course and is graded by the professors who teach MAT 5151 and MAT 5152 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9905 Examen de synthèse: Topologie II / Comprehensive Exam: Topology II

Cet examen porte sur le contenu du cours MAT 5552 . Cet examen est l'examen final du cours et est corrigé par les professeurs qui enseignent MAT 5551 et MAT 5552 dans l'année académique. Noté S (satisfaisant) ou NS (non satisfaisant). / This exam covers the content of the course MAT 5152 . This exam is the final exam of the course and is graded by the professors who teach MAT 5151 and MAT 5152 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9906 Examen de synthèse: Équations différentielles I / Comprehensive Exam: Differential Equations I

Cet examen porte sur le contenu du cours MAT 5531 . Cet examen est l'examen final du cours et est corrigé par les professeurs qui enseignent MAT 5531 et MAT 5533 dans l'année académique. Noté S (satisfaisant) ou NS (non satisfaisant). / This exam covers the content of the course MAT 5131 . This exam is the final exam of the course and is graded by the professors who teach MAT 5131 and MAT 5133 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9907 Examen de synthèse: Équations différentielles II / Comprehensive Exam: Differential Equations II

Cet examen porte sur le contenu du cours MAT5533. Cet examen est l'examen final du cours et est corrigé par les professeurs qui enseignent MAT 5531 et MAT 5533 dans l'année académique. Noté S (satisfaisant) ou NS (non satisfaisant). / This exam covers the content of the course MAT 5133 . This exam is the final exam of the course and is graded by the professors who teach MAT 5131 and MAT 5133 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9908 Examen de synthèse: Mathématiques discrètes I / Comprehensive Exam: Discrete Mathematics I

Cet examen porte sur le contenuu du cours MAT5505. Cet examen est l'examen final sur cours et est corrigé par les professeurs qui enseignent MAT 5505 et MAT5507 dans l'année acedémique. Noté S (satisfaisant) ou NS (non satisfaisant). / This exam covers the content of the course MAT 5105 . This exam is the final exam of the course and is graded by the professors who teach MAT 5105 and MAT 5107 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9909 Examen de synthèse: Mathématiques discrètes II / Comprehensive Exam: Discrete Mathematics II

Cet examen porte sur le contenu du cours MAT5507. Cet examen est l'examen final du cours et est corrigé par les professeurs qui enseignent MAT5505 et MAT5507 dans l'année académique. Noté S (Satisfaisant) et NS (non satisfaisant). / This exam covers the content of the course MAT 5107 . This exam is the final exam of the course and is graded by the professors who teach MAT 5105 and MAT 5107 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9910 Examen de synthèse: Théories des probabilités I / Comprehensive Exam: Probability Theory I

Cet examen porte sur le contenu du cours MAT5570. Cet examen est l'examen final du cours et est corrigé par les professeurs qui enseignent MAT 5570 et MAT5571 dans l'année académique. Noté S (satisfaiant) et NS (non satisfaisant). / This exam covers the content of the course MAT 5170 . This exam is the final exam of the course and is graded by the professors who teach MAT 5170 and MAT 5171 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9911 Examen de synthèse: Théories des probabilités II / Comprehensive Exam: Probability Theory II

Cet examen porte sur le contenu du sours MAT5571. Cet examen est l'examen final du cours et est corrigé par les professeurs qui enseignent MAT5570 et MAT5571 dans l'année académique. Noté S (satisfansant) ou NS (non satisfaisant). / This exam covers the content of the course MAT 5171 . This exam is the final exam of the course and is graded by the professors who teach MAT 5170 and MAT 5171 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9912 Examen de synthèse: Statistique mathématiques I / Comprehensive Exam: Mathematical Statistics I

cet examen porte sur le contenu du cours MAT5590. Cet examen est l'examen final du cours et est corrigé par les professerus qui enseignent MAT5590 et MAT5591 dans l'année académique. Noté S (satisfaisant) ou NS (non satisfaisant).. / This exam covers the content of the course MAT 5190 . This exam is the final exam of the course and is graded by the professors who teach MAT 5190 and MAT 5191 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9913 Examen de synthèse: Statistique et mathématiques II / Comprehensive Exam: Mathematical Statistics II

Cet examen porte sur le contenu du cours MAT5591. Cet examen est l'examen final du cours et est corrigé par les professeurs qui enseignent MAT5590 et MAT5591 dans l'année académique. Noté S (satisfaisant) ou NS (non satisfaisant). / This exam covers the content of the course MAT 5191 . This exam is the final exam of the course and is graded by the professors who teach MAT 5190 and MAT 5191 in the academic year. Graded S (satisfactory) or NS (not satisfactory).

MAT 9998 Examen de synthèse avancé / Advanced Comprehensive Examination

Le syllabus pour l'examen de synthèse avancé est déterminé par le comité consultatif de thèse (CCT). Le syllabus devrait être fournni à l'étudiant au moins six mois avant la date de l'examen. Le syllabus doit contenir la forme, le contenu et les attentes pour l'examen de synthèse avancé. L'examen de synthèse avancé peut être écrit ou/et oral. Noté S (satisfaisant) ou NS (non satisfaisant). / The syllabus of the advanced comprehensive examination is prescribe by the thesis advisory committee (TAC). The syllabus should be given to the student at least six months before the date of the examination. The syllabus must provide the form, contents and expectations for the advanced comprehensive examination. The advanced comprehensive examination can be written and/or oral. Graded S (satisfactory) or NS (non satisfactory).

Undergraduate Studies

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• Department of Mathematics

Graduate Studies

• Mathematics, PhD

Doctor of Philosophy in Mathematics (PhD)

Requirements outline.

The Ph.D. degree is a research degree and the principal requirement is that a student writes an original research thesis. The thesis is produced under the supervision of a faculty member and is examined by a committee of three departmental faculty and an outside expert. To qualify to write a thesis, a candidate for a Ph.D. in mathematics first must pass three Preliminary Examinations. It is recommended that Ph.D. candidates discuss possible research opportunities with the Director of Graduate Studies and/or faculty members soon after they enter the Ph.D. Program. Entering students should outline an appropriate sequence of courses to learn the essential material for pursuing their research interests. After a student has passed the Preliminary Examinations they must choose an advisor from the Mathematics Department faculty. A candidate's thesis usually is developed and written with the guidance of this advisor who will later chair the thesis defense committee. The time required to obtain a Ph.D. degree varies a lot. The department does not support graduate students as Teaching Assistants for more than five academic years.

