phd in maths duration

Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Learn more about Harvard’s Math community and our statement on diversity and inclusion.

The Harvard Griffin GSAS Office of Equity, Diversity, Inclusion & Belonging offers diversity resources and student affinity groups for graduate students.

The Harvard University Office for Gender Equity has dedicated GSAS Title IX resource coordinators who work with and support graduate students.

open. The application deadline is December 15, 2021. -->

The pure math PhD admissions application is open. The application submission deadline is December 15, 2024.

For information on admissions and financial support , please visit the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Harvard Griffin GSAS is committed to ensuring that our application fee does not create a financial obstacle. Applicants can determine eligibility for a fee waiver by completing a series of questions in the Application Fee section of the application. Once these questions have been answered, the application system will provide an immediate response regarding fee waiver eligibility.

Note for Harvard College Undergraduates

Since it is better for a student’s mathematical development to learn mathematics at different institutions so as to be exposed to a broader range of mathematical perspectives, ordinarily applications for the mathematics PhD program from Harvard College undergraduates are not considered. If exceptional circumstances warrant an application from a Harvard undergraduate, an advisor or mentor of that student should seek approval from the Director of Graduate Studies before the student submits an application.

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COLLEGE OF LIBERAL ARTS AND SCIENCES

Department of Mathematics

• Ph.D. in Mathematics
• General Information
• Financial Aid
• Answers to FAQ
• M.S. in Mathematics
• Ph.D. in Mathematics with Thesis in Actuarial Science
• M.S. in Actuarial Science
• M.S. in Applied Financial Mathematics
• M.S. in Applied Financial Mathematics – Actuarial Science
• Course Schedule
• Preliminary Exams

Overview of Graduation Requirements

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

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

Preliminary Examination and Core Course Requirements

Pure Mathematics

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

Applied Mathematics

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

Past Prelim Exams

Graduate Program

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

Chenyang Xu

Jill leclair.

Ph.D. Degree Programs

The UCSD Mathematics Department admits students into the following Ph.D. programs:

• Ph.D. in Mathematics -- Pure or Applied Mathematics.
• Ph.D. in Mathematics with a  Specialization in Computational Science .
• Ph.D. in Mathematics with a  Specialization in Statistics .

In addition, the department participates in the following Ph.D. programs:

• Ph.D. in  Bioinformatics .
• Ph.D. in  Mathematics and Science Education  (joint program between UCSD and SDSU).

For application information, go to  How to Apply (Graduate) .  

Ph.D. in Mathematics

The Ph.D. in Mathematics allows study in pure mathematics, applied mathematics and statistics. The mathematics department has over 60 faculty, approximately 100 Ph.D. students, and approximately 35 Masters students. A list of the UCSD mathematics faculty and their research interests can be found at  here . The Ph.D. in Mathematics program produces graduates with a preparation in teaching and a broad knowledge of mathematics. Our students go on to careers as university professors, as well as careers in industry or government.

In the first and second years of study, Ph.D. students take courses in preparation for three written qualifying examinations (quals). One qual must be taken in Algebra or Topology, and another in Real or Complex Analysis. A third qual may be taken in Numerical Analysis or Statistics or one of the remaining topics in the first two groups. All three quals must be passed by the start of the third year. After the qualifying exams are passed, the student is expected to choose an advisor and follow a course of study agreed on by the two of them. At this point, the student chooses a thesis topic, finds a doctoral committee and presents a talk on his or her proposed research topic. If the committee is satisfied with this talk, the student has "Advanced to Candidacy." The student will then pursue their research agenda with their advisor until they have solved an original problem. The student will submit a written dissertation and reconvene his or her committee for a Final Defense. At the Final Defense, the student gives a seminar talk that is very similar to a talk that he or she might give for a job interview.

Nearly every admitted Ph.D. student gets financial support. The financial support is most commonly in the form of a Teaching Assistantship, however, Research Assistantships and other fellowships are also available.

Because of the large faculty to student ratio, graduate students have many opportunities to interact with faculty in courses or smaller research seminars. The graduate students also run their own "Food for Thought" seminar for expository talks as well as a research seminar where they give talks about their research.

UCSD has excellent library facilities with strong collections in mathematics, science, and engineering. Ph.D. students are provided with access to computer facilities and office space.

Full-time students are required to register for a minimum of twelve (12) units every quarter, eight (8) of which must be graduate-level mathematics courses taken for a letter grade only. The remaining four (4) units can be approved upper-division or graduate-level courses in mathematics-related subjects (MATH 500 may not be used to satisfy any part of this requirement). After advancing to candidacy, Ph.D. candidates may take all course work on a Satisfactory/Unsatisfactory basis. Typically, students should not enroll in MATH 299 (Reading and Research) until they have passed at least two Qualifying Examinations at the PhD or Provisional PhD level, or obtained approval of their faculty advisor.  

Written Qualifying Examinations

Effective Fall Quarter 1998, the department made changes in their qualifying exam requirements with a view to:

• improving applied mathematics' access to students and the attractiveness of its program to applicants; and
• broadening the education of our doctoral students and leading more of them towards applied areas.

The department now offers written qualifying examinations in  SEVEN (7)  subjects. These are grouped into three areas as follows:  

• Three qualifying examinations must be passed. At least one must be passed at the Ph.D. level and a second must be passed at either the Ph.D. or Provisional Ph.D. level.
• Of the three qualifying exams, there must be at least one from each of Areas 1 and 2. 
• Students must pass at least two exams from distinct areas with a minimum grade of Provisional Ph.D. (For example, a Ph.D. pass in Real Analysis, Provisional Ph.D. pass in Complex Analysis, M.A. pass in Algebra would  NOT  satisfy this requirement, but a Ph.D. pass in Real Analysis, M.A. pass in Complex Analysis, Provisional Ph.D. pass in Algebra would, as would a Ph.D. pass in Numerical Analysis, Provisional Ph.D. pass in Applied Algebra, and M.A. pass in Real Analysis.) All exams must be passed by the September exam session prior to the beginning of the third year of graduate studies. (Thus, there is no limit on the number of attempts, encouraging new students to take exams when they arrive, without penalty.) Except for this deadline, there is no limit on the number of exams a student may attempt.

After qualifying exams are given, the faculty meet to discuss the results of the exams with the Qualifying Exam and Appeals Committee (QEAC). Exam grades are reported at one of four levels:  

Department policy stipulates that at least one of the exams must be completed with a Provisional Ph.D. pass or better by September following the end of the first year. Anyone unable to complete this schedule will be terminated from the doctoral program and transferred to one of our Master's programs. Any grievances about exams or other matters can be brought before the Qualifying Exam and Appeals Committee for consideration.

Exams are typically offered twice a year, one scheduled late in the Spring Quarter and again in early September (prior to the start of Fall Quarter). Copies of past exams are available on the  Math Graduate Student Handbook .

In choosing a program with an eye to future employment, students should seek the assistance of a faculty advisor and take a broad selection of courses including applied mathematics, such as those in Area 3.  

Master's Transferring to Ph.D.

Any student who wishes to transfer from masters to the Ph.D. program will submit their full admissions file as Ph.D. applicants by the regular closing date for all Ph.D. applicants (end of the fall quarter/beginning of winter quarter). It is the student's responsibility to submit their files in a timely fashion, no later than the closing date for Ph.D. applications at the end of the fall quarter of their second year of masters study, or earlier. The candidate is required to add any relevant materials to their original masters admissions file, such as most recent transcript showing performance in our graduate program. Letters of support from potential faculty advisors are encouraged. The admissions committee will either recommend the candidate for admission to the Ph.D. program, or decline admission. In the event of a positive recommendation, the Qualifying Exam Committee checks the qualifying exam results of candidates to determine whether they meet the appropriate Ph.D. program requirements, at the latest by the fall of the year in which the application is received. For students in the second year of the master's program, it is required that the student has secured a Ph.D. advisor before admission is finalized. An admitted student is supported in the same way as continuing Ph.D. students at the same level of advancement are supported. Transferring from the Master's program may require renewal of an I-20 for international students, and such students should make their financial plans accordingly. To be eligible for TA support, non-native English speakers must pass the English exam administered by the department in conjunction with the Teaching + Learning Commons.  

Foreign Language Requirement

There is no Foreign Language requirement for the Ph.D. in Mathematics.  

