To apply for admissions and financial aid, or for additional information on admissions requirements for the Ph.D. program in pure mathematics, please go to the appropriate Harvard Kenneth C. Griffin Graduate School of Arts and Sciences website listed below. All other inquiries may be directed to the Graduate Program Administrator of the Mathematics Department.

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Graduate Program Administrator

The Department values diversity among its members, is committed to building a diverse intellectual community, and strongly encourages applications from women and minorities.

Preparing the Application The statement of purpose for graduate applications is carefully weighted by the admissions committee. The applicant’s statement should convince the committee that they are able to communicate effectively and with a deep understanding of mathematics. It is not intended to be a biographical sketch or a reflection on one’s decision to enter the field.

Three letters of recommendation are required. Letter writers should be faculty or others qualified to evaluate the applicant’s potential for graduate study in mathematics. The letters must be submitted online and by the application deadline.

Applicants should include any research papers, publications, and other original works they would like to have evaluated by the admissions committee.

The department requests that applicants submit GRE Mathematics Subject Test scores if practical. Applicants should check on the ETS website for test dates in their area to ensure the scores will be submitted before the application deadline. An official score report should be sent to Harvard Kenneth C. Griffin Graduate School of Arts and Sciences using code 3451.

While the admissions committee reviews all applications submitted before the deadline, missing math subject test scores provide one less data point available to evaluate the application. Depending on the strength of the application, the missing subject test scores may put the application at a disadvantage.

Applicants who are non-native English speakers and who do not hold an undergraduate degree from an institution at which English is the primary language of instruction must submit scores from the Internet Based Test (IBT) of the Test of English as a Foreign Language (TOEFL) or the International English Language Testing System (IELTS) Academic test.

Harvard Griffin GSAS requires applicants to upload an electronic copy of undergraduate transcripts. Hard copies of official transcripts are not required at the time of application.

Ph.D. Program in Pure Mathematics The department does not grant a terminal Master’s degree, but the Master’s can be obtained “on the way” to the Ph.D. by fulfilling certain course and language exam requirements.

In general, there is no transfer status application to the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences or to the Department of Mathematics. No formal credit is given for an MSc or MA earned elsewhere. All applicants are considered to be applying as first-year graduate students. The only difference Master’s study may make is to better prepare students for the Qualifying Exam.

All graduate students are admitted to begin their studies in the fall term. The department plans on an entering class of about twelve students. Since the admissions committee receives a few hundred applications, the competition is keen.

Funding Graduate Study Applicants are urged to apply for all funding available to them. If no outside funding is available to the applicant, financial aid in the form of scholarships, research assistantships, and teaching fellowships is available. In general, students who do not have outside support will get scholarship support in their first year, but students are required to act as a teaching fellow for one-half course (i.e. for a one-term course) in their second through fifth years.

The department strongly recommends applicants to seek out and apply for all sources of financing available to them for graduate study. Recommended sources for funding US graduate students are NSF Graduate Fellowships and NDSEG Fellowships . Applicants from the UK are urged to also apply for the Kennedy fellowships and applicants from UK, New Zealand, Canada and Australia for Knox fellowships . International students may apply for the Fullbright IIE or any home country fellowships available for study abroad.

Harvard John A. Paulson School of Engineering and Applied Sciences The Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) offers programs for both the Master’s degree and the Ph.D. degree in Applied Mathematics. Please visit the SEAS website for more information on degrees in applied mathematics at www.seas.harvard.edu

Applied Mathematics

Prospective ph.d. students, applied mathematics ph.d. program.

The Division of Applied Mathematics is devoted to research, education and scholarship. Our faculty engages in research in a range of areas from applied and algorithmic problems to the study of fundamental mathematical questions. By its nature, our work is and always has been inter– and multidisciplinary. Among the research areas represented in the division are dynamical systems and partial differential equations, control theory, probability and stochastic processes, numerical analysis and scientific computing, fluid mechanics, computational biology, statistics, and pattern theory. Our graduate program in applied mathematics includes around 50 Ph.D. students, with many of them working on interdisciplinary projects. Joint research projects exist with faculty in various biology and life sciences departments and the departments of Chemistry, Computer Science, Cognitive and Linguistic Sciences, Earth, Environmental, and Planetary Sciences, Engineering, Mathematics, Physics and Neuroscience, as well as with faculty in the Warren Alpert Medical School of Brown University.

Prospective PhD applicants who are interested in visiting the campus and meeting with a faculty member to discuss graduate and research programs are encouraged to contact Candida Hall , Student Affairs Manager (401.863.2463).

Get to know us: Virtual workshop

Attend talks by faculty and graduate students. Ask questions at the Q&A panel with faculty and students.

Saturday, December 2, 2023

How to Apply

Please visit our webpage on the Graduate School for information and guidance on the application process, all relevant deadlines, and required materials. 