Ph.D. Degree Requirements

The requirements that must be satisfied for a candidate to receive a Ph.D. include:

• The candidate must pass Preliminary Examinations .
• The candidate must obtain a grade of B or better in at least 24 semester credit hours of courses in the Mathematics Ph.D. program. Students should take doctoral research classes MATH 8x98 (where “x” is the number of credit hours) while conducting thesis research. Students must register for. the course MATH 8x99 “Doctoral Dissertation” in the semester when they intend to graduate
• After passing all three Preliminary Examinations the candidate is subject to Annual Performance Review (APR). The APR evaluates research progress of the candidate. The APR is conducted in oral or written form by a committee consisting of at least two faculty members of the Mathematics Department. The APR committee is chaired by the candidate’s advisor. Candidates failing the APR are subject to termination from the Ph.D. program.
• The candidate must be in residence, and take 9 semester credit hours of courses, in two consecutive long semesters, Fall followed by Spring. Alternatively, the candidate must be in residence and take a full load in consecutive Spring, Summer, and Fall terms.
• The candidate must write a Doctoral Dissertation with the guidance of an advisor who is a regular faculty member of the Mathematics Department.
• The candidate must defend their Dissertation in a public examination by a thesis committee consisting of at least 4 members, three of whom are faculty members in the Mathematics Department and at least one member outside UH Mathematics Department.
• NSM Thesis and Dissertation General Guidelines and Instructions
• NSM Thesis and Dissertation Formatting Instructions
• NSM Thesis and Dissertation Submission Instructions
• NSM Checklist for Thesis and Dissertation Review
• NSM Deadlines & Academic Calendar : This link provides deadlines for the submission of Dissertations.
• *The Graduate Record Examination (GRE) is waived for the Ph.D program within the Department of Mathematics.
• International students can not exclusively register for online courses.

Course Selection:

• Information about courses may be found at this link .
• Students can discuss advisor selection process with the Director of Graduate Studies.
• The above is only an outline of the primary requirements for the degree. The Director of Graduate Studies and others can provide more detailed information about conditions. The college and the university may have further requirements as listed at College and websites.
• PhD students can take topics classes at Rice University, UT Health, UTMB, or Baylor College of Medicine. Students must submit the Inter-Institutional Course Registration Form to the Graduate Director for approval. Taking an outside class must be essential for the completion of graduate degree. Thus, students must obtain a prior approval of their PhD avisor (signature on the form).
• Course Selection Requests: Please contact the Director for Instructional Support and Coordination < [email protected] > for more information.

Teaching Opportunities for Ph.D. Students:

As a condition, a student should have experiences of teaching Calculus recitation class with reasonable teaching evaluation. For an international student, by Texas law, the student must pass the English SPEAK test or its equivalence.

All PhD applicants who submit their complete application before the appropriate deadline are automatically considered for Teaching Assistantship.

Please contact the Director for Instructional Support and Coordination for more information about course selection requests .

Preliminary Examinations:

The Preliminary Examination is the final step in assessing the student’s ability and appropriate mathematical background to undertake a program of supervised research and study leading to a Ph.D. in Mathematics. Students who have completed their Master's degree in Mathematics may often be ready to take the Preliminary Examination without further course study.

Preliminary Examinations are three-hour, closed book written examinations that are given in each of the topics listed below. The questions in the examination emphasize problem solving skills and mathematical ability as opposed to rote memorization.

Preliminary Examinations are usually offered twice a year: at the end of the Fall and Spring semesters.

Students who receive support from the Department of Mathematics are expected to pass the Preliminary Examination according to the rules below. For non-supported students, the University rules apply.

All students are supposed to pass three Preliminary Examinations before the beginning of their third year in the Ph.D. program.

The following rules apply:

1. Students must pass three Preliminary Examinations from the different topic groups listed below

2. At least one out of the three Preliminary Examinations must be a core sequence. Core sequences are:

Review information for the preliminary written examinations:

Additional problems from past preliminary exams:

All preliminary exams are based on the content of the corresponding course. Please contact the instructor who taught the corresponding course most recently to obtain the up-to-date information.

Graduate Study in Logic at Berkeley

The Ph.D. Program in Philosophy . Students who choose to specialize in logic within the context of this program are expected to obtain a broad education in philosophy.

The Group in Logic and the Methodology of Science administers a program leading to the degree of Ph.D. in Logic and the Methodology of Science. The Group is not a part of the Department of Mathematics or of the Department of Philosophy; rather, it is an independent program staffed by faculty members from Mathematics and Philosophy, along with several from Electrical Engineering and Computer Science. Students who want to pursue the Ph.D. in Logic and the Methodology of Science should apply directly to the Graduate Program in Logic and the Methodology of Science, rather than to Mathematics or Philosophy.

Students in the L&M program are expected to study both mathematics and philosophy, though they need not meet all the breadth requirements for a Ph.D. in either field. They must pass one examination in the foundations of mathematics, one examination in philosophy (Area I), and a third in either mathematics or philosophy. Although there are no graduate instructorships in Logic and Methodology of Science, students in this program may, if qualified, hold graduate student instructorships in the Department of Mathematics or in the Department of Philosophy.

The Department of Mathematics administers a program leading to a Ph.D. in Mathematics. Students in this program may specialize in the foundations of mathematics, but are also expected to study other aspects of mathematics. In particular, they must pass departmental qualifying examinations in two other areas as well as in the foundations of mathematics. The Department of Mathematics also has a program leading to an M.A. degree.

Logic Events

Logic colloquium.

The Group in Logic and the Methodology of Science sponsors a biweekly logic colloquium , with talks by mathematicians, computer scientists, and philosophers.

Working Group in the History and Philosophy of Logic, Mathematics, and Science

The Working Group in the History and Philosophy of Logic, Mathematics, and Science , jointly sponsored by the Philosophy Department and the Doreen B. Townsend Center for the Humanities , sponsors monthly talks, many of them on topics connected to logic.

Berkeley-Stanford Circle in Logic and Philosophy

The Berkeley-Stanford Circle in Logic and Philosophy brings together graduate students from UC Berkeley and Stanford University to discuss research at the intersection of Logic and Philosophy.

• Doctor of Philosophy in Mathematics (PhD)
• Graduate School
• Prospective Students
• Graduate Degree Programs

Go to programs search

Mathematicians use theoretical and computational methods to solve a wide range of problems from the most abstract to the very applied. UBC's mathematics graduate students work in many branches of pure and applied mathematics. The PhD program trains students to operate as research mathematicians. The focus of the program is on substantial mathematical research leading to the PhD dissertation. Students also develop their skills in presenting and teaching mathematics and its applications.

For specific program requirements, please refer to the departmental program website

What makes the program unique?

UBC has one of the largest and most vigorous departments of mathematics in Canada. Our faculty routinely win national and international awards for their research and teaching achievements. We have an engaged and sociable cohort of graduate students who are essential members of a broad selection of active research groups. Each group holds a variety of seminars and events that allow graduate students, postdoctoral fellows, visitors and faculty to enjoy regular interaction.

UBC is the headquarters for the Pacific Institute of Mathematical Sciences (PIMS). PIMS hosts a plethora of mathematical events such as conferences and summer schools, greatly enriching the scientific environment in the quantitative sciences at UBC. Our mathematics students are also regular participants at the nearby Banff International Research Station for Mathematical Innovation and Discovery. Finally, our Institute for Applied Mathematics provides options for interdisciplinary studies for PhD students who wish to work in applied and computational mathematics.