Advancement to Candidacy

It is expected that by the end of the third year (9 quarters), students should have a field of research chosen and a faculty member willing to direct and guide them. A student will advance to candidacy after successfully passing the oral qualifying examination, which deals primarily with the area of research proposed but may include the project itself. This examination is conducted by the student's appointed doctoral committee. Based on their recommendation, a student advances to candidacy and is awarded the C. Phil. degree.  

Dissertation and Final Defense

Submission of a written dissertation and a final examination in which the thesis is publicly defended are the last steps before the Ph.D. degree is awarded. When the dissertation is substantially completed, copies must be provided to all committee members at least four weeks in advance of the proposed defense date. Two weeks before the scheduled final defense, a copy of the dissertation must be made available in the Department for public inspection.  

Time Limits

The normative time for the Ph.D. in mathematics is five (5) years. Students must be advanced to candidacy by the end of eleven (11) quarters. Total university support cannot exceed six (6) years. Total registered time at UCSD cannot exceed seven (7) years.  

It may be useful to describe what the majority of students who have successfully completed their Ph.D. and obtained an academic job have done. In the past some students have waited until the last time limit before completing their qualifying exams, finding an advisor or advancing to candidacy. We strongly discourage this, because experience suggests that such students often do not complete the program. Although these are formal time limits, the general expectation is that students pass two qualifying exams, one at the Ph.D. level and one at the masters level by the beginning of their second year. (About half of our students accomplish this.) In the second year, a student begins taking reading courses so that they become familiar with the process of doing research and familiarize themselves with a number of faculty who may serve as their advisor. In surveying our students, on average, a student takes 4 to 5 reading courses before finding an advisor. Optimally, a student advances to candidacy sometime in their third year. This allows for the fourth and fifth year to concentrate on research and produce a thesis. In contrast to coursework, research is an unpredictable endeavor, so it is in the interest of the student to have as much time as possible to produce a thesis.

A student is also a teaching assistant in a variety of courses to strengthen their resume when they apply for a teaching job. Students who excel in their TA duties and who have advanced to candidacy are selected to teach a course of their own as an Associate Instructor. Because there are a limited number of openings to become an Associate Instructor, we highly recommend that you do an outstanding job of TAing in a large variety of courses and advance to candidacy as soon as possible to optimize your chances of getting an Associate Instructorship.

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Ph.D. Program in Mathematics

Degree requirements.

A candidate for the Ph.D. degree in mathematics must fulfill a number of different departmental requirements.

NYU Shanghai Ph.D. Track

The Ph.D. program also offers students the opportunity to pursue their study and research with Mathematics faculty based at NYU Shanghai. With this opportunity, students generally complete their coursework in New York City before moving full-time to Shanghai for their dissertation research. For more information, please visit the  NYU Shanghai Ph.D. page .

Sample course schedules (Years 1 and 2) for students with a primary interest in:

Applied Math (Math Biology, Scientific Computing, Physical Applied Math, etc.)

Additional information for students interested in studying applied math is available here .

Probability

PDE/Analysis

The Written Comprehensive Examination

The examination tests the basic knowledge required for any serious mathematical study. It consists of the three following sections: Advanced Calculus, Complex Variables, and Linear Algebra. The examination is given on three consecutive days, twice a year, in early September and early January. Each section is allotted three hours and is written at the level of a good undergraduate course. Samples of previous examinations are available in the departmental office. Cooperative preparation is encouraged, as it is for all examinations. In the fall term, the Department offers a workshop, taught by an advanced Teaching Assistant, to help students prepare for the written examinations.

Entering students with a solid preparation are encouraged to consider taking the examination in their first year of full-time study. All students must take the examinations in order to be allowed to register for coursework beyond 36 points of credit; it is recommended that students attempt to take the examinations well before this deadline. Graduate Assistants are required to take the examinations during their first year of study.

For further details, consult the page on the written comprehensive exams .

The Oral Preliminary Examination

This examination is usually (but not invariably) taken after two years of full-time study. The purpose of the examination is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation. The phrase "mathematical knowledge" is intended to convey rather broad acquaintance with the basic facts of mathematical life, with emphasis on a good understanding of the simplest interesting examples. In particular, highly technical or abstract material is inappropriate, as is the rote reproduction of information. What the examiners look for is something a little different and less easy to quantify. It is conveyed in part by the word "maturity." This means some idea of how mathematics hangs together; the ability to think a little on one's feet; some appreciation of what is natural and important, and what is artificial. The point is that the ability to do successful research depends on more than formal learning, and it is part of the examiners' task to assess these less tangible aspects of the candidate's preparation.

The orals are comprised of a general section and a special section, each lasting one hour, and are conducted by two different panels of three faculty members. The examination takes place three times a year: fall, mid-winter and late spring. Cooperative preparation of often helpful and is encouraged. The general section consists of five topics, one of which may be chosen freely. The other four topics are determined by field of interest, but often turn out to be standard: complex variables, real variables, ordinary differential equations, and partial differential equations. Here, the level of knowledge that is expected is equivalent to that of a one or two term course of the kind Courant normally presents. A brochure containing the most common questions on the general oral examination, edited by Courant students, is available at the Department Office.

The special section is usually devoted to a single topic at a more advanced level and extent of knowledge. The precise content is negotiated with the candidate's faculty advisor. Normally, the chosen topic will have a direct bearing on the candidate's Ph.D. dissertation.

All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points of credit. It is recommended that students attempt the examinations well before this deadline.

The Dissertation Defense

The oral defense is the final examination on the student's dissertation. The defense is conducted by a panel of five faculty members (including the student's advisor) and generally lasts one to two hours. The candidate presents his/her work to a mixed audience, some expert in the student's topic, some not. Often, this presentation is followed by a question-and-answer period and mutual discussion of related material and directions for future work.

Summer Internships and Employment

The Department encourages Ph.D. students at any stage of their studies, including the very early stage, to seek summer employment opportunities at various government and industry facilities. In the past few years, Courant students have taken summer internships at the National Institute of Health, Los Alamos National Laboratory, Woods Hole Oceanographic Institution, Lawrence Livermore National Laboratory and NASA, as well as Wall Street firms. Such opportunities can greatly expand students' understanding of the mathematical sciences, offer them possible areas of interest for thesis research, and enhance their career options. The Director of Graduate Studies and members of the faculty (and in particular the students' academic advisors) can assist students in finding appropriate summer employment.

Mentoring and Grievance Policy

For detailed information, consult the page on the Mentoring and Grievance Policy .

Visiting Doctoral Students

Information about spending a term at the Courant Institute's Department of Mathematics as a visiting doctoral student is available on the Visitor Programs  page.

• 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.

Being affiliated with the Institute for Applied Mathematics meant I could easily collaborate with other departments and not get stuck in a box for my degree. I also wanted a program where I could develop my skills as a teacher because it is something I enjoy and is useful should I stay in academia.

Nicholas Richardson

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

• 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 (Mathematical optimization; Machine learning; Mathematical operations research; Numerical optimization; Machine Learning; Stochastic algorithms; Min-max games; Monotone operator theory)
• 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.

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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.

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PhD in Applied Mathematics

Phd in applied mathematics degree.

Applied Mathematics at the Harvard John A. Paulson School of Engineering is an interdisciplinary field that focuses on the creation and imaginative use of mathematical concepts to pose and solve problems over the entire gamut of the physical and biomedical sciences and engineering, and increasingly, the social sciences and humanities. The program has focuses on understanding nature through the fusion of Artificial Intelligence, Computing (classical to quantum), and Mathematics. We value foundational contributions, societal impact, and ethics in our work. Our program uniquely interfaces with diverse fields, including physics, neuroscience, materials science, economics, biology and fluid mechanics, to tackle some of the most pressing challenges of our time, such as sustainability, responsible digital transformations, and health and well-being.

Working individually and as part of teams collaborating across the University and beyond, you will partner with faculty to quantitatively describe, predict, design and control phenomena in a range of fields. Projects current and past students have worked on include collaborations with mechanical engineers to uncover some of the fundamental properties of artificial muscle fibers for soft robotics and developing new ways to simulate tens of thousands of bubbles in foamy flows for industrial applications such as food and drug production.

Our core mission is to provide students with individualized programs tailored to their interests, needs, and background. We welcome students from diverse technical backgrounds. Our program is dedicated to the principles of diversity, equity, and inclusion. We celebrate and value differences among our members, and we strive to create an equitable and inclusive environment for people of all backgrounds.