Inquire or Apply to our Ph.D. Program

  • Applied Math code for GRE:  3094, GREs are not required for the Academic Year,  2023-2024
  • Applied Math code for TOEFL:  3094
  • Brown University code for ETS:  3094

Ph.D. Program in Computational Biology

The Division of Applied Mathematics is one of four Brown academic units that contribute to the doctoral program administered by the Center for Computational Molecular Biology. Graduate students in this program who choose applied mathematics as their home department will receive a PhD in Applied Mathematics (with Computational Biology Annotation). For further information about this program, including the application process, please visit the  CCMB Graduate Program page .

Frequently Asked Questions

Applications which are missing materials will be considered, but may be at a disadvantage in regards to admission decisions.    

Admission to our programs depends on many factors. We cannot assess your chances of admission prior to reviewing your entire application. 

The Admission Committee reviews all aspects of your application, including personal statement, recommendation letters, grades, GRE scores, research experience and related original publications, etc. There is no precise formula followed to make an admission decision, but a strong showing in the above components is likely to increase your chances of admission. 

The Admission Committee reviews all aspects of your application when making decisions. The fact that a candidate attended a particular University X (whether X is Brown or any other institution) does not mean that an application will be treated any differently from other applications.

We expect to send the results to you before March 1. Our Student Affairs Manager, Candida Hall , can be contacted if you need information prior to that date.

Yes, we will organize a common Visiting Day for all admitted students sometime in March, and make arrangements for a visit on another day, if needed, to accommodate any schedule conflicts.  

Students are admitted to the Division of Applied Mathematics as a whole, and not to a particular professor or group. 

Over recent years, the incoming PhD class has averaged about 12-15 students per year. The target and actual enrollment for our program varies each year based on a number of factors.  For the academic year 2023-2024, the GRE scores are not required, and the deadline of application is December 9, 2023.

Each year, roughly half of the intake consists of international students. However, we do not have set quotas and decisions are made depending on the quality of the applicant. We are strongly committed to maintaining a fair and equitable admission process and to cultivating diversity in our student body. 

Your chances of admission depend on many factors including test scores (both the TOEFL score and the regular and subject GRE scores), transcripts, recommendation letters, research experience, statement of purpose and research interests, as well as the general background of the students. Improving any or all of these would improve your chances of admission.  For the academic year 2023-2024, the GRE scores are not required.  

Information about the research conducted in the Division can be found on the Division's webpages. If you have specific questions regarding a particular professor's research, you may e-mail that professor directly. 

If you have any technical difficulties with your applications or any other administrative questions related to your application, contact our Student Affairs Manager, [email protected] .

A Bachelors' degree is required, but the area does not have to be in mathematics.  Applicants are expected to have a strong background in mathematics. 

No, you only need to have a Bachelors' degree to apply for the PhD degree. However, you may also apply for a PhD degree after having completed the Masters' degree. 

A $75 application fee must be paid when an application is submitted. Applicants who want to be evaluated by more than one graduate program must submit a separate application and a separate fee for each additional program.

Applicants who are U.S. citizens or permanent residents may be eligible for fee waivers. (Please note that your completed application must be submitted 14 days in advance of the program’s application deadline in order to be considered for a fee waiver. Please choose the “Request a fee waiver” option as your method of payment on the payment information page.) Application fee waivers are not available for international applicants. 

Admission to our PhD program includes at least five years of guaranteed funding, including stipend, tuition, health services fee, and health insurance, for students who maintain good standing in the program.  

For the PhD program, the GRE general test is required and the GRE (mathematics) subject test is highly recommended.  Please note that although the subject test is not required, the absence of a subject score makes determining the quality of your application more challenging.  Nevertheless, it is possible that other portions of your application, such as general GRE scores, grades, letters of recommendation, etc. may provide enough information for a decision to be made.  For the academic year 2023-2024, the GRE scores are not required.

Yes, it is in your own interests to provide as much information as you can.  The more information we have, the more likely that we will be able to assess your application accurately.

Yes. The TOEFL cannot be waived unless you have completed an undergraduate or Masters degree at an accredited institution in which the medium of instruction is English in a predominantly English-speaking country (e.g., the United States, United Kingdom, Australia, New Zealand). The IELTS exam can be substituted for TOEFL. 

The minimum score for admission consideration is 577 on the paper-based test and 90 on the Internet-based test. For IELTS, the recommended minimum overall band score is 7. These exams should be taken early enough to allow the scores to reach the Graduate School by your program's deadline. Performance on the tests is one of many factors considered in making admission decisions. 

Admissions decisions are based on many factors of which test scores are just one (see Q11).  It is your overall performance which will be considered, so your performance in any particular area need not preclude your application being successful.  

We do not track and share average GRE or TOEFL scores. 

Brown University requires official and original test scores sent by ETS.  You may self-report your test scores and upload copies of your score report(s) into your application, prior to the reception of original test scores. 

All international applicants whose native language is not English must submit an official Test of English as a Foreign Language (TOEFL) or International English Language Testing System (IELTS) score.  Language proficiency exams are not required of those students who have earned a degree from a non-U.S. university where the primary language of instruction is English, or from a college or university in the United States, or in any of a number of countries.