I was intrigued and inspired by my professors and advisors to take on the program because of the collaborative aspects with Honeywell. This real-world focus motivated many interesting questions in my research.

Nathan Lawrence

Quick Facts

Program enquiries, admission information & requirements, 1) check eligibility, minimum academic requirements.

The Faculty of Graduate and Postdoctoral Studies establishes the minimum admission requirements common to all applicants, usually a minimum overall average in the B+ range (76% at UBC). The graduate program that you are applying to may have additional requirements. Please review the specific requirements for applicants with credentials from institutions in:

• Canada or the United States
• International countries other than the United States

Each program may set higher academic minimum requirements. Please review the program website carefully to understand the program requirements. Meeting the minimum requirements does not guarantee admission as it is a competitive process.

English Language Test

Applicants from a university outside Canada in which 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 your application.

Minimum requirements for the two most common English language proficiency tests to apply to this program are listed below:

TOEFL: Test of English as a Foreign Language - internet-based

Overall score requirement : 100

IELTS: International English Language Testing System

Overall score requirement : 7.0

Other Test Scores

Some programs require additional test scores such as the Graduate Record Examination (GRE) or the Graduate Management Test (GMAT). The requirements for this program are:

The GRE is not required.

2) Meet Deadlines

3) prepare application, transcripts.

All applicants have to submit transcripts from all past post-secondary study. Document submission requirements depend on whether your institution of study is within Canada or outside of Canada.

Letters of Reference

A minimum of three references are required for application to graduate programs at UBC. References should be requested from individuals who are prepared to provide a report on your academic ability and qualifications.

Statement of Interest

Many programs require a statement of interest , sometimes called a "statement of intent", "description of research interests" or something similar.

• Supervision

Students in research-based programs usually require a faculty member to function as their thesis supervisor. Please follow the instructions provided by each program whether applicants should contact faculty members.

Instructions regarding thesis supervisor contact for Doctor of Philosophy in Mathematics (PhD)

Citizenship verification.

Permanent Residents of Canada must provide a clear photocopy of both sides of the Permanent Resident card.

4) Apply Online

All applicants must complete an online application form and pay the application fee to be considered for admission to UBC.

Tuition & Financial Support

Financial Support

Applicants to UBC have access to a variety of funding options, including merit-based (i.e. based on your academic performance) and need-based (i.e. based on your financial situation) opportunities.

Program Funding Packages

All full-time students who begin a UBC-Vancouver PhD Mathematics program in September 2018 or later will be provided with a funding package of at least $24,256 for each of the first four years of their PhD. The funding package may consist of any combination of internal or external awards, teaching-related work, research assistantships, and graduate academic assistantships.

Average Funding

• 52 students received Teaching Assistantships. Average TA funding based on 52 students was $13,784.
• 48 students received Research Assistantships. Average RA funding based on 48 students was $11,580.
• 3 students received Academic Assistantships. Average AA funding based on 3 students was $1,814.
• 54 students received internal awards. Average internal award funding based on 54 students was $13,279.
• 4 students received external awards. Average external award funding based on 4 students was $27,083.

Scholarships & awards (merit-based funding)

All applicants are encouraged to review the awards listing to identify potential opportunities to fund their graduate education. The database lists merit-based scholarships and awards and allows for filtering by various criteria, such as domestic vs. international or degree level.

Graduate Research Assistantships (GRA)

Many professors are able to provide Research Assistantships (GRA) from their research grants to support full-time graduate students studying under their supervision. The duties constitute part of the student's graduate degree requirements. A Graduate Research Assistantship is considered a form of fellowship for a period of graduate study and is therefore not covered by a collective agreement. Stipends vary widely, and are dependent on the field of study and the type of research grant from which the assistantship is being funded.

Graduate Teaching Assistantships (GTA)

Graduate programs may have Teaching Assistantships available for registered full-time graduate students. Full teaching assistantships involve 12 hours work per week in preparation, lecturing, or laboratory instruction although many graduate programs offer partial TA appointments at less than 12 hours per week. Teaching assistantship rates are set by collective bargaining between the University and the Teaching Assistants' Union .

Graduate Academic Assistantships (GAA)

Academic Assistantships are employment opportunities to perform work that is relevant to the university or to an individual faculty member, but not to support the student’s graduate research and thesis. Wages are considered regular earnings and when paid monthly, include vacation pay.

Financial aid (need-based funding)

Canadian and US applicants may qualify for governmental loans to finance their studies. Please review eligibility and types of loans .

All students may be able to access private sector or bank loans.

Foreign government scholarships

Many foreign governments provide support to their citizens in pursuing education abroad. International applicants should check the various governmental resources in their home country, such as the Department of Education, for available scholarships.

Working while studying

The possibility to pursue work to supplement income may depend on the demands the program has on students. It should be carefully weighed if work leads to prolonged program durations or whether work placements can be meaningfully embedded into a program.

International students enrolled as full-time students with a valid study permit can work on campus for unlimited hours and work off-campus for no more than 20 hours a week.

A good starting point to explore student jobs is the UBC Work Learn program or a Co-Op placement .

Tax credits and RRSP withdrawals

Students with taxable income in Canada may be able to claim federal or provincial tax credits.

Canadian residents with RRSP accounts may be able to use the Lifelong Learning Plan (LLP) which allows students to withdraw amounts from their registered retirement savings plan (RRSPs) to finance full-time training or education for themselves or their partner.

Please review Filing taxes in Canada on the student services website for more information.

Cost Estimator

Applicants have access to the cost estimator to develop a financial plan that takes into account various income sources and expenses.

Career Outcomes

88 students graduated between 2005 and 2013: 1 is in a non-salaried situation; for 19 we have no data (based on research conducted between Feb-May 2016). For the remaining 68 graduates:

Sample Employers in Higher Education

Sample employers outside higher education, sample job titles outside higher education, phd career outcome survey, career options.

A great majority of our PhD graduates move on to postdoctoral fellowships and faculty positions at universities and research institutes in North America and around the world. However, a significant fraction of students move into careers in industry. Students considering non-academic careers are encouraged to complete an industrial internship (for instance through the Mitacs Accelerate program - headquartered at UBC) during their studies.

Enrolment, Duration & Other Stats

These statistics show data for the Doctor of Philosophy in Mathematics (PhD). Data are separated for each degree program combination. You may view data for other degree options in the respective program profile.

ENROLMENT DATA

Completion Rates & Times

Upcoming doctoral exams, tuesday, 17 september 2024 - 2:00pm - room 203.

• Research Supervisors

Advice and insights from UBC Faculty on reaching out to supervisors

These videos contain some general advice from faculty across UBC on finding and reaching out to a supervisor. They are not program specific.

This list shows faculty members with full supervisory privileges who are affiliated with this program. It is not a comprehensive list of all potential supervisors as faculty from other programs or faculty members without full supervisory privileges can request approvals to supervise graduate students in this program.