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Applied Mathematics PhD Degree

Harvard School of Engineering offers a  Doctor of Philosophy (Ph.D.) degree in Applied Mathematics conferred through the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences . Doctoral students may earn the masters degree en route to the Ph.D. Prospective students apply through Harvard Griffin GSAS; in the online application, select  “Engineering and Applied Sciences” as your program choice and select “PhD Applied Math” in the Area of Study menu.

The Applied Mathematics program does not offer an independent Masters Degree.

Applied Mathematics PhD Career Paths

Our graduates have gone on to careers such as start-up pioneers, social innovators, and a range of careers in industry in organizations like the Kingdom of Morocco, Meta, and Bloomberg. Others have secured faculty positions at Dartmouth, Imperial College in London, and UCLA. More generally, students with a PhD in Applied Mathematics can go on to careers in academia, banking, data science, bioinformatics, management consulting, government/military research, and more. Also, r ead about some of our Applied Mathematics alumni .

Admissions & Academic Requirements

Please review the  admissions requirements and other information  before applying. Our website also provides  admissions guidance ,   program-specific requirements , and a PhD program academic timeline .

Academic Background

Applicants typically have bachelor’s degrees in the natural sciences, mathematics, computer science, or engineering. 

Standardized Tests

GRE General: Not Accepted

Applied Mathematics Faculty & Research Areas

View a list of our  Applied Mathematics faculty and applied mathematics  affiliated research areas , Please note that faculty members listed as “Affiliates" or "Lecturers" cannot serve as the primary research advisor.  

Applied Mathematics Centers & Initiatives

View a list of the research centers & initiatives at SEAS and the Applied Mathematics faculty engagement with these entities .

Graduate Student Clubs

Graduate student clubs and organizations bring students together to share topics of mutual interest. These clubs often serve as an important adjunct to course work by sponsoring social events and lectures. Graduate student clubs are supported by the Harvard Kenneth C. Griffin School of Arts and Sciences. Explore the list of active clubs and organizations .

Funding and Scholarship

Learn more about financial support for PhD students.

• How to Apply

Learn more about how to apply  or review frequently asked questions for prospective graduate students.

In Applied Mathematics

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Speeding up document analysis ahead of negotiations

Academics , AI / Machine Learning , Applied Computation , Computer Science

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Using drones to rapidly assess disaster sites

Study Postgraduate

Phd in mathematics (2025 entry).

Course code

6 October 2025

3-4 years full-time

Qualification

Mathematics Institute

University of Warwick

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Find out more about our Mathematics PhD at Warwick

The PhD in Mathematics offers an intellectually stimulating and dynamic research course. Study at the University of Warwick's Mathematics Institute, an international centre of research excellence, ranked 3rd for research power and 3rd for the number of 4* research outputs in REF 2021 (amongst UK universities).

Course overview

Mathematics at Warwick covers the full spectrum of mathematics and its applications. The Mathematics Postgraduate Degrees are appropriate for students with a strong and broad mathematical background who wish to engage in advanced mathematical techniques and attack mathematical research problems in their postgraduate work.

All students are required to undergo training in Year One and are encouraged to make use of further training opportunities available in subsequent years. Training ranges from gaining a broader knowledge of mathematics through taught modules, seminars and workshops, to enhancing your professional and transferrable skills. Our PhD students undertake high quality original research and are being well-prepared for a career, either in academia or elsewhere.

Teaching and learning

Students are required to complete a series of modules in their first year (from a very wide selection of bespoke modules), with assessment including an oral examination component. Upon the successful completion of these modules, students are required to complete a research project before being formally upgraded to a PhD at the end of the first year.

Training will be supplemented with attendance to seminars, cohort building activities, and additional transferable skills training.

General entry requirements

Minimum requirements.

First Class Honours undergraduate integrated Master's (4-year) degree from a UK university in Mathematics or a science degree with high mathematical content, or the equivalent qualification and grade from a non-UK university.

Alternatively, applicants who have a Bachelor's degree AND a Distinction in a postgraduate Master's degree would be considered.

English language requirements

You can find out more about our English language requirements Link opens in a new window . This course requires the following:

• IELTS overall score of 6.5, minimum component scores not below 6.0

International qualifications

We welcome applications from students with other internationally recognised qualifications.

For more information, please visit the international entry requirements page Link opens in a new window .

Additional requirements

There are no additional entry requirements for this course.

Our research

The mathematics department covers a wide range of research areas in mathematics and its applications.

You may also wish to explore the research interest of current Warwick academics .

Find a supervisor

The 'Find A Supervisor' link below will allow you to explore the research interests of academics within the department. Please include in your application the names of potential supervisors, with interests aligned with yours, or people you would like to work with.

The mathematics department, unlike some other departments, does not require students to make any arrangements with any potential supervisors before applying, though of course you are welcome to contact them directly and discuss your interests and any potential projects they may offer.

Mathematics staff directory Link opens in a new window  

Research proposals

Warwick academics can supervise thesis research in a wide range of topics in mathematics and its applications. In addition, all PhD projects are expected to be co-supervised by an external partner, bringing knowledge, data and experience to the modelling of real-world problems.

The mathematics department covers a wide range of research areas Link opens in a new window in mathematics and its applications.

Research proposal guidance

In many cases, applicants have not settled on a specific area or project and have rather broad interests. If that is the case, this document can be used to describe your interests, your background on those areas, and what attracts you to those topics for example. This will help in assessing your application and help us determine potential supervisors and projects that you might be interested in.

Find out more about writing a research proposal.

Tuition fees

Tuition fees are payable for each year of your course at the start of the academic year, or at the start of your course, if later. Academic fees cover the cost of tuition, examinations and registration and some student amenities.

Find your research course fees

Fee Status Guidance

We carry out an initial fee status assessment based on the information you provide in your application. Students will be classified as Home or Overseas fee status. Your fee status determines tuition fees, and what financial support and scholarships may be available. If you receive an offer, your fee status will be clearly stated alongside the tuition fee information.

Do you need your fee classification to be reviewed?

If you believe that your fee status has been classified incorrectly, you can complete a fee status assessment questionnaire. Please follow the instructions in your offer information and provide the documents needed to reassess your status.

Find out more about how universities assess fee status

Additional course costs

As well as tuition fees and living expenses, some courses may require you to cover the cost of field trips or costs associated with travel abroad.

For departmental specific costs, please see the Modules tab on the course web page for the list of core and optional core modules with hyperlinks to our  Module Catalogue  (please visit the Department’s website if the Module Catalogue hyperlinks are not provided).

Associated costs can be found on the Study tab for each module listed in the Module Catalogue (please note most of the module content applies to 2022/23 year of study). Information about module department specific costs should be considered in conjunction with the more general costs below:

• Core text books
• Printer credits
• Dissertation binding
• Robe hire for your degree ceremony

Scholarships and bursaries

Scholarships and financial support.

Find out about the different funding routes available, including; postgraduate loans, scholarships, fee awards and academic department bursaries.

Living costs

Find out more about the cost of living as a postgraduate student at the University of Warwick.

Mathematics Funding Opportunities

Find out more about the various funding opportunities that are available in our department.

Mathematics at Warwick

Our challenging Mathematics degrees will harness your strong mathematical ability and commitment, enabling you to explore your passion for mathematics.

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Our courses

• Mathematics (Diploma plus MSc)
• Mathematics (MSc)
• Mathematics (PhD)

How to apply

The application process for courses that start in September and October 2025 will open on 2 October 2024.

For research courses that start in September and October 2025 the application deadline for students who require a visa to study in the UK is 2 August 2025. This should allow sufficient time to complete the admissions process and to obtain a visa to study in the UK.

How to apply for a postgraduate research course  

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See Warwick’s postgraduate admissions policy.

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Explore ways to connect with us

We understand how important it is to visit and explore your future university before you apply. That's why we have put together a range of online and in-person options to help you discover more about your course, visit campus, and get a sense of postgraduate life at Warwick. Our events offer includes:

• Warwick hosted events
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Why Warwick

Discover why Warwick is one of the best universities in the UK and renowned globally.

9th in the UK

of the UK's best universities (The Guardian University Guide 2024, The Times and Sunday Times Good University Guide 2024.)

6th Most Targeted University

by the UK's top 100 graduate employers (The Graduate Market in 2024, High Fliers Research Ltd.)

69th in the World

out of 1,500 institutions across 104 locations (QS World University Rankings 2025.)

10th in the UK

for our 'Graduate Prospects' score. (The Times and Sunday Times Good University Guide 2024.)