We really cannot advise you on this or similar matters since we are not familiar with you or your history, and suggest that you contact an advisor at University X for advice about what choice of courses would be best for your specific circumstances. 

Transferring to the PhD program from the PhD program at another university happens only in very rare circumstances, and depends on many factors. It is unusual for a student's mathematical preparation to be sufficient to merit a transfer and in most cases, the student would need to start the program afresh as a new student. This is best accomplished by applying to the program as a regular applicant for admission in the following Fall.

Stanford University

PhD Qualifying Exams

Current Requirement: To qualify for the Ph.D. in Mathematics, students must pass two examinations: one in algebra and one in real analysis. 

Requirement for students starting in Autumn 2023 and later:  To qualify for the Ph.D. in Mathematics, students must choose and pass examinations in two of the following four areas: (i) algebra, (ii) real analysis, (iii) geometry and topology, (iv) applied mathematics. 

The exams each consist of two parts. Students are given three hours for each part.

Topics Covered on the Exams:

Algebra Syllabus

Applied Mathematics Syllabus

 Geometry and Topology Syllabus

Real Analysis Syllabus

Past and Practice Qualifying Exams

Timeline for Completion:

Current Requirement: Students must pass both qualifying exams by the autumn of their second year. Ordinarily first-year students take courses in algebra and real analysis throughout the year to prepare them for the exams. The exams are then taken at the beginning of Spring Quarter. A student who does not pass one or more of the exams at that time is given a second chance in Autumn. 

Because some students have already taken graduate courses as undergraduates, incoming graduate students are allowed to take either or both of the exams in the autumn. If they pass either or both of the exams, they thereby fulfill the requirement in those subjects. However, they are in no way penalized for failing either of the exams.

Requirement for students starting in Autumn 2023 and later: Students must choose and pass two out of the four qualifying exams by the autumn of their second year. Students take courses in algebra, real analysis, geometry and topology, and applied math in the autumn and winter quarters of their first year to prepare them for the exams. The exams are taken during the first week of Spring Quarter. A student who does not pass one or more of the exams at that time is given a second chance in Autumn. 

Because some students have already taken graduate courses as undergraduates, incoming graduate students are allowed to take any of the exams in the autumn. If they pass any of the exams, they thereby fulfill the requirement in those subjects. However, they are in no way penalized for failing any of the exams.

Exam Schedule

Unless otherwise noted, the exams will be held each year according to the following schedule:

Autumn Quarter:  The exams are held during the week prior to the first week of the quarter. Spring Quarter:  The exams are held during the first week of the quarter.

The exams are held over two three-hour blocks. The morning block is 9:30am-12:30pm and the afternoon block is 2:00-5:00pm.

For the start date of the current or future years’ quarters please see the  Academic Calendar

Upcoming Exam Dates

Autumn 2023.

The exams will be held on the following dates: 

Tuesday, September 19: Algebra

Wednesday, September 20: Geometry and Topology

Thursday, September 21: Real Analysis

© Stanford University . Stanford , California 94305 .

Overview of the Application Procedure

Welcome to the MIT Mathematics Graduate Admissions page. This page explains the application process in general. For complete details, go to the on-line application which is available mid-September to December. These instructions are repeated there.

MIT admits students starting in the Fall term of each year only. Admission is to the PhD program only; there is no Masters program. There is no separate application for financial support; all admitted students are offered support.

Submitting GRE scores is entirely optional: We will accept scores if submitted (and are most interested in the Math Subject test result, if any) but it will not hurt your application if not included.

To apply, follow these steps:

Fill out the on-line application by 23:59, EST, December 15.

You will be submitting:

  • Field(s) of interest
  • Personal information/addresses
  • International student data
  • Three or more names and e-mail addresses of letter writers
  • Educational and work history, including IELTS/TOEFL scores (preferably from this year), and honors
  • Grades in math/science/engineering courses and overall
  • Statement of objectives
  • Outside financial support and potential outside support
  • Credit/debit card payment of $75
  • The Math department requires applicants to upload an electronic copy of undergraduate transcripts. Hard copies of official transcripts are not required at the time of application.

Arrange for submission of (official reports only)

  • Letters of recommendation
  • For international students, IELTS (or TOEFL iBT)

We recommend that before November 15 you notify your letter writers that you will be needing evaluations from them, so that they have time to prepare them and submit them by December 15. Once you have submitted your on-line application, instructions to your letter writers will be generated for you. You are responsible for making sure that your letter writers have copies of these instructions.

You self-reported your grades in step 1, but we require an official transcript for all admitted students. If/when we request this, arrange for an official copy of your college transcript to be sent to:

Academic Services, Room 2-110 Dept of Mathematics, MIT 77 Massachusetts Ave. Cambridge MA 02139-4307 USA

TOEFL reporting codes Institution code: MIT = 3514 Mathematics Department code: 72

International Students

IELTS is the English language proficiency test we prefer, but we also accept the TOEFL iBT . (On the other hand, we generally do not accept the TOEFL PBT.) To have IELTS results reported, indicate "Mathematics Department, Massachusetts Institute of Technology (MIT)" on your IELTS test application; no code or address is needed. To have TOEFL iBT results reported, use the codes above (3514 for MIT, and 72 for Mathematics).