• Adem, Alejandro (Cohomology of finite groups, orbifolds, stringy topology, algebra, sporadic simple group, group actions, arithmetic groups, K-theory, homotopy theory, spaces of homomorphisms)
• Alacaoglu, Ahmet
• Angel, Omer (Probability theory, percolation, random graphs, random walks, particle processes, scaling limits)
• Bachmann, Sven (Mathematics and statistics; Mathematical Analysis; quantum phenomena; Mathematical physics; Quantum statistical physics; Topological states of matter)
• Balmforth, Neil (Fluid mechanics, nonlinear dynamics and applied partial differential equations)
• Behrend, Kai (Moduli spaces, Gromov-Witten invariants, string theory, Donaldson-Thomas invariants, Euler characteristics, categorification)
• Bennett, Michael (Number Theory, Diophantine Approximation and Classical Analysis)
• Bryan, Jim (Algebraic and differential geometry; Algebraic geometry, moduli spaces, enumerative invariants related to theoretical physics.)
• Cautis, Sabin (Mathematics and statistics; Geometry)
• Chau, Albert (Differential Geometry and Partial Differential Equations)
• Chen, Jingyi (Algebraic and differential geometry; Differential Geometry, Partial Differential Equations)
• Colliander, James (hamiltonian dynamical systems; partial differential equations; harmonic analysis)
• Coombs, Daniel (Mathematical biology; Cellular immunology; Complex physical systems; Epidemiology (except nutritional and veterinary epidemiology); Cell Signaling and Infectious and Immune Diseases; Cell biophysics; Disease models; Epidemiology; Immune cell signalling; Mathematics)
• Cytrynbaum, Eric (Bacterial cell division, Microtubule and cellular organization, Wave propagation in excitable media)
• Dao Duc, Khanh (Genomics; Mathematical biology; Neurocognitive patterns and neural networks; Agricultural spatial analysis and modelling; combine mathematical,computational and statistical tools to study fundamental biological processes; regulation and determinants of gene expression and translation; Machine Learning for Biological Imaging and Microscopy; Database development and management; Biological and Artificial Neural Networks for geometric representation)
• Doebeli, Michael Walter (Mathematical ecology and evolution, evolution of diversity, adaptive speciation, evolution of cooperation, game theory, experimental evolution in microorganisms)
• Feng, James (Chemical engineering; Mathematics and statistics; Biophysics; Complex fluids; Fluid mechanics; Mathematical biology)
• Fraser, Ailana (Differential Geometry, Geometric Analysis)
• Friedlander, Michael (numerical optimization, numerical linear algebra, scientific computing, Scientific computing)
• Frigaard, Ian (Fluid mechanics (visco-plastic fluids))
• Ghioca, Dragos (Drinfeld modules, isotrivial semiabelian varieties, Lehmer inequality)
• Gordon, Julia Yulia (Representation theory of p-adic groups and motivic integration; Trace Formula and its applications)
• Gustafson, Stephen James (Mathematics and statistics; Mathematical Analysis; Differential Equation; Global and Non-Linear Analysis; Mathematical physics; Nonlinear partial differential equations; Nonlinear waves; Topological solitons)
• Hauert, Christoph (Mathematics and statistics; Modelization and Simulation; Evolution and Phylogenesis; Biological Behavior; dynamical systems; evolution; game theory; social dilemmas; stochastic processes)
• Hermon, Jonathan (probability theory; Markov chains and the cutoff phenomenon; particle systems; percolation)

Doctoral Citations

Sample Thesis Submissions

• Set-restricted isometry for sub-Gaussian matrices and inversion of deep generative models
• On problems of regularity and existence for critical drift elliptic equations and Navier-Stokes equations
• Symmetry-breaking bifurcations in compartmental-reaction diffusion systems with comparable diffusivities
• The polynomial method over finite rings and fields
• Global well-posedness and localized patterns of several reaction-diffusion systems involving advection
• Topics in arithmetic combinatorics
• Free boundary minimal submanifolds in geodesic balls of simply connected space forms
• On a completion of cohomological functors generalizing Tate cohomology
• Distribution of integral points on varieties
• Effective and explicit S-unit equations with many terms
• Classifying space for commutativity and unordered flag manifolds
• Finite-size scaling of a few statistical physics models in high dimensions
• Residual supersingular Iwasawa theory and μ-invariants for Zₚ²-extensions
• Numerical methods for biological flows laden with deformable capsules and solid particles
• The construction of blow-up solutions for some evolution equations

Related Programs

Same specialization.

• Master of Science in Mathematics (MSc)

At the UBC Okanagan Campus

Further information, specialization.

Mathematicians use theoretical and computational methods to solve a wide range of problems from the most abstract to the very applied. UBC's mathematics graduate students work in many branches of pure and applied mathematics.

UBC Calendar

Program website, faculty overview, academic unit, program identifier, classification, social media channels, supervisor search.

Departments/Programs may update graduate degree program details through the Faculty & Staff portal. To update contact details for application inquiries, please use this form .

Pardis Semnani

When I was admitted to the department of mathematics by my advisor and learned about her area of research, algebraic statistics, I found it intriguing that her problems of interest build a bridge between pure and applied mathematics. That is why I decided to work under her supervision and study at...

Nicholas Richardson

Having grown up outside of Toronto and completed my undergrad and master's degree at the University of Waterloo, I was ready to change the scenery and go study somewhere else. I joke that is it the farthest I could move without leaving Canada, but more truthfully it was the campus that felt "right...

Gabriel Currier

I quite like the kind of math that people do here, and enjoy working with my supervisors. The campus is also a beautiful place and the graduate student community is pretty laid back and friendly.

Curious about life in Vancouver?

Find out how Vancouver enhances your graduate student experience—from the beautiful mountains and city landscapes, to the arts and culture scene, we have it all. Study-life balance at its best!

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Doctor of Philosophy (DPhil)

What is a dphil.

A DPhil is Oxford's name for a PhD - a higher research degree which allows you to make an original contribution to mathematics in the form of a thesis. A DPhil takes three to four years to complete. During your DPhil, you will be supervised by at least one academic, although some students will have more than one supervisor (particularly if they are working across disciplines). Unlike CDT courses (and PhDs in other countries), you will begin to do research straight away and there is no prescribed taught component. 

As part of your study toward a DPhil in Mathematics at Oxford, you will also be required to complete broadening and skills training and deliver class teaching to undergraduates, to enhance your broader mathematical knowledge and develop your career. You are very welcome to attend seminars and there may also be journal clubs or seminar series specific to your area of study. 

If you enjoy doing mathematics, and would like to be part of a lively and world-class research institute, take a look at our research groups to see if they align with your own interests. 

How to apply

All applications should be submitted online through the University's Graduate Application Form . Before you apply, check that you can meet the entry requirements , and read the   University of Oxford's graduate application guide .

Key Deadlines

Application deadlines for the DPhil in Mathematics:

• 8th January 2025
• 4th March 2025

Please apply by the 8th January deadline to be considered for available University-administered or Departmental scholarships. 