Gold Standard Teaching

Gold, the highest possible rating across all three categories (student experience, student outcomes, and overall) (Teaching Excellence Framework 2023)

Page updates

We may have revised the information on this page since publication. See the edits we have made and content history .

About the information on this page

This information is applicable for 2025 entry. Given the interval between the publication of courses and enrolment, some of the information may change. It is important to check our website before you apply. Please read our terms and conditions to find out more.

Mathematics Education PhD

Doctor of philosophy.

The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching-learning process, including studies of verbal learning and laboratory practice or historical studies.

Admissions Information

Displaying requirements for the Spring 2025, Summer 2025, and Fall 2025 terms.

• Points/Credits: 75
• Entry Terms: Spring, Summer, Fall
• Enrollment Formats: Full-Time, Part-Time

Application Deadlines

Select programs remain open beyond our standard application deadlines , such as those with an extended deadline or those that are rolling (open until June or July). If your program is rolling or has an extended deadline indicated above, applications are reviewed as they are received and on a space-available basis. We recommend you complete your application as soon as possible as these programs can close earlier if full capacity has been met.

Application Requirements

Requirements from the TC Catalog (AY 2023-2024)

Displaying catalog information for the Fall 2023, Spring 2024 and Summer 2024 terms.

View Full Catalog Listing

Doctoral Degrees

All candidates for the Ed.D., Ed.D.C.T., or Ph.D. degrees are expected to demonstrate both mathematics and mathematics education competencies through a series of certification examinations taken upon the completion of 60 graduate points. Certification examinations test the student’s knowledge of current research and theory in mathematics education and mathematics content. Examinations are offered once in the fall, spring, and summer terms. Courses recommended as preparation for the examinations in mathematics education include MSTM 6037,  MSTM 4019, and other mathematics education courses; Courses recommended as preparation for the examinations in mathematics are 6000- level mathematics content courses.

Students must demonstrate acceptable proficiency in at least three of the following six mathematics content areas: algebra, analysis, discrete mathematics, foundations of mathematics, geometry and topology, and probability and statistics. Students may sit for the examination in mathematics content during the regular certification examination times. Alternatively, they may register for advanced content courses and, with permission of the program, sit for the content area certification examination upon completion of the course. Incoming doctoral candidates should register for MSTM 6037 Professional Seminar in Mathematics during the first year of doctoral studies.

Doctoral students whose dissertations require statistical analysis should include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as research electives.

Doctor of Philosophy in Mathematics Education

The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree program requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching-learning process, including studies of verbal learning and laboratory practice or historical studies.

Candidates are encouraged to develop an association with a faculty member early in their studies to identify a problem area of mutual interest to plan a course of studies that leads to the competencies needed to complete dissertation research and prepare for a professional role. Further details are available in the brochures on doctoral studies and in the general descriptions of doctoral programs available from the Office of Doctoral Studies (ODS).

A program of study for the Doctor of Philosophy degree must include at least 45 points taken under Teachers College registration. In order to permit the acquisition of broad and basic scholarship, each program of study should include at least 60 points in mathematics, mathematics education, statistics, and computing. At least 35 points should be in advanced courses – including research courses (MSTM 6500 or 6501 and MSTM 7500). (Any Teachers College course at the 6000 level or above, any Columbia University Graduate School of Arts and Sciences course with a “G” prefix, any “W” course numbered above 4000, or any transferred course with a graduate-level prerequisite will be considered an advanced course.) Further, 15 points in the philosophical, psychological, and curricular foundations of education must be included in every Ph.D. degree program. Students whose dissertations require statistical analysis should include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as research electives.

Candidates for the Ph.D. degree are required to demonstrate competency in two languages chosen from among French, German, and Russian. Students who require other languages for the preparation of their dissertation may petition the program to request one substitution. Students in mathematics may not use computer languages or statistics to satisfy the language requirement.

The Ph.D. dissertation is a scholarly study contributing new theoretical knowledge to the field and should be planned early in the program when sufficient advanced courses have been completed to permit the candidate to enroll in relevant research courses. Ph.D. dissertations in mathematics education should be (1) experimental studies in learning, (2) analytical studies in policy theory in mathematics education, or (3) other scholarly investigations of problems and issues of broad significance in the field.

The website of the Program offers a list of Topic study groups which doctoral students are recommended to join.

• View Other Degrees

Program Director : Professor Alexander Karp

Teachers College, Columbia University 323 Thompson

Phone: (212) 678-3381 Fax: (212) 678-8319

Email: tcmath@tc.edu

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Ph.D. Mathematics Course, Eligibility, Entrance Exams, Syllabus, Colleges, Jobs and Scope 2024

Satyam Purwar

Content Curator

Ph.D. (Mathematics) - Latest Notifications

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Ph.D. Mathematics is a Doctorate of Mathematics course . It is the study of structure, space, quantity, and change. It seeks out patterns and formulates new conjectures. On the completion of a doctorate, scholars should submit their ‘thesis’ and, then they deserve the respective degree they are pursuing. 

The duration of the program is a minimum of 3 years and a maximum of 5-6 years . The minimum qualifications and other eligibility criteria for admission are M.Sc. Degree in Mathematical or Physical Sciences/ B. Tech Candidates from any discipline can also apply/ Some Institutes also offer direct admission for Graduate students with excellent academic performance. Ph.D. Mathematics is a broad-based course involving a minimum course credit requirement and a research thesis.

After completion of this course, graduates may work in fields like Banks, Investment Firms, Commerce Industry, Business Industry, Colleges, Universities, Research and Development Firms, Indian Civil Services, Inventory Management, Insurance Agencies, Statistics, etc. These professionals may work in positions like Mathematician, Statistician, Loan Officer, Accountant, Economist, Demographer, etc. The average salary for these professionals ranges between INR 3 to 9 Lakhs as per their experience and expertise in this field.

Ph.D. Mathematics: Course Highlights

Ph.D. Mathematics: What is it about?

Ph.D. Mathematics is the program of choice for students who wish to pursue a career in a mathematical research field.

• The minimum duration of this course is 2-years , whereas you can complete this course in a maximum time span of 3-5 years .
• Ph.D. Mathematics is a full-time doctoral degree.
• In Ph.D. Mathematics, students study statistical concepts relating to inspection, engineering design, and quality assurance.
• Ph.D. in Mathematics course involves research that uses various methods of mathematical types associated with the graph theory, asymptotic analysis, scientific computation, bifurcation theory, probability and statistics, ordinary and partial differential equations, stability theory, singular perturbations, and stochastic processes.
• In this course, major topics studied by the students are correlation, normality, probability, sampling, regression, and confidence intervals in reliability. This course is designed to enrich the applications like algebra and trigonometry, systems of linear equations, algebraic fractions, literal equations, quadratic equations, right triangles, vectors, word problems, and their solutions.

Why study the Ph.D. Mathematics course?

Candidates who are inclined towards a research career, many positions are available in research institutions and universities for them. And who wish to pursue a teaching career, well-paying teaching positions are available in plenty in private engineering colleges. Many research labs of multinational companies, financial services companies, and others are massively recruiting Indian mathematicians.

Some of the popular reasons why Ph.D. Mathematics must be pursued is as follows:

• This program prepares someone to keep momentum with the expanding frontiers of knowledge and provides research training relevant to the present social and economic objectives of the country.
• It comprehends to write a good research report and acquires the skill of presenting data in graphical form.
• They can also go for accountancy and business services , banking, investment and insurance, government, and public administration.
• They can become teachers and lecturers in schools and colleges/universities respectively; for becoming a lecturer in colleges they should pass the NET exam and the UGC guidelines.

Ph.D. Mathematics: Admission Process

Most colleges and institutes offering Ph.D. Mathematics courses admit students based on the graduate degree level examination marks. Some institutes, however, do conduct entrance examinations to judge a candidate’s capability.

The following are the two major pathways through which Ph.D. Mathematics admissions takes place:

Merit-Based Admission:

Most private universities such as Lovely Professional, AMU, and others that offer Ph.D. (Mathematics) courses usually admit students based on the marks secured at the master’s/ graduate degree. Apart from this, these colleges may conduct a Personal Interview or a small Written Test to further know the candidate and his/her skills.

Entrance Exam Based:

Top Ph.D. Colleges like Chandigarh University, RKMVCC, Stella Maris College, etc. offer admission in the Ph.D. (Mathematics) program through entrance examinations that usually consist of MCQ based questions related to Algebra, Analysis, Discrete Mathematics, etc. helping the college to screen the deserving candidates for admission.