If you are an international student, you should take the IELTS (or TOEFL iBT) by December 31. If you will receive an undergraduate degree from an English-language university in an English-speaking country after attending it for at least three years, then the Math Department will waive the English language proficiency test requirement.

Paper Forms

If for some reason, you are unable to use the on-line system, you may use paper forms. But note that on-line documents allow us to consider your application more quickly and conveniently. Your letter writers may also use paper forms, if necessary.

Please address questions about the application process to [email protected] . You can find more information about MIT graduate admissions in general at the MIT Graduate Admissions site .

Computational Science and Engineering

Students with primary interest in Computational Science may also consider applying to the interdisciplinary Computational Science and Engineering (CSE) program, with which the Mathematics Department is affiliated. For more information, see https://oge.mit.edu/programs/computational-science-and-engineering-phd/ .

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Ph.D. Admissions

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The application window for Fall 2024 is closed.

The Mathematics Department offers two programs to obtain a Ph.D. Applicants can pursue a Ph.D. in  Applied & Interdisciplinary Mathematics or Mathematics.  Please use the "Programs" link at the left to explore our offerings.

  • Three Letters of Recommendation  (May submit up to 5 letters, but only 3 are required.)
  • Curriculum Vitae or Resume
  • Academic Statement of Purpose (concise - no limit)
  • Personal Statement (500 word limit)
  • TOEFL iBT Special Home Edition and IELTS Indicator online test are accepted.
  • Exemption rules:   https://rackham.umich.edu/admissions/applying/tests/
  • List of  International English Exclusive Institutions  approved by Rackham

GRE General Test scores are no longer included in the admission process in accordance with a  policy of the Rackham Graduate School .

GRE Mathematics Subject Test scores are strictly optional. However, if an applicant chooses so, they may submit them as a combined pdf file with their transcript or personal statement.

Application Timeline

The Mathematics Department's graduate programs only accept applications for Fall semesters. 

General Requirements for Admission

A student must have completed a bachelor's degree at an accredited college or university by the time of entry in order to be considered for admission.

Applied & Interdisciplinary Mathematics (AIM) Ph.D. Admissions Requirements

Successful AIM Ph.D. applicants will demonstrate an interest in an interdisciplinary area of applied mathematics in addition to substantial mathematical ability. Two types of students are generally considered for admission to the AIM Ph.D. program:

  • Mathematics majors with excellent grades in mathematics courses and excellent letters of recommendation. The admissions committee will also take into account other scholarly activities such as summer research experience, published papers, or courses in other fields.
  • Non-mathematics majors from the physical, life, or engineering sciences, or from other appropriate areas of study. Such students are expected to have completed at least two upper division mathematics courses, and/or have substantial exposure to mathematics in other courses, and may submit a GRE mathematics subject test score. Other experience in working with mathematics (for instance, summer research positions) will also be taken into account, as well as grade point average and letters of recommendation.

Mathematics Ph.D.  Admission Requirements The undergraduate major need not be mathematics, but a student should have mastered material roughly equivalent to the undergraduate mathematics major at The University of Michigan including:

  • three semesters of calculus
  • one or two semesters of differential equations
  • one semester courses in modern algebra, linear algebra, geometry or topology
  • advanced calculus of one and several variables

In addition, a student should have completed at least three additional mathematics courses and at least two courses in related fields such as statistics, computer science, or the physical sciences. Students with strong records in less comprehensive programs will be considered for admission but if admitted should expect to spend the first one or two semesters in graduate school completing their undergraduate preparation in mathematics. Based on historical data, we expect that successful applicants to the Ph.D. program will have an overall GPA of at least 3.3 on a 4.0 scale.

Application Requirement Details

GRE, TOEFL, and IELTS Tests

  • GRE General test scores are not required. 
  • GRE Mathematics Subject Test scores may be submitted as a combined pdf file with your transcript or personal statement. (Optional)
  • TOEFL or IELTS exam is required for students whose native language is not English
  • TOEFL and IELTS exams should not be older than two years as of the Admission Deadline.
  • Minimum TOEFL and IELTS scores must meet Rackham's requirements here .
  • TOEFL or IELTS Exemptions are only given per Rackham's rules here .
  • ETS school code for the University of Michigan Rackham Graduate School is 1839

Letters of Recommendation

Letters of recommendation play an especially crucial role in the admission process. At least three letters are required, and up to five may be submitted. Applicants should choose as recommenders people who know their strengths and weaknesses relevant to graduate study in mathematics. The most useful letters are those which list in some detail the accomplishments of the student and make direct comparisons with other students who have succeeded at major U.S. graduate schools. International students already in the U.S. should submit letters from their U.S. institution, whenever possible.  Please register your recommenders for the electronic Letters of Recommendation when using the Online Application.  Letters received after the application deadline will be accepted, but should be received within 1 week of that deadline.