Martingale Foundation Postgraduate Scholarships

The Martingale Foundation awards fully funded Scholarships for postgraduate degrees in the mathematical sciences at research universities in the UK. 

Tuition fees and research expenses are fully covered, and Scholars receive a tax free living wage stipend. Martingale Scholars also receive access to leadership and career develop through a multi-year programme of training and support. Visit the Martingale website for more information.  

Applications for the 2025 academic year are open until 27 October 2024.  

Why do a PhD?

Research interests:  group theory, representation theory and algebraic aspects of geometry.

Who's who in Algebra

Find out more about the group

Combinatorics

Research interests: extremal combinatorics, graph theory, and combinatorial number theory.

Who's who in Combinatorics

Functional Analysis

Research interests: operator theory, including unbounded operators, and abstract differential equations.

Who's who in functional analysis

Research interests: algebraic geometry,  geometric representation theory , and differential geometry.

Who's who in Geometry

History of Mathematics

Research interests: history of algebra (19th and 20th century), history of modern algebra, and Soviet mathematics. 

Research interests: analytic topology,  geometric stability theory, and the model theory of p-adic fields and diophantine geometry.

Who's who in Logic

Machine Learning and Data Science

Machine Learning and Data science are being developed using wide ranging mathematical techniques. Our particular research expertise include: applied and computational harmonic analysis, networks, optimisation, random matrix theory, rough paths, topological data analysis, and the application of these methods.

Who's who in machine learning and data science

Mathematical & Computational Finance

Research interests: behavioural finance, financial big data, high dimensional numerical methods, stochastic analysis.

Who's who in Mathematical and Computational Finance

Mathematical Biology

Research interests:  cancer modelling, collective behaviour, gene regulatory networks, multiscale modelling, pattern formation, and sperm dynamics.

Who's who in Mathematical Biology

Mathematical Physics

Research interests: gauge and gravity theories (quantum field theories), string theory, twistor theory, Calabi-Yau manifolds, quantum computation and cryptography.

Who's who in Mathematical Physics

Number Theory

Research interests: analytic number theory, arithmetic geometry, prime number distribution, and Diophantine geometry.

Who's who in Number Theory

Numerical Analysis

Research interests: complexity in optimisation, symmetric cone programming, numerical solutions of PDEs. 

Who's who in Numerical Analysis

Oxford Centre for Industrial and Applied Mathematics

Research interests: energy, industry, geoscience, networks, finance, methodologies.

Who's who in OCIAM

Oxford Centre for Nonlinear Partial Differential Equations

Research interests: geometric analysis, inverse problems, nonlinear hyperbolic systems, specific PDE systems.

Who's who in OxPDE

Stochastic Analysis

Research interests:  rough path theory, Schramm-Loewner evolution, mathematical population genetics, financial mathematics, self-interacting random processes.

Research interests: geometric group theory, 3-manifold topology and knot theory, K-theory, algebraic topology.

Who's who in Topology

Doctor of Philosophy (PhD) Degree in the field of Mathematics

Program learning outcomes for the ma and phd degrees in the field of mathematics.

Upon completing the MA and PhD degrees in the field of Mathematics, students will be able to:

• Apply abstract structures from algebra, analysis, and topology to analyze and solve both concrete problems and conceptual questions.
• Learn fundamental mathematics independently, outside the structure of a regular course.
• Present mathematical results and reasoning in a compelling way to an audience of mathematicians.
• Use the mathematical literature and databases to find theorems, constructions, or counterexamples.
• Write clear and convincing proofs of one's own original mathematical results.

Requirements for the MA and PhD Degrees in the field of Mathematics

Students may not be admitted directly to the Master of Arts degree program in mathematics. Instead, graduate students in the Doctor of Philosophy degree program in the field of mathematics may earn the MA as they work towards the PhD in the field of mathematics. Admission to the PhD program in the field of mathematics is granted to a limited number of students who have illustrated an ability for advanced and original work. Normally, students take one or two years after the BA degree to obtain an MA degree, and they take four or five years to obtain a PhD. An MA is not a prerequisite for the PhD. For additional requirements, regulations, and procedures for all graduate programs, please see  All Graduate Students . 

A number of graduate scholarships and fellowships are available, awarded on the basis of merit. As part of the graduate education in mathematics, students also engage in teaching or other instructional duties, generally for no more than six hours a week.

For courses carrying dual undergraduate and graduate numbers, (e.g., MATH 463 / MATH 563 ), the 500-level version is intended to prepare students for advanced work in mathematics. In particular, written assignments should be prepared to high professional standards. Mathematics graduate students should enroll in the 500-level version.

MA Degree Program

The MA degree can be either a thesis or a non-thesis master's degree depending on the option the student pursues. For general university requirements for thesis master's degrees, please see  Thesis Master’s Degrees . For general university requirements for non-thesis master's degrees, please see  Non-Thesis Master’s Degrees . For additional requirements, regulations, and procedures for all graduate programs, please see  All Graduate Students .

Doctoral students may petition for these once they have satisfied all university and departmental requirements.

Student pursuing the MA degree in the field of Mathematics must complete:

• Complete with a grade of B (3.00 grade points) or better a course of study approved by the department. (Students may transfer credits from another university only with the approval of both the department and the University Graduate Council.)
• Perform satisfactorily on the general examinations in algebra, analysis, and topology or prepare and present an oral defense of an original thesis acceptable to the department

The requirements listed in the General Announcements (GA) satisfy the minimum requirements for this degree program. In certain instances, courses (or requirements) not officially listed here may be substituted upon approval of the program's academic advisor or, where applicable, the department or program's Director of Graduate Studies. Course substitutions or any exceptions to the stated official curricular requirements must be approved by the Office of Graduate and Postdoctoral Studies . Students and their academic advisors should identify and clearly document the courses to be taken.

Requirements for the PhD Degree in the field of Mathematics

Phd degree program.

For general university requirements, please see  Doctoral Degrees . For additional requirements, regulations, and procedures for all graduate programs, please see  All Graduate Students . Students pursuing the PhD degree in the field of Mathematics must:

• Complete with a grade of B (3.00 grade points) or better a course of study approved by the department (students may transfer credits from another university only with the approval of both the department and the University Graduate Council)
• Perform satisfactorily on qualifying examinations (see below)
• Write an original thesis acceptable to the department
• Perform satisfactorily on a final oral examination on the thesis

Qualifying Examinations

The qualifying examinations in mathematics consist of the general examinations and the advanced oral examination.

To complete the general examinations , students must take exams, one each in algebra, analysis, and topology. Exams are offered every August, January, and May. Students may take any combination of exams at any time during their first four semesters in the program. Students must perform satisfactorily on all three exams by the May exams at the end of their fourth semester. The judgment of satisfactory performance on the general examinations for either the MA or PhD degree is the responsibility of the department graduate committee. Students may take an exam several times.