After the result declaration of these Entrance Exams, colleges may further conduct a Personal Interview Round of the qualified candidates to know their interest in the course, skills, and career and might go through their Art Portfolio as well.

Ph.D. Mathematics: Eligibility

The common Ph.D. (Mathematics) eligibility criteria to be successfully admitted into a college offering this course is as follows:

• M.Sc./ Master’s Degree in Mathematical or Physical Sciences
• B. Tech Candidates from any discipline can also apply, it may vary by Institutes.
• Some Institutes also offer direct admission for Graduate Students with excellent academics records.
• Each college also further has a set minimum aggregate marks. Overall, it should be 55% (50% for SC / ST).

The above-stated eligibility criteria are the basic eligibility criteria. Each college will have its criterion on which prospective candidates are judged.

Ph.D. Mathematics: Entrance Exams

Some colleges that offer Ph.D. (Mathematics) programs require their candidates to sit for an entrance examination. This paper carries a total of 100 marks where candidates need to conclude writing the exam within a period of 3 hours.

Listed below are some of the popular Ph.D. Mathematics entrance exams.

• CSIR-UGC NET for JRF Entrance Exam: CSIR UGC NET is a national-level exam conducted by the National Testing Agency (NTA) on behalf of Council of Scientific and Industrial Research (CSIR) to shortlist candidates for the award of Junior Research Fellowship (JRF) or lectureship in Indian universities and colleges.
• UGC NET Entrance Exam: The UGC NET for JRF, also known as National Eligibility Test (NET) or NTA-UGC-NET, is the test for determining the eligibility for the post of Junior Research Fellowship (JRF) or Asst. Professor award in Indian universities and colleges.
• NBHM Entrance Exam: National Board for Higher Mathematics is a board in India that conducts a national entrance exam intended to foster the development of higher mathematics, help in the establishment and development of mathematics centers, and give financial assistance to research projects and to doctoral and postdoctoral scholars.

There are few private colleges like Chandigarh University , LPU , etc. conducts their own entrance tests for this course.

How to Prepare for a Ph.D. Mathematics Entrance Exams?

The syllabus for Ph.D. Mathematics entrance exams will vary from institute to institute. However, most exams concentrate on mathematics-related subject knowledge and skills.

The paper shall have two different parts,

• Part I - Here 10 questions will be given. Out of these, 6 will have to be answered. This part will carry 40 marks.
• Part II - Here also 10 questions will be given, out of this 6 ought to be answered. This part will carry 60 marks.

The following sections are generally covered in Ph.D. Mathematics entrance exams syllabus:

• Abstract Algebra
• Complex Analysis
• Elements of Numerical Analysis
• Linear Algebra
• Ordinary Differential Equations
• Partial Differential Equations
• Real Analysis

Students should consider buying study material and practice material of Ph.D. Mathematics entrance exams so that they prepare well for the same. This paper carries a total of 100 marks where candidates will need to conclude writing the exam within a period of 3 hours.

How to get admission in a good Ph.D. Mathematics college?

To get admission in top Ph.D. Mathematics colleges, the following points must be kept in mind:

• The application process for most of the institutes starts in January every year and the classes begin in August.
• The Colleges shortlist candidates through respective entrance exams followed by an interview.
• The best way is to appear for CSIR-NET and UGC-NET exams to get a good college for Ph.D. and for some of the colleges’ GATE is also used as a prerequisite.
• For example, ISI Kolkata uses the GATE score for admission in its Ph.D. Mathematics program. Some institutes also take admission through the NBHM Screening test conducted for Ph.D. Scholarships.

Ph.D. Mathematics: Syllabus

Although the Ph.D. Mathematics course curriculum varies from college to college, it mostly consists of some common foundation courses that students can select based on his/her interests.

The table below shows common subjects that are included in the structured Ph.D. Mathematics syllabus and subjects included in it:

Ph.D. Mathematics: Books

Tabulated below are some of the Ph.D. Mathematics subject books that can help students to have a broader and better understanding of the course. The books mentioned below will also help the students in cracking various Ph.D. Mathematics exams.

Ph.D. Mathematics: Top Colleges

The table below shows the best Ph.D. Mathematics colleges and universities that offer the course in a full-time mode.

View More   Top Ph.D. Mathematics Colleges

College Comparison

The tabulation below shows the comparison made among the three top Ph.D. Mathematics colleges in India.

Source: Official Websites of Colleges and Universities

Course Comparison

Ph.D. Mathematics Vs Ph.D. Economics

Both Ph.D. Mathematics and Ph.D. Economics have a bright future in the field of research with several aspects. There are many colleges in India who prefer both of the courses in their academic structure. Check the table below for more comparative details:

Source: Official Surveys

The eligibility and admission criteria for both these degrees are the same. In terms of Career and Salary, both Ph.D. Mathematics and Ph.D. Economics almost have the same career prospects and job opportunities, and individuals can earn an average salary of around INR 2-9 Lakhs per annum or more in some cases depending upon candidate's skills, knowledge, and experience.

Ph.D. Mathematics: Job Prospects and Career Options

In India, Ph.D. Mathematics is one of the top career choices made by students. There are lots of job opportunities available in India as well as in foreign countries for Mathematical graduates.

• Ph.D. graduates may work in a wide range of mathematical areas like Numerical Analysis, Computational Complex Analysis Group, Biomathematics Group, Complexity and Networks, Dynamical Systems, Fluid Dynamics, Mathematical Physics, etc.
• Graduates who have the ability to handle customers and basic knowledge about the industry may also work in both private and government banks.
• They can also seek employment in various sectors such as in markets research, public accounting firms, government and private banks, government and private financial sectors, budget planning, consultancies, and corporations.
• Top companies that offer jobs for these professionals are Aquis, Airtel, ITC Infotech, IBM Global Services, ABC Consultants, NEXT Techno Enterprises, Brainfuse, etc.

The table below shows some of the most common Ph.D. Mathematics job profiles and career prospects after completing the course is as follows:

Source: Payscale

Ph.D. Mathematics: Future Scope

Students having a Ph.D. mathematics degree are importantly serving the education industry and due to the laws of UGC one position of Head of Department is always secured for Ph.D. holders only.

• Employment of mathematicians in India is expected to grow by 23% as the surging demand for knowledge and expertise in private sector analytics firms.
• The private sector offers better pay and opportunities. The package can also increase if they add advanced computing skills and statistical tools in their profile.

Ph.D. Mathematics: FAQs

Ques. What are the top colleges for Ph.D. Mathematics?

Ans. The top institutes and colleges for Ph.D. Mathematics are Banaras Hindu University, Aligarh Muslim University, Amity University Noida, Birla Institute of Technology Ranchi, Queen Mary’s College, among others.

Ques. What are the subjects in Ph.D. Mathematics?

Ans. Some of the subjects taught in Ph.D. Mathematics are Algebra, Calculus, Discrete Mathematics, Differential Equations, Computational Techniques, Differential Geometry, etc.

Ques. Which job profiles are available for a Ph.D. Mathematics?

Ans. Students of Ph.D. Mathematics can work as Mathematician, Loan Officer, Accountant, Economist, Researcher, Personal Banker, Demographer, Professor, etc.

Ques. What is the annual average tuition fee charged for a Ph.D. Mathematics program?

Ans. The annual average tuition fee at the top Ph.D. Mathematics colleges is between INR 2K to INR 3 Lakh.

Ques. What is the scope of the Ph.D. Mathematics course?

Ans. Students can choose for both private and public sector jobs in several sectors like the professor, loan counselor, Insurance Manager, etc.

Ques. What is the average salary in Ph.D. Mathematics?

Ans. The salary ranges from INR 3-9 Lakhs per annum as per the job profile.

Ques. What are the job positions in the Ph.D. Mathematics field?

Ans. Job positions like Mathematician, Statistician, Loan Officer, Accountant, Economist, Researcher, Personal Banker, Cryptographer, Demographer, Professor, etc. are available in the Ph.D. Mathematics field.

Most Popular Tags

12 Reviews found

research in MANIT

Campus life.

You can avail free internet, computer labs, library, e-library (all reputeted Journals like scopus, sci, scie, ugc, ieee etc) and most important support of yor guide. anuual function, conferences, workshop, tranning session which will help you for exploring the research and enhance your knowldge. also time to time sports activities, social activities are held and you can take part accordinly.