Those students who will have completed a Master's degree in Mathematics by the time they begin studies at the University of Michigan must apply to the Ph.D. program. Others may apply to either program. 

Academic Statement of Purpose

Focus your academic statement on your mathematical interests, research experience, published papers, math camps, teaching & tutoring experience etc. Be sure to mention any specific faculty with whom you wish to work.

Personal Statement:

Focus your personal statement on what makes you unique, any struggles you have experienced and overcome, and why you feel U-M Math is the right place for you.  Be sure to include any hardships you have experiencedand how you overcame them. These could be financial, familial, or personal.

Transcript Submission:

The Mathematics Admissions Committee will review uploaded transcripts with university logos during the application process.  While these are considered "unofficial" transcripts because they have been opened from their original sealed envelopes, they are acceptable.  If an applicant receives an offer of admission, an official transcript in a sealed envelope will need to be mailed from the institution directly to the Rackham Graduate School.

Please submit your most current transcript with your online application by the due date.  If you would like the Admissions Committee to see your Fall term scores, you may email them to [email protected] after the due date, and they will be included with your application.

Additonal Application Materials: If you have additional materials you would like to submit with your application, you may email them to [email protected].  Be sure to include your name and umid number in the email and attach files in pdf format.

Note:  All credentials submitted for admission consideration become the property of the University of Michigan and will not be returned in original or copy form.

Additional Information:  Please visit the admissions page of the Rackham Graduate School for additional information regarding admission including: minimum graduate school requirements, residency, and application fees.    Unfortunately, application fee waivers are not available for international students.

Financial Support for Ph.D. Students

Ph.D. Programs

Most students enrolled in the Ph.D. program in Mathematics are granted full financial support including an annual stipend, tuition waiver, and health insurance for a period of five years, subject to satisfactory progress. The Department offers aid in the form of Graduate Student Instructorships, Research Assistantships, and Fellowships.

All entering Ph.D. students will be considered for Graduate Student Instructorships, which normally require four classroom hours of teaching per week plus additional office hours during the Fall and Winter terms. The stipend for such an appointment in 2021-2022 is $11,598 per term. In addition, Graduate Student Instructors receive a full tuition waiver. Teaching duties may involve teaching a section of a first-year calculus or pre-calculus course or serving as an instructor for recitation sections attached to a faculty lecture in multivariable calculus or elementary differential equations. The Department of Mathematics has many fellowship opportunities, including the Copeland, Glover, Rainich, and Shields Fellowships which may provide a stipend, tuition waiver and in some cases a reduced teaching load. Other fellowships administered by the Rackham Graduate School can be found at their  Fellowships office .  The University of Michigan is part of the CIC consortium, which also awards fellowships to outstanding underrepresented applicants. Also available are prestigious Rackham Science Award’s given out by the Rackham Graduate School.

After Admission

All new Graduate Student Instructors are required to attend an orientation and training program which is held the week before classes begin. New Graduate Student Instructors whose Undergraduate Degree is not from an English speaking University must pass an English Evaluation which tests the specific oral skills needed for classroom teaching and are required to attend a three-week cultural orientation program starting in July.

Research Assistantships are awarded mainly to senior Ph.D. students to relieve them of teaching duties during the final part of their dissertation research. Students at this point may also compete for Rackham Dissertation Fellowships, which provide full support for one year, or Research Partnerships. A small number of positions as paper-graders for the larger advanced courses is available each term.

Some additional funds are often available for support during the summer. More advanced students who are actively involved in research may be supported from NSF grants awarded to faculty members. For other students there is a limited number of Departmental fellowships and a few teaching positions are available. No advanced graduate courses are offered in either the Spring or Summer half-terms and students are encouraged to spend some of their summers attending workshops, doing research, working in government, or seeking internships in industry.

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Marjorie Lee Browne (MLB) Scholars Program - an MS bridge to PhD program for diverse students

The Department of Mathematics at the University of Michigan is pleased to offer the Marjorie Lee Browne (MLB) Scholars Program. The program is named for Dr. Marjorie Lee Browne, who in 1949 became the first African-American woman to earn a Ph.D. in Mathematics at the University of Michigan. The MLB Scholars Program is an enhanced option for the M.S. degree in either Mathematics or Applied and Interdisciplinary Mathematics that is designed to give students professional knowledge of pure or applied mathematics in order to prepare them for continuing toward a Ph.D.  Please see this Marjorie Lee Brown Scholars webpage for eligibility and details.

If you have any questions regarding the application process, please contact the Department of Mathematics at [email protected].

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NYU Courant Department of Mathematics

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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.

Ph.D. Program

Degree requirements.

In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.

  • Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics
  • Pass the six-hour written Preliminary Examination covering calculus, real analysis, complex analysis, linear algebra, and abstract algebra; students must pass the prelim before the start of their second year in the program (within three semesters of starting the program)
  • Pass a three-hour, oral Qualifying Examination emphasizing, but not exclusively restricted to, the area of specialization. The Qualifying Examination must be attempted within two years of entering the program
  • Complete a seminar, giving a talk of at least one-hour duration
  • Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee
  • Meet the University residence requirement of two years or four semesters

Detailed Regulations

The detailed regulations of the Ph.D. program are the following:

Course Requirements

During the first year of the Ph.D. program, the student must enroll in at least 4 courses. At least 2 of these must be graduate courses offered by the Department of Mathematics. Exceptions can be granted by the Vice-Chair for Graduate Studies.