To complete the advanced oral examination , students must select a special field (e.g., homotopy theory, several complex variables, or group theory) and submit it to the department graduate committee for approval. The committee schedules an advanced examination in the selected field, normally 6 to 12 months after the student completes the general examinations. While students failing the advanced examination may, with the approval of the committee, retake it on the same or possibly on a different topic, they generally are not allowed to take the advanced examination more than twice.

Policies for the PhD Degree in the field of Mathematics

Department of mathematics graduate program handbook.

The General Announcements (GA) is the official Rice curriculum. As an additional resource for students, the department of Mathematics publishes a graduate program handbook, which can be found here:  ​ https://gradhandbooks.rice.edu/2024_25/Mathematics_Graduate_Handbook.pdf .

Transfer Credit 

For Rice University’s policy regarding transfer credit, see  Transfer Credit . Some departments and programs have additional restrictions on transfer credit. Requests for transfer credit must be approved for Rice equivalency by the appropriate academic department offering the Rice equivalent course (corresponding to the subject code of the course content) and by the Office of Graduate and Postdoctoral Studies (GPS). Students are encouraged to meet with their academic program’s advisor when considering transfer credit possibilities.

Additional Information

For additional information, please see the Mathematics website:  https://math.rice.edu/ .

Opportunities for the PhD Degree in the field of Mathematics

For additional information please see the Mathematics website:  https://math.rice.edu/ .

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Department of Philosophy

Dietrich college of humanities and social sciences, doctorate program in logic, computation and methodology.

The LCM Ph.D. is primarily intended for students interested in a career outside of Philosophy, be it academic or in industry.

The program's flexible requirements are geared towards establishing relevant domain specialization (e.g., within mathematics, machine learning, statistics, logic, etc.) while incorporating steady involvement in research and the opportunity to practice the craft of teaching in a top-notch undergraduate environment. Students are expected to complete a Master’s thesis (or obtain a master’s degree from another discipline) by the middle of their third year, and a Ph.D. thesis by the end of their fifth year.

Core (2 courses)

Core Seminar I & II are required for all students with no exceptions.

• 80600 (fall term)
• 80602 (spring term)

Formal Methods (1 course)

2 Formal Methods Minis (FMM)

• Excluding 80603 FMM: Tools & Techniques
• 80604 FMM: Computability Theory
• 80607 FMM: Topology
• 80608 FMM: Evolutionary Game Theory
• 80609 FMM: Classical Logic
• 80613 FMM: Language and Meaning
• 80616 FMM: Decisions and Games
• 80617 FMM: Causation
• 80618 FMM: Algorithmic Complexity
• 80619 FMM: Epistemic Logic and Topology

Target Field Breadth (3 courses)

• 3 graduate level courses in Mathematical Sciences, School of Computer Science, Statistics & Data Science, or the relevant technical discipline (which might include Philosophy) outside the area of specialization.

These courses must be sufficiently different from one another to provide breadth in the target field.

• One of these course requirements can be satisfied through one or more internships, subject to advisor and DGS approval.

Philosophy Breadth (1 course)

1 graduate course in Philosophy outside the area of specialization.

Specialization (3 courses)

3 graduate level courses in the area of specialization (Mathematical Sciences, School of Computer Science, Statistics & Data Science, Machine Learning, etc.)

At least 1 of these courses must be in Philosophy.

Master’s thesis

• Can be replaced by a master’s degree in another discipline

Prospectus Ph.D. Thesis

This is 10 courses in total.

• No course may be used to satisfy more than one requirement. (Exception: courses used towards a master’s degree can also be used to satisfy the “Target Field Breadth” and “Specialization” requirements.)
• All courses must be approved each year by a “topic advisor” for use in the individual categories. This is to ensure that the breadth courses are truly broad and that the target field makes sense.

The department's interdisciplinary research thrust affords an unusually broad range of career possibilities. Graduates of the program have been offered positions in Philosophy, Mathematics, Psychology, Computer Science, and Statistics, as well as research positions in industry. This wide range of interesting career opportunities reflects the department's unique dedication to serious, interdisciplinary research ties.

For a complete listing of our graduates and placement record, see our Ph.D. alumni page .

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Can I pursue philosophy while studying mathematics?

I am a math major and I currently am preparing for admissions in a masters program.

Though late, but I realised that I have interest in philosophy as well and I think I want to pursue it professionally.

I would like to pursue philosophy of mathematics.

Is a change of stream necessary/possible? How can I go about this as I get into a masters program in mathematics?

• 1 I know this may seem like an obvious question, but what can you do with a philosophy degree? I am a computer science student focusing on network security and would like to do security research professionally. I am currently also working towards a philosophy minor. I have an enormous interest in it, which is almost exclusively why I'm pursuing it, but what can I do with a philosophy masters degree? Thanks. –  Goodies Commented Feb 14, 2016 at 22:15
• Some related threads: Switching to philosophy after a PhD in mathematics academia.stackexchange.com/questions/49020/… How important is studying higher mathematics for graduate study in philosophy? philosophy.stackexchange.com/questions/31395/… Does undergraduate math major make an applicant for philosophy phd more competitive? academia.stackexchange.com/questions/61340/… –  Conifold Commented Feb 15, 2016 at 3:39
• 1 @goodies I would like to do research that's why –  Non-Being Commented Feb 15, 2016 at 5:58

5 Answers 5

I would like to add some issues, which possibly complement virmaior's answer.

Anybody who works in philosophy of mathematics should have his own experience in a broad field of mathematics. He needs an overview over different fields of mathematics. And he should have done own research, e.g., on the level of a PhD in pure mathematics.

Why not continuing with mathematics and in addition taking some courses in philosophy, in order to base a later decision on a broader experience with both disciplines, mathematics and philosophy?

I am aware of very few places where you could simultaneously pursue a masters in math and the "professional pursuit of philosophy." You would need to research programs specifically.

But most of these are not going to be targeted at the MS/MA level. Instead, what I would suggest is to do your masters in math and take a course or two in philosophy -- outside of the philosophy of math during your MA. Then apply to PhD programs for the philosophy of math (The Philosophical Gourmet -- formerly under Brian Leiter's management would be a good place to find the list of good programs).

Without a PhD, there's not much you can do professionally in philosophy. And diversifying at the MA level is not going to help you much. Instead, it will mostly hurt your chances. The key to getting into a good philosophy of math PhD would be strong math skills (demonstrated by coursework and a recommendation letter from someone on the math faculty) and competent philosophical writing (demonstrated by your writing sample).

There is an area of specialization within many mathematics programs focussed on 'Foundations', or 'Symbolic Logic', (although that latter is often 'Symbolic Logic and Combinatorics', and may lie closer to hard-core computer science than philosophy in some programs.)

If you find a relatively 'old school' advisor, courses in the history and philosophy of mathematics (and/or science) are still part of this 'Logic' concentration, and will be sometimes cross-listed with philosophy and also with computer science, as some old, deep ideas still influence 'Cognitive Science' and AI. Interdisciplinary studies at that 'triple-point' are sometimes encouraged.