Loan/ Scholarship Provisions

@ the time of my admission tution fees is 26000 per year in two installment and 20000 thesis submission fees and no other fees included. If you are GATE/ NET qualified then eligible for stipends (25000/ month) which is a good amount. Otherwise no stipends for scholars. other stationary amount yo have to bear. after completion of PhD you can apply for projects and earn monthly.

Life of campus is good.It has students from various regions of India and also from countries like Africa ,Niziria etc. Most of students of the CUP are from Kerala and South .It has a good library wher you can stay upto midnight.

If you have any external funding then you can easily avail that fellowship.But if you don't have any fellowship then university provide a fellowship of 8000 per month to scholors which doesn't have any external funding.

Home of the traditional- SRC

Course curriculum overview.

Actually I like mathematics from my childhood itself. That's why I chose Mathematics in UG. And also I like teaching profession. So I would like to complete PhD. My guide help me lot for my research. And also other faculties of my department are also so supportive and motivating for my research.

Placement Experience

Usually at the final semester students get the opportunities for the placement. Lot of schools and companies around Trichy came here for the interview. Capgemini, SRV higher secondary school from samayapuram and AKT school from kallakurichi are the most visited schools for our campus.

Campus Life at NIT Rourkela

NIT Rourkela has nice research environment and many professsor are collaborating with some foreign unoversity professsor. The infrastructure and campus are the main attraction to many students and PhD scholars. NIT Rourkela has also actively working placement Cell. 3 students got 45 lakh package and 9 students got 43 lakh package during this pandemic year. The statistic for placement shows that its placement percentage is going to increase in upcoming days.

I have joined in this course because I want to do research in Optimization.Faculties are highly motivated towards research. Most of the Faculties have done their PhD in Top IITs and Teaching standard is upto the mark. There are two term. One is mid semi and another is End term. We have to solve the assignment regularly to perform well in the exam and exam paper are mostly moderate to difficult level.

The revolutionary mathematics research institute

Though I was doing my Master's in mathematics I had to focus more on the TIFR GS entrance exam to pursue my Ph.D. in Mathematics. Not only that, after I qualified the exam with good ranking, but only 1.5 % of top merit list students were being considered! It was such a critical situation, yet eventually, I was noticed and called for the interview that went quite well.

TIFR is financed by the Department of Atomic Energy of Government of India. A minimal (or no) fee is charged for the course, in fact, an effective amount as accommodation is given to the students depending on the course they choose.

Pursuing PhD mathematics

I want to take a doctoral degree in mathematics because I always have a huge interest in mathematics so that's the reason I opt that course. Chandigarh university provided a huge area of research so that reason i choose Chandigarh university. Firstly fill the registration forms for the entrance test then give entrance test.

College Events

Chandigarh university celebrates every festival of all religions and they organize various events eveRy month like DJ night, tech events, fresher party, farewell parties also hostels night. Bollywood and Hollywood celebrities are visiting the campus for promotion of their movies.

IIT Patna PhD in mathematics

After doing PhD we can apply for assistant professor. IIT Patna provide stipend and fellowship by mhrd, csir, ugc, dst, nbhm, pmrf e. t. c. I am a CSIR fellow whuch give fellowship very late but IIT Patna provide some help if we needed money which you can return after getting money.

PhD is higer degree and needed for to be a professor. We have to do 5 courses from elective including English literature. After that we have labs for research and computational work. We are free to choose our course paper so it reduces our complications for unwanted subjects.

My college experience

An annual book/contingency grant of Rs. 32,000 and support for research-related domestic and international travel is available to students. Junior Research Fellowships are awarded to all selected PhD students. These fellowships include a monthly stipend ranging from Rs. 25,000/- to Rs. 28,000/-, hostel accommodation (or a house rent allowance) and medical benefits.

They are various extra-cirricular activities provided by the college. They are various grounds provided for badminton, soccer and cricket. They are coaches too if you want to learn a sport and they are various events conducted. They are also labs provides for yoir research and they are well equipped.

Phd admission to Math dept

All students of the elite Indian Institutes of Technology, patna whose annual family income is less than ? 9 lakh will be eligible for interest-free education loans for a period of of five years.if you are admitted though external fellowship you give rs 31000 per month for initial three months which can be returned after start external fellowship. And if you admitted through gate you will get 31000 per month which credited first week of the month.

Research Scholars' Day (popularly known as RSD) is an annual event celebrated by the research scholars of IIT Patna. In this programme, the students are present there research paper and many of famous scientists are invited in this program.

My Doctoral College

'Anwesha', is IIT Patna’s annual 3-day techno-cultural festival organised by the student community. Indian Institute of technology Patna each year celebrates its Technical Fest, christened as ''CELESTA'. This is a great beginning, which strives to inculcate interest in young minds to pursue technology and make it their passion. It was started in 2008 and since then it has gained unmatched popularity. It is a cultural celebration held around 'Diwali'. Beautiful decoration through lights added with fantastic cultural performances makes IIT Patna really reverberate with joy during the ‘Reverberance’. The Students' Gymkhana Building, situated in the IIT Patna hostel compound, has a synthetic badminton court and a gymnasium. In addition, the students have access to a basketball court, a volleyball court, table tennis tables and a football-cum-cricket ground within the transit campus. State-of-the-art facilities for all sports are planned at IIT Patna’s main campus in Bihita. We have good gender ration in campus. There is no such problems.

All students of the Indian Institutes of Technology Patna (IITP) whose annual family income is less than Rs.9 lakh will be eligible for interest-free education loans for a period of five years, the human resource development ministry said on Thursday. Earlier, the interest subvention scheme was for students whose annual family income was Rs.4.5 lakh.

Wastage of time and life

Worst among all the IITs, characterless, rude, unethical, all the works to be performed by teaching assistants which are research scholars. Institute lacks faculty and research scholars have to perform all the academic tasks of guide as well as teaching supervisor.

Need to fulfill the required CGPI in a year and then a comprehensive examination will be held. After successful completion of comprehensive exam including written test and presentation of the work done in past, finally registered as a Ph D. student.

Jadavpur University is the great

Fee structure and facilities.

The fee structure is very low in this university so that any poor student can effort their expenses. In addition, there are few scholarships available in this university like Merit cum means fellowship.

Internships Opportunities

Engineering faculty of this university offers various internship in India as well as abroad also. During the internship, some stipend was offered by the various companies/institute.

Ph.D. (Chemistry)

Ph.d. (physics), ph.d. (biotechnology), ph.d. (zoology), ph.d. (botany), ph.d. (english), master of science [ms], master of science [m.sc] (biotechnology), ph.d. (mathematics) colleges in india.

IIT Madras - Indian Institute of Technology - [IITM]

IIT Delhi - Indian Institute of Technology [IITD]

IIT Bombay - Indian Institute of Technology - [IITB]

IIT Kharagpur - Indian Institute of Technology - [IITKGP]

IIT Kanpur - Indian Institute of Technology - [IITK]

IIT Roorkee - Indian Institute of Technology - [IITR]

BITS Pilani (Pilani Campus)

IIT Guwahati - Indian Institute of Technology - [IITG]

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Mathematics Education, PHD

On this page:, at a glance: program details.

• Location: Tempe campus
• Second Language Requirement: No

Program Description

Degree Awarded: PHD Mathematics Education

This transdisciplinary PhD program in mathematics education accommodates students from a variety of academic backgrounds. It provides students with a solid foundation in graduate-level mathematics as well as research skills and perspectives that enable them to incorporate mathematics into such core educational areas as:

Conducting individual and collaborative research in the learning and teaching of mathematics is an integral part of the program.

Degree Requirements

Curriculum plan options.

• 84 credit hours, a written comprehensive exam, an oral comprehensive exam, a prospectus and a dissertation

Required Core (12 credit hours) MTE 501 Research in Undergraduate Mathematics Education I (3) MTE 502 Research in Undergraduate Mathematics Education II (3) MTE 503 Research in Undergraduate Mathematics Education Ill (3) MTE 504 Research in Undergraduate Mathematics Education IV (3)

Electives (42 credit hours)

Area Courses (12 credit hours)

Research (6 credit hours) MTE 792 Research (6)

Culminating Experience (12 credit hours) MTE 799 Dissertation (12)

Additional Curriculum Information Four to five graduate-level (500 and above) elective courses from mathematics, cognitive science, psychology, educational technology, philosophy or research should be taken as approved by the advisor.