Preliminary Examination

The Preliminary Examination consists of 6 hours (total) of written work given over a two-day period (3 hours/day). Exam questions are given in calculus, real analysis, complex analysis, linear algebra, and abstract algebra. The Preliminary Examination is offered twice a year during the first week of the fall and spring semesters.

Qualifying Examination

To arrange the Qualifying Examination, a student must first settle on an area of concentration, and a prospective Dissertation Advisor (Dissertation Chair), someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective advisor, the student forms an examination committee of 4 members.  All committee members can be faculty in the Mathematics Department and the chair must be in the Mathematics Department. The QE chair and Dissertation Chair cannot be the same person; therefore, t he Math member least likely to serve as the dissertation advisor should be selected as chair of the qualifying exam committee . The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval, it is to be circulated to all faculty members of the appropriate research sections. The Qualifying Examination must cover material falling in at least 3 subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one section of the department. Sample syllabi can be reviewed online or in 910 Evans Hall. The student must attempt the Qualifying Examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program. For a student to pass the Qualifying Examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student.

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Graduate Preliminary Exam

The Preliminary Exam is taken by incoming mathematics masters graduate students at the University of Pennsylvania, just prior to the start of the fall semester. It is also required of submatriculant students. It plays a double role:

  • It serves as a placement exam, to help determine which courses are appropriate for the student.
  • It provides an incentive for incoming grad students to review basic material, which will then help them in their beginning graduate classes.

Students who do not pass the exam the first time will have a second chance to pass it at the end of the spring semester (generally in late April or early May).  This exam is no longer required of PhD students starting in 2023 and beyond.

The prelim exam focuses on the key material from undergraduate mathematics that is most important to those entering a mathematics graduate program. It is given in two parts (I & II), in the morning and afternoon of the same day. Each of these two parts consists of six problems, and students are given two and a half hours for each part (which is intended to be more time than is necessary for those who know the material).

The exam consists of problems in algebra (including linear algebra), analysis (both real and complex), and basic geometry-topology. Some problems are computational, some ask for proofs, and some ask for examples or counterexamples. Each part (I & II) of the exam contains a mixture of types of problems, and a mixture of analysis and algebra problems.

The following list of topics gives a general idea of the material that is covered on the exam:

I. Calculus and Real Analysis (four problems)

Continuity, uniform continuity, properties of real numbers, intermediate value theorem, epsilon-delta proofs.

Differentiable functions of one variable: differentiation, Riemann integration, fundamental theorem of calculus, mean-value theorem, Taylor's theorem

Sequences and series of numbers and functions, uniform convergence, equicontinuity, interchange of limit operations, continuity of limiting functions.

Ordinary differential equations (separable, exact, first order linear, second order linear with constant coefficients), applications such as orthogonal trajectories.

Multivariable calculus: partial derivatives, chain rule, multiple integrals, integrals in various coordinate systems, inverse and implicit function theorems.

Fourier series.

 II. Complex Analysis (Two problems)

  • Basic properties of complex numbers including roots of unity.  Basic properties of the more common complex functions including the geometric series, complex logarithm, exponential, square root, and trigonometric functions.  Analytic continuation, the argument principle, the maximum modulus principle, computation of integrals using the Cauchy residue theorem.

 III. Algebra (four problems)

  • Vector spaces over  R ,  C , and other fields: subspaces, linear independence, basis and dimension.
  • Linear transformations and matrices: constructing matrices of abstract linear transformations, similarity, change of basis, trace, determinants, kernel, image, dimension theorems, rank; application to systems of linear equations.
  • Eigenvalues and eigenvectors: computation, diagonalization, characteristic and minimal polynomials, invariance of trace and determinant. Jordan canonical forms.
  • Inner product spaces: real and Hermitian inner products, orthonormal bases, Gram-Schmidt orthogonalization, orthogonal and unitary transformations, symmetric and Hermitian matrices, quadratic forms.
  • Groups: finite groups, matrix groups, symmetry groups, examples of groups (symmetric, alternating, dihedral), normal subgroups and quotient groups, homomorphisms, structure of finite abelian groups, Sylow theorems.
  • Rings: ring of integers, induction and well ordering, polynomial rings, roots and irreducibility, unique factorization of integers and polynomials, homomorphisms, ideals, principal ideals, Euclidean domains, prime and maximal ideals, quotients, fraction fields, finite fields. 

IV. Geometry-topology (two problems)

  • Vector calculus: vector fields in Euclidean space (divergence, curl, conservative fields), line and surface integrals, vector calculus (Green's theorem, divergence theorem and Stokes' theorem).
  • Point-set topology: metric spaces, compactness, connectedness, topological spaces, convergence in metric spaces and topological spaces.