Taking this path as broadly as possible does not prepare one to 'pursue philosophy professionally', just to have a more meaningful, humanistic basis behind your mathematics. At the same time, a terminal Master's in Mathematics is also not generally adequate to constitute 'pursuing mathematics professionally'. Instead, it provides a more abstract and more thoroughly grounded basis for some kind of computing, scientific, or engineering career, or for teaching those who will pursue such careers.

There is also no shame in multiple Bachelor's degrees instead of a Master's or multiple Master's degrees instead of a Doctorate. All forms of thinking reinforce one another. And given the ubiquity of education and the way jobs have changed, breadth and flexibility may trump dedication in a market where people don't work "in their field" most of the time.

And if it is a real issue, you might want to work this out at the MS level. From personal experience, I do not suggest attempting a Doctorate in math if your loyalties are in any way divided. The level of focus necessary to even 'qualify as a candidate' much less find an advisor and a problem, in a good program does not leave room for indecision.

• Yes. Foundations of mathematics/set theory is an area which I look forward to –  Non-Being Commented Feb 15, 2016 at 5:59

The answer really depends on what type of philosophy you are interested in. If you are interested solely in the philosophy of mathematics, you might not need to make a change at all --there's a reason a PhD is a "Doctorate of Philosophy." Upper level coursework in any field tends to touch on the philosophy of the field, and mathematics is no exception.

When I was working towards a grad degree in philosophy, I took some upper level mathematics courses, and they were very abstract and philosophical, quite similar to the upper-level logic courses I was taking at the same time. I was actually shocked how little computation they actually involved, as opposed to conceptual work. You'll probably find them very different from your undergraduate courses.

Depending on your program, you may be able to take a limited number of courses outside your department, assuming they're related. Philosophy of mathematics courses would almost certainly be considered on topic --you might even be mandated to take some of those. So the only real reason to switch would be if you have strong philosophical interests OUTSIDE of philosophy of mathematics.

Given that the other answers have given very good advice on the means towards philosophy, I'll concentrate, here, on the ends .

Given the heavy representation of foundations in the philosophy of mathematics, it might be worth looking more broadly to at least find where you are situated in this philosophical landscape.

For example, this article on the philosophy of Lautmon begins by saying:

Albert Lautmon, is a rare example of a philosopher whose engagement with contemporary mathematics goes beyond the 'foundational areas' of mathematical logic and Set Theory.

he insists that the new areas of topology, abstract algebra, analytic number theory and class field theory have a philosophical significance that distinguishes them from earlier eras.

As Lautmon was writing in the first half of the 20th C, one should add computer science, and category theory.

Lautman classification goes dialectic ally, by:

continuous/discontinuous

infinite/finite

symmetric/anti-symmetric

From this post by Gowers one could add

• abstraction/concretisation

Zalamea from what I've read about his work moves on from here. Badiou takes a very different tack, taking perhaps a cue from Heidegger:

Our epoch, can be said to have been stamped and signed by the return of the question of being.

But whereas H appeals to poesis ; B posits ontology itself to be mathematical.

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Mathematics and Philosophy

• Admissions Requirements
• Fees and Funding
• Studying at Oxford

Course overview

UCAS code: GV15 Entrance requirements: A*A*A with the A*s in Maths and Further Maths if taken. Course duration: 3 years (BA); 4 years (MMathPhil)

Subject requirements

Required subjects: Maths Recommended subjects: Further Maths Helpful subjects: Not applicable

Other course requirements

Admissions tests:  MAT Written Work: None

Admissions statistics*

Interviewed: 39% Successful: 12% Intake: 19 *3-year average 2021-23

Maths contact

Email:  [email protected]

Philosophy contact

Tel: +44 (0) 1865 276926 Email:  [email protected]

Unistats information for this course can be found at the bottom of the page

Please note that there may be no data available if the number of course participants is very small.

About the course

This course brings together two of the most fundamental and widely applicable intellectual skills.

Mathematical knowledge, and the ability to use it, is the most important means of tackling quantifiable problems. Philosophical training enhances the ability to analyse issues, question received assumptions and clearly articulate understanding. The combination provides a powerful background from which to proceed to graduate study in either mathematics or philosophy or to pursue a diverse range of careers.

Historically, there have been strong links between mathematics and philosophy. Logic, an important branch of both subjects, provides a natural bridge between the two, as does the Philosophy of mathematics module.

The degree is founded on the belief that the parallel study of these related disciplines can significantly enhance your understanding of each.

The Philosophy Faculty is the largest in the UK, and one of the largest in the world. We have more than 70 full-time members and admit around 450 undergraduates annually to read our various degrees involving philosophy.

Many faculty members have a worldwide reputation, and the faculty has one of the highest research ratings of any philosophy department in the UK. The Philosophy Library is among the best in the country.

The large number of undergraduates and graduates reading philosophy with a variety of other disciplines affords the opportunity to participate in a diverse and lively philosophical community.

In turn the Mathematics Department, housed in the Andrew Wiles Building, is also one of the largest and best in the UK and contains within it many world-class research groups. This is reflected in the wide choice of mathematics topics available to you, especially in the fourth year.

Unistats information

Discover Uni  course data provides applicants with Unistats statistics about undergraduate life at Oxford for a particular undergraduate course.

Please select 'see course data' to view the full Unistats data for Mathematics and Philosophy. 

Please note that there may be no data available if the number of course participants is very small. 

Visit the Studying at Oxford section of this page for a more general insight into what studying here is likely to be like.

A typical week

• Years 1 and 2: up to ten lectures a week, two–three tutorials a week
• Years 3 and 4: up to eight lectures a week. Equivalent of eight units taken each year. Weekly tutorials per philosophy subject. Fortnightly classes per mathematics unit. 

Tutorials are usually 2-4 students and a tutor. Class sizes may vary depending on the options you choose. There would usually be around 8-12 students though classes for some of the more popular papers may be larger. 

Most tutorials, classes, and lectures are delivered by staff who are tutors in their subject. Many are world-leading experts with years of experience in teaching and research. Some teaching may also be delivered by postgraduate students who are usually studying at doctoral level.

To find out more about how our teaching year is structured, visit our  Academic Year  page.

Course structure

There are two Mathematics and Philosophy degrees, the three-year BA and the four-year MMathPhil. Decisions regarding continuation to the fourth year do not have to be made until the third year.

The mathematics units in this joint course are all from the single-subject Mathematics course. Accordingly the standard in mathematics for admission to the joint course is the same as for admission to the single-subject Mathematics course.

The compulsory core mathematics for the joint course consists mainly of the pure (as opposed to applied) mathematics from the compulsory core for the single-subject Mathematics course. The philosophy units for the Mathematics and Philosophy course are mostly shared with the other courses with philosophy.

In the first year, all parts of the course are compulsory.

In the second and third years some subjects are compulsory. These consist of core mathematics and philosophy and bridge papers on philosophy of mathematics and on foundations (logic and set theory), but you also choose options.