For the area courses, students are required to take four graduate-level courses from the following areas of interest: mathematics, applied mathematics or statistics. Students should see the academic unit for the approved course list.

Students should see the school's website for information about qualifier and comprehensive examinations based on math coursework.

The doctoral dissertation culminating experience consists of a dissertation prospectus, oral dissertation defense and the submission of a final revised, formatted dissertation document to the Graduate College. Dissertations are composed under chair- and committee-supervised research, including literature review, research, data collection and analysis, and writing.

When approved by the student's supervisory committee and the Graduate College, up to 30 credit hours from a previously awarded master's degree may be used for this program. If students do not have a previously awarded master's degree, the remaining coursework is made up of electives and research.

Admission Requirements

Applicants must fulfill the requirements of both the Graduate College and The College of Liberal Arts and Sciences.

Applicants are eligible to apply to the program if they have earned a bachelor's or master's degree in mathematics or a closely related area, with exceptionally high grades in advanced coursework in mathematics, from a regionally accredited institution.

Applicants must have a minimum cumulative GPA of 3.00 (scale is 4.00 = "A") in the last 60 hours of their first bachelor's degree program or a minimum cumulative GPA of 3.00 (scale is 4.00 = "A") in an applicable master's degree program.

All applicants must submit:

• graduate admission application and application fee
• official transcripts
• statement of education and career goals
• writing sample
• three letters of recommendation
• proof of English proficiency

Additional Application Information An applicant whose native language is not English must provide proof of English proficiency regardless of their current residency.

At least two of the letters of recommendation must be from faculty.

Next Steps to attend ASU

Learn about our programs, apply to a program, visit our campus, application deadlines, learning outcomes.

• Able to complete original research in applied mathematics.
• Able to incorporate mathematical concepts into novel teaching methods.
• Address an original research question in mathematics education.

Career Opportunities

Graduates of the doctoral program in mathematics education have opportunities in Arizona, the U.S. and internationally. Opportunities are typically at research universities and liberal arts colleges, community colleges, and education consulting firms and in roles such as:

• faculty-track academic
• education consultant or analyst
• mathematics professor, instructor or researcher

Program Contact Information

If you have questions related to admission, please click here to request information and an admission specialist will reach out to you directly. For questions regarding faculty or courses, please use the contact information below.

• [email protected]
• 480/965-3951

Graduate Degree in Statistics

Overview of the statistics graduate program.

The Department of Mathematics and Statistics offers graduate degrees in statistics at the MS and PhD levels. Note that until 2023, these degrees were granted as concentrations of the corresponding math degrees.  This page summarizes the main features of the Statistics degrees, and contains the most up-to-date information. The information on this page supersedes the information in the Axioms (Handbook), which are in the process of being updated.

The MS degree provides students with training in statistical applications, statistical computing and theory, preparing them for statistics and data science careers in industry, government, educational organizations, consulting firms, health care and research organizations, or for moving on to a PhD in Statistics or Biostatistics. The PhD provides a combination of theory and application preparing students for positions in academia, industry or government. The Certificate in Statistical and Computational Data Science is a joint program with Statistics and Computer Science. Each of these programs is described in more detail below.

MS Degree in Statistics

The MS program in Statistics is designed to prepare students for statistics and data science positions in industry, government, educational organizations, consulting firms, health care and research organizations. It also serves as a basis for future work towards a PhD in Statistics or Biostatistics. This program is designed to provide the student with a background in basic theory along with experience in various applications, including computational aspects. As part of their training, students will receive comprehensive exposure to popular statistical software packages. In addition to courses offered within the department, the program allows room for the students to take statistics courses in other departments on campus.

Prerequisites:  Students entering the MS program are expected to have had Linear Algebra and Calculus up through Multivariate Calculus (this is typically covered by a three-semester sequence in U.S. schools).

The requirements for the MS degree in Statistics involve coursework, a project and consulting or qualifying exams.

The student must complete 30 hours of coursework with grades of C or better, including at least 24 hours with grades of B or better (pass or fail grades cannot be used to satisfy this requirement). In addition, the student must have at least an overall B average.

The required 30 hours must include:

• Stat 625: Regression Modeling
• Stat 607-608: Probability and Mathematical Statistics I, II
• Stat 535: Statistical Computing
• At least five other courses which are either Statistics courses numbered 526 or above, from within the department, or some courses outside the department numbered 500 and above subject to prior approval by the Statistics coordinator (pre-approved list below).

Consulting or Basic Exam

Students completing the MS program in Statistics are required to either complete at least one credit of statistical consulting (typically STAT 598C) or pass two of three basic exams we offer: applied statistics, probability, and statistics, which are based on ST625 and ST535, ST607, and ST608, respectively. The Basic Exam is given twice a year, in January and in August.

The project is completed under the guidance of a faculty member. This project must have prior approval of the Statistics coordinator and involves 3 credit hours which may be used to satisfy the 30 hour coursework requirement. The project can take many forms; an expository report on a particular area, an examination of methods through simulations or a detailed statistical analysis of real data. A final report is required. This requirement is typically satisfied by the successful completion of the project seminar course Stat 691P.

Accelerated (4+1) M.S. in Statistics

This section explains how a UMass Amherst or Five College student can complete the M.S. degree in statistics in a fifth year.

Preparing and Applying for the Accelerated (4+1) M.S. in Statistics

In order to enter the Accelerated M.S. in Statistics program, students need to do the following.

• a maximum of 6 credits can be counted toward both the MS in Statistics and the baccalaureate degree ("double-counted")**, and
• an additional 6 credits completed as an undergraduate student may be applied to the M.S. degree if completed "over and above" the requirements for the Baccalaureate degree, meaning the course(s) cannot be used to satisfy any undergraduate degree requirements.
• Apply in their senior years to the Accelerated M.S. program in Statistics program by following instructions  here . The priority deadline to apply is January 10 for fall admission.

Important notes regarding preparing for the 4+1 in Statistics:

1. Taking fewer than 12 transferable credits is permitted to pursue the Accelerated M.S. in Statistics, but taking the full 12 makes for the smoothest path to completing the M.S. in 1 year. Students who enter the accelerated program with less than 12 credits may need additional semester(s) to complete their M.S. degree.

2. **Per the University's multiple credentials policy, a course can only be counted towards two credentials. If a course is already double-counted towards two undergraduate majors, or a major and a minor, it is not eligible to be used as a double-counted course for the M.S. in Statistics. 

3. Any graduate-level coursework completed by a 4+1 applicant that is not Stat 535, 607, 608, or 625 must be approved by the Statistics Coordinator in order to be eligible for transfer to the M.S. in Statistics.

4. The Accelerated M.S. in Statistics can be completed at either the Amherst or Newton (Mt. Ida) campus. When submitting an application for the 4+1 program, please submit an application for the campus you are applying for.

Finishing the 4+1 M.S. in Statistics

After being accepted into the program, students

• need to take additional 18 credits and fulfill the requirements for the regular MS degree in statistics in the fifth year (typically 9 credits in fall and 9 credits in spring), if eligible to transfer all 12 credits to the graduate program as stated above
• may take longer than 2 semesters to complete the M.S. in Statistics if transferring less than 12 credits (depending on the number of remaining credits)
• are not obligated to finish the program in the fifth year, although financial assistantship, if any, is only guaranteed for the fifth year

Please note that students who are interested in the fifth year MS program in statistics should start planning during the fall of the their junior year and contact the  coordinator of the statistics program  if there are any questions. To process the transfer of credits from undergraduate to the graduate degree, students must submit a  Transfer of Credit  form. This must be submitted to Graduate Program Manager Kaitlyn O'Konis at  @email . It is recommended that this form be submitted during the summer between your undergraduate senior year and first semester in the graduate program.

MS in Statistics at Newton Satellite Campus (Boston Area), Completely Flexible (In Person/Remote or 100% Remote)

-For information regarding this program, please see the following link.

-A 100 percent remote option is available for this program.

http://people.math.umass.edu/~conlon/statmtida/

-Note: non-degree students can register for graduate statistics courses at Newton Mount Ida starting one week before the beginning of classes each semester. See:

http://www.umass.edu/graduate/apply/non-degree-students

PhD Degree in Statistics

The PhD degree in statistics prepares students for academic positions or positions in academia, or as applied statisticians in industry or government. Entering students are expected to have had linear algebra, calculus, and advanced calculus. Typically, an incoming student in the PhD program in statistics will have had an introductory course or two in statistics at the undergraduate level. Students seeking the PhD degree in statistics must complete the following: coursework, qualifying exams, language requirement, and dissertation.