Sample & Old Preliminary Exams: (Warning: starting with the Spring 2022 Prelim the syllabus has been changed to include complex analysis, and a few other topics like Fourier series, which do not appear in previous prelims; some problems of this type may be found in copies of recent prelim exams for our AMCS program here: https://www.amcs.upenn.edu/exams/written-preliminary-exam )

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Doctor of Philosophy (PhD) in Mathematics Education

Graduate Programs

The Ph.D. program emphasizes research and requires a written dissertation for completion. The program is individualized to meet the needs of graduate students. The student must develop, with the guidance from the major professor and committee, a program that is applicable to their background and interest. The average Ph.D. program requires 4-6 years beyond a master’s degree. The program is comprised of coursework in four major areas.

  • Mathematics Education
  • Mathematics or a related area
  • Cognate Area
  • Research Core

This residential program has rolling admission Applications must be fully complete and submitted (including all required materials) and all application fees paid prior to the deadline in order for applications to be considered and reviewed. For a list of all required materials for this program application, please see the “Admissions” section below.

  • July 1 is the deadline for Fall applications.
  • November 15 is the deadline for Spring applications.
  • March 15 is the deadline for Summer applications.

This program does not lead to licensure in the state of Indiana or elsewhere. Contact the College of Education Office of Teacher Education and Licensure (OTEL) at [email protected] before continuing with program application if you have questions regarding licensure or contact your state Department of Education about how this program may translate to licensure in your state of residence.

APPLICATION PROCEDURE

Application Instructions for the Mathematics Education PhD program from the Office of Graduate Studies:

In addition to a submitted application (and any applicable application fees paid), all completed materials must be submitted by the application deadline in order for an application to be considered complete and forwarded on to faculty and the Purdue Graduate School for review.

Here are the materials required for this application:

  • Transcripts (from all universities attended, including an earned bachelor’s degree from a college or university of recognized standing)
  • Minimum undergraduate GPA of 3.0 on a 4.0 scale
  • 3 Recommendations
  • Academic Statement of Purpose
  • Personal History Statement
  • Writing Sample
  • International Applicants must meet English Proficiency Requirements set by the Purdue Graduate School

We encourage prospective students to submit an application early, even if not all required materials are uploaded. Applications are not forwarded on for faculty review until all required materials are uploaded.

When submitting your application for this program, please select the following options:

  • Select a Campus: Purdue West Lafayette (PWL)
  • Select your proposed graduate major: Curriculum and Instruction
  • Please select an Area of Interest: Mathematics Education
  • Please select a Degree Objective: Doctor of Philosophy (PhD)
  • Primary Course Delivery: Residential

Program Requirements

I. mathematics education courses (15 – 18 hours).

In mathematics education, students engage in courses that cover topics in the cognitive and cultural theories of learning and teaching mathematics, and the role of curriculum in mathematics education. A three (3) course sequence is required that consists of:

  • EDCI 63500 – Goals and Content in Mathematics Education
  • EDCI 63600 – The Learning of Mathematics: Insights and Issues
  • EDCI 63700 – The Teaching of Mathematics: Insights and Issues

In addition, students are encouraged to take (6 – 9) hours of EDCI 620: Developing as a Mathematics Education Researcher

II. Related Course Work (minimum 6 hours)

All students should have appropriate course work in mathematics, statistics, educational technology, or a related field. Students without a master’s level background in mathematics may be required to take more courses in mathematics. This will be determined by the student’s major professor and advisory committee.

III. Cognate (9 hours)

Students will take three graduate courses in a self-selected cognate area. Cognate area selection should be discussed with the student’s major professor and advisory committee. Possible cognate areas include: mathematics, psychology, philosophy, sociology, technology.

IV. Research Core Courses (15 hours)

All doctoral students in the Department of Curriculum and Instruction must complete five (5) courses from areas in research methodology and analysis before beginning their dissertation:

  • EDPS 53300 – Introduction to Research in Education
  • EDCI 61500 – Qualitative Research Methods in Education
  • MA 51200 – Introductory Statistics
  • Advance electives in either quantitative or qualitative methods
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Admission to Ph.D programme in Mathematics and Statistics

2016 ). With state-of-the art infrastructural facilities and a sound research base, IITB Mathematics offers a Ph.D. programme in a wide variety of areas. The program leading to the Ph.D. degree involves a course credit requirement and a research project leading to thesis submission. All that you need to know about admissions to our PhD program can be found in the information brochure for PhD admissions, which can be found at the following link. ----- A special welcome to all who wish to pursue a career in Mathematics and Statistics research. The Department of Mathematics, IITB offers a Ph.D. program in a wide variety of areas. To know more about the research interests of faculty members, please visit the page here . The program leading to the Ph.D. degree involves a course credit requirement, clearing of qualifier examinations and a research project leading to thesis submission. For more details, follow one of the links below

A special welcome to all who wish to pursue a career in Mathematics and Statistics research. The Department of Mathematics, IITB offers Ph.D. program in the areas of Mathematics and Statistics. Admission to the PhD program is based on a written test and interview. There are separate written tests and interviews for students in Mathematics and Statistics. The syllabus is given below. Students are required to choose one option specifying either Mathematics or Statistics.