In the fourth year there are no compulsory subjects, and you can do all mathematics, all philosophy, or a combination of the two.

Years 2 and 3

The content and format of this course may change in some circumstances. Read further information about potential course changes .

Academic requirements 

Wherever possible, your grades are considered in the context in which they have been achieved.

Read further information on  how we use contextual data .

If a practical component forms part of any of your science A‐levels used to meet your offer, we expect you to pass it.

If English is not your first language you may also need to meet our English language requirements .

All candidates must follow the application procedure as shown on our  Applying to Oxford  pages.

The following information gives specific details for students applying for this course.

Admissions test

All candidates must take the  Mathematics Admissions Test (MAT)  as part of their application.

All the information you need to arrange to take your test as well as how best to prepare can be found on  your test page .

Written work

You do not need to submit any written work when you apply for this course.

What are tutors looking for?

During the interview for philosophy you will be given the opportunity to show a critical and analytical approach to abstract questions and the ability to defend a viewpoint by reasoned argument.

In mathematics you may find yourself asked to look at problems of a type that you have never seen before. Don’t worry, we will help you! We want to see if you can respond to suggestions as to how to tackle new things, rather than find out simply what you have been taught. 

Visit the  Mathematics website  and  Philosophy website  for more detail on the selection criteria for this course.

Graduates secure positions in diverse areas, both in the UK and abroad, such as:

• software development
• the public sector, including the Civil and Diplomatic Services
• journalism.

Around 30% of graduates go on to further academic study.

Katherine currently works for the Bodleian Libraries. She found that the logical problem-solving skills and attention to detail she gained from studying mathematics came in useful when tackling new technical challenges in her work and whilst she completed a second graduate degree.

The experience of studying both subjects so intensely, and having to pick up and apply new knowledge quickly, gave her the confidence to work with new subject areas, including legal and medical research libraries.

We don't want anyone who has the academic ability to get a place to study here to be held back by their financial circumstances. To meet that aim, Oxford offers one of the most generous financial support packages available for UK students and this may be supplemented by support from your college.

Please note that for full-time Home undergraduate students, current university policy is to charge fees at the level of the cap set by the government. The cap is currently set at £9,250 in 2024/25 and this has been included below as the guide annual course fee for courses starting in 2025. However, this page will be updated once the government has confirmed course fee information for full-time Home undergraduates starting courses in 2025. For details of annual increases, please see our guidance on likely increases to fees and charges .

Further details about fee status eligibility can be found on the fee status webpage.

For more information please refer to our  course fees page . Fees will usually increase annually. For details, please see our  guidance on likely increases to fees and charges.

Living costs

Living costs at Oxford might be less than you’d expect, as our  world-class resources  and  college provision  can help keep costs down.

Living costs for the academic year starting in 2025 are estimated to be between £1,425 and £2,035 for each month you are in Oxford. Our academic year is made up of three eight-week terms, so you would not usually need to be in Oxford for much more than six months of the year but may wish to budget over a nine-month period to ensure you also have sufficient funds during the holidays to meet essential costs. For further details please visit our  living costs webpage .

• Financial support

**If you have studied at undergraduate level before and completed your course, you will be classed as an Equivalent or Lower Qualification student (ELQ) and won’t be eligible to receive government or Oxford funding

Fees, Funding and Scholarship search

Additional Fees and Charges Information for Mathematics and Philosophy

There are no compulsory costs for this course beyond the fees shown above and your living costs.

Contextual information

Unistats course data from Discover Uni provides applicants with statistics about a particular undergraduate course at Oxford. For a more holistic insight into what studying your chosen course here is likely to be like, we would encourage you to view the information below as well as to explore our website more widely.

The Oxford tutorial

College tutorials are central to teaching at Oxford. Typically, they take place in your college and are led by your academic tutor(s) who teach as well as do their own research. Students will also receive teaching in a variety of other ways, depending on the course. This will include lectures and classes, and may include laboratory work and fieldwork. However, tutorials offer a level of personalised attention from academic experts unavailable at most universities.

During tutorials (normally lasting an hour), college subject tutors will give you and one or two tutorial partners feedback on prepared work and cover a topic in depth. The other student(s) in your tutorials will be doing the same course as you. Such regular and rigorous academic discussion develops and facilitates learning in a way that isn’t possible through lectures alone. Tutorials also allow for close progress monitoring so tutors can quickly provide additional support if necessary.

Read more about tutorials and an Oxford education

College life

Our colleges are at the heart of Oxford’s reputation as one of the best universities in the world.

• At Oxford, everyone is a member of a college as well as their subject department(s) and the University. Students therefore have both the benefits of belonging to a large, renowned institution and to a small and friendly academic community. Each college or hall is made up of academic and support staff, and students. Colleges provide a safe, supportive environment leaving you free to focus on your studies, enjoy time with friends and make the most of the huge variety of opportunities.
• Porters’ lodge (a staffed entrance and reception)
• Dining hall
• Lending library (often open 24/7 in term time)
• Student accommodation
• Tutors’ teaching rooms
• Chapel and/or music rooms
• Green spaces
• Common room (known as the JCR).
• All first-year students are offered college accommodation either on the main site of their college or in a nearby college annexe. This means that your neighbours will also be ‘freshers’ and new to life at Oxford. This accommodation is guaranteed, so you don’t need to worry about finding somewhere to live after accepting a place here, all of this is organised for you before you arrive.
• All colleges offer at least one further year of accommodation and some offer it for the entire duration of your degree. You may choose to take up the option to live in your college for the whole of your time at Oxford, or you might decide to arrange your own accommodation after your first year – perhaps because you want to live with friends from other colleges.
• While college academic tutors primarily support your academic development, you can also ask their advice on other things. Lots of other college staff including welfare officers help students settle in and are available to offer guidance on practical or health matters. Current students also actively support students in earlier years, sometimes as part of a college ‘family’ or as peer supporters trained by the University’s Counselling Service.

Read more about Oxford colleges and how you choose

FIND OUT MORE

• Visit the Mathematics Department's website
• Visit the Faculty of Philosophy's website

Our 2024 undergraduate open days will be held on 26 and 27 June and 20 September.

Register to find out more about our upcoming open days.

Mathematics Open Days  - 20 April 2024 in person and 27 April 2024 online. 

Mathematical Sciences Research 

Mathematical Sciences at The University of Oxford was one listed as of the best in the UK in the most recent (2021) Research Excellence Framework (REF). 

RELATED PAGES

• Which Oxford colleges offer my course?
• Your academic year

RELATED COURSES

Students interested in this course might also like to consider other  Mathematics  courses or  Computer Science and Philosophy .

FEEL INSPIRED?

Why not have a look at the reading lists for prospective Mathematics and Philosophy applicants on the  Maths Department's website ?

You can also find out more about the department's research at the  Oxford Mathematics Alphabet . 

For an introduction to philosophy have a look at Myles Burnyeat and Ted Honderich’s  Philosophy , Martin Hollis'  An Invitation to Philosophy  and Simon Blackburn’s  Think.

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