• The student must complete successfully 36 hours of coursework, including Math 523 (or Math 623, or Math 605), Stat 535, 607, 608, 625, 705, and 725.
• The student must also complete five elective courses, including two 600 level statistics courses, and 3 courses of the student’s choice, which require prior approval by the statistics coordinator (pre-approved list below).
• Qualifying Exams

There are two tiers of exams, basic and advanced, which are intended to measure a student's overall mastery of standard material. The exams are administered during the week preceding each semester (August and January).

Basic Exams:  The student must pass three basic exams at the PhD level: the Applied Statistics exam and the Basic Probability and Basic Statistics exams, which cover the material from Stat 535 and Stat 625, Stat 607 and Stat 608 respectively.

Advanced Exams:  The student must pass the Advanced Exam in advanced statistics and the oral literature-based exam. The advanced statistics exam version I is based on advanced topics in Stat 607 and Stat 608, and topics from Stat 705. The advanced statistics exam version II is based on advanced topics in Stat 607 and Stat 608, and topics from Stat 725. The two versions are offered in alternate years depending which of Stat 705 and Stat 725 is offered in a year. For the literature-based exam, students need to choose a topic from the list of topics in the Axioms and form an exam committee that includes the primary faculty of that topic and two secondary faculty. Students are then given reference papers on the chosen topic to read. The exam is in the form of oral presentation and responding questions in front of the exam committee. A student may select a non-standard exam topic, in which case, the student must have the agreement of their committee members on the topic and the reading list. In order to take the literature-based exam, a student is responsible for forming an exam committee by the end of September for a January exam, or by the last day of spring classes for an August exam. Decisions on passing the exam are by unanimous consent of the exam committee. A student who does not pass will have one more chance to pass the literature-based exam. The second attempt may be on the same or a different topic.

Dissertation

After passing the Advanced Exam, the student becomes a PhD in statistics candidate. The student must write a satisfactory dissertation and pass a final oral examination (primarily a defense of the dissertation) and must satisfy all other requirements of his or her dissertation committee. The student is required to register for a minimum of 18 dissertation credits.

Data Science Certificate (possible to earn completely remotely/online)

The Certificate in Statistical and Computational Data Science is offered jointly between statistics and computer science. The certificate can be completed in one year and requires five courses total, with a minimum of two courses each of statistics and computer science.

It is possible to earn the certificate completely remotely/online. Please visit:  https://people.math.umass.edu/~conlon/statmtida/datascience.html

For more information on the certificate, please visit:

https://www.cics.umass.edu/academics/graduate-certificate-programs/certificate-statistical-and-computational-data

Approved Courses Outside the Department

The following courses are pre-approved to count toward STAT MS and PhD degrees (as specified) without additional prior approval.  Please contact the statistics coordinator for pre-approval of any other courses outside the department.

Toward MS degree only:

• PHYSICS 597D (ST- Topics in Statistics and Data Analysis)
• COMPSCI 514 (Algorithms for Data Science), CS 590V (Data Visualization and Exploration)
• Biostats 597D, Biostats 650, Biostat 690Z  

Toward MS or PhD degree:

• CS589 (Machine Learning), CS 682 (Neural Networks), CS 688 and CS690OP, CS 690D, CS 696DS, CS 611 (Advanced Algorithms), COMPSCI 688 (PROBABILISTIC GRAPHICAL MODELS),
• Biostat 683/Biostat 690B (intro to causal inference), Biostat 690T (Applied Statistical Genetics), Biostat 730, Biostat 740 (Analysis of Mixed Models Data), Biostat 743 (Categorical), Biostat 748 (Applied Survival Analysis), Biostat 749 (Clinical Trials), Biostat 750 (Applied Statistical Learning), Biostat  790A,
• Psych 891FM
• PoliSci 797TA (Text as Data)

Related Information

• Program Overview
• Applied Mathematics MS
• Remote Statistics MS
• How to Apply
• Financial Aid
• Admissions FAQ
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Lederle Graduate Research Tower, 1654 University of Massachusetts Amherst 710 N. Pleasant Street Amherst, MA 01003-9305, USA

Department Phone: (413) 545-2762 Department Fax: (413) 545-1801 Department Office: LGRT 1657

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Mathematical Sciences

Where Numbers Meet Innovation

Seminars and colloquia.

• Summer Math Modeling Program for High Schoolers
• Mathematical Sciences Learning Laboratory
• Math 010 – Intermediate Algebra
• Math 113 - Contemporary Mathematics
• Math 114 - Mathematics and Statistics
• Math 115 - Pre-Calculus
• Math 117 - Pre-Calculus for Scientists and Engineers
• Math 221 - Calculus
• Math 231/232 Integrated Calculus IA and IB
• Math 241 - Analytic Geometry and Calculus A
• Intermediate and Advanced Courses

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The Department of Mathematical Sciences at the University of Delaware offers undergraduate and graduate programs in mathematics, applied mathematics, economics, secondary math education and more. Our world-class faculty are dedicated to providing students with a rigorous education, cutting-edge research opportunities, and personalized mentoring. Students gain analytical and problem-solving skills for successful careers in academia, industry, and government. Discover the power and beauty of mathematics at UD.

Math Placement Exam >

Math course registration >, transfer of credit >, wh​y ud mathematical sciences .

Our f​​​​​​​​aculty do cutting-edge research, publishing over 100 papers per year in refereed journals and conference proceedings. 

• The department is helping to train the next generation of mathematicians, awarding approximately eight doctoral degrees, 12 master's degrees, and 65 bachelor's degrees each year.
• Most of our graduate students are funded as teaching assistants, and we are constantly improving the training we provide on how to teach effectively. Students aiming for academic careers have the opportunity to serve as instructor of record.

Nearly 100%

The placement rate for nearly 100% of our graduates as future teachers of mathematics.

According to a recent New York Federal Reserve study, mathematics is one of the top 12 highest-paying college majors, five years after graduation.

31% growth in careers

Employment of mathematicians is projected to grow 31 percent from 2021 to 2031, much faster than the average for all occupations.

College of Arts and Sciences Announces New Faculty & Chairs

Forging stem’s next generation, for the love of math, upcoming events.

​The Department of Mathematical Sciences hosts a regular series of seminars and colloquia in the mathematical sciences and in the teaching and learning of mathematics. 

• Applied Mathematics and Mathematical Medicine and Biology
• Departmental Colloquia
• Discrete Mathematics
• Hallenbeck Graduate Student Seminar
• Mathematics Education Seminar
• Mathematics of Quantum Science
• Numerical Analysis and PDE
• Probability and Stochastic Processes
• Teaching Seminar

View our Seminars and Colloquia >

Working together to ensure your success.

The purpose of math placement exam is to ensure that students begin their mathematical studies at UD in a course for which they are prepared and can succeed.

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OpenAI Unveils New ChatGPT That Can Reason Through Math and Science

Driven by new technology called OpenAI o1, the chatbot can test various strategies and try to identify mistakes as it tackles complex tasks.

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By Cade Metz

Reporting from San Francisco

Online chatbots like ChatGPT from OpenAI and Gemini from Google sometimes struggle with simple math problems . The computer code they generate is often buggy and incomplete. From time to time, they even make stuff up .

On Thursday, OpenAI unveiled a new version of ChatGPT that could alleviate these flaws. The company said the chatbot, underpinned by new artificial intelligence technology called OpenAI o1, could “reason” through tasks involving math, coding and science.

“With previous models like ChatGPT, you ask them a question and they immediately start responding,” said Jakub Pachocki, OpenAI’s chief scientist. “This model can take its time. It can think through the problem — in English — and try to break it down and look for angles in an effort to provide the best answer.”

In a demonstration for The New York Times, Dr. Pachocki and Szymon Sidor, an OpenAI technical fellow, showed the chatbot solving an acrostic, a kind of word puzzle that is significantly more complex than an ordinary crossword puzzle. The chatbot also answered a Ph.D.-level chemistry question and diagnosed an illness based on a detailed report about a patient’s symptoms and history.

The new technology is part of a wider effort to build A.I. that can reason through complex tasks. Companies like Google and Meta are building similar technologies, while Microsoft and its subsidiary GitHub are working to incorporate OpenAI’s new system into their products.

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