To know more about the research interests of faculty members, please visit the page here . The program leading to the Ph.D. degree involves a course credit requirement, clearing of qualifier examinations and a research project leading to thesis submission. For more details, follow one of the links below

Syllabus for Entrance exam can be found here Past question papers can be found here

Syllabus for Mathematics Entrance Exam

Syllabus for Statistics Entrance Exam

Past Question Papers

PhD Admissions

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PhD Written Entrance Exam

List of examination subjects for applicants to the phd program.

  • The test for subject 0 (BMA) consists of 10 multiple choice questions. No explanation is needed in this part.
  • Tests for subjects 1-11 consist of 4-5 questions. Each subject will be marked out of 100. Here you have to show your work for full mark – results without explanation may earn you very few marks.
  • Here is a sample exam from 2018.
  • Here is the detailed list of conditions of the exam together with topics for the subjects .
  • While preparing for the exam, you may also find helpful the table containing the description of BSc courses .

The stucture of the written entrance exam

When applying for PhD studies, applicants must choose a wider area of studies in which they would want to pursue research. Note that under certain conditions, changes are possible later, during the studies. However, for the purpose of the entrance examination one such area should be chosen from the list below (see below ). Once the choice is made, the tests of the entrance examination should be chosen according to the following rules:

  • Each applicant has to write the test from 0. (BMA) BASIC MATHEMATICS.
  • Applicants have to write the mandatory test for the chosen area (subjects 1-7).
  • Applicants have to choose one test marked as elective for the chosen area (subjects 1-11).
  • Applicants should choose one test from the remaining subjects (not excluding the remaining elective subjects).
  • Thus altogether each exam will consist of four different subjects.
  • The tests will be sent electronically to the applicant and the scanned solutions should be sent back within 6 hours to the address given on the cover sheet of the exam. In order to assess your work accurately, please, make sure that your solution pages are numbered and each page contains your name and country plus the subject and the number of problem .
  • In case the applicant is not sure about the chosen research topic, a secondary choice may be taken into account by choosing for free subject the mandatory subject of the second choice.

Areas and the corresponding mandatory and elective subjects for the entrance exam

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The Faculty of Mathematics offers three doctoral (PhD) and one MPhil research programmes.

Select a course below to visit the University’s Course Directory where you can read about the structure of the programmes, fees and maintenance costs, entry requirements and key deadlines.

Research Areas and Potential Supervisors

Determining whether your interests and ambitions align with our research and expertise is a vital part of the application and admissions process. When we receive your formal application, we will consider the information you provide on your research interests carefully, alongside other factors such as your academic suitability and potential, how you compare to other applicants in the field, and whether we have a suitable academic supervisor with the capacity to take on new students.

We are committed to widening participation in mathematical research at Cambridge. We welcome and encourage applications from people from groups underrepresented in postgraduate study.

Before making an application to study with us we recommend you:

  • Investigate our areas of research and consider how they fit with your interests and ambitions.

A list of broad research areas is provided below, together with links to further information. Your interests may span more than one area. On your application form you will be asked to indicate at least one broad area of interest. This is to help us direct your application to the most suitable group of people to review it.

  • Identify 2 or 3 appropriate supervisor(s) with whom you might work.

The information linked below will take you to lists of supervisors working in each broad research area, with an indication of their availability. You are encouraged to make informal contact with potential supervisors prior to making an application. Initial contact should be made by email. In your email we recommend you provide a concise explanation of your areas of interest, how your research interests align with the supervisor(s) research, and that you highlight any relevant work you have done in this area. We recommend that you attach an up-to-date CV. The purpose of this contact is to enquire on supervisor capacity and willingness to supervise, and to see if there is a good fit between your interests and theirs.

If you haven’t had a response to an informal enquiry, you are still welcome to apply and list the individual concerned on your application form, although you may also wish to consider other options.

  • Give some thought to your intended research and why you want to study with us.

On your application form you will be asked to submit a short research summary, details of your research experience and your reasons for applying to undertake a PhD/MPhil with us. Whilst you are not expected to submit a detailed research proposal at any stage of the process, we do want to know that you have considered the areas of research that you wish to pursue.

Research areas

Click on a research area to find out more about available supervisors and their research:

Please note that a  large majority of the successful applicants for PhD studentships with  the High Energy Physics, and General Relativity & Cosmology (GR) groups   will have taken Part III of the Mathematical Tripos.

Funding Opportunities

Each Department works hard to secure funding for as many offer holders as possible, either from within its own funds, in collaboration with funding partners, or via the University Postgraduate Funding Competition. However, funding is not guaranteed via these routes, and you should investigate funding opportunities early in the process to be sure that you can meet advertised deadlines.

All application deadlines are 23:59pm (midnight) UK time on the stated date. So that your application can be given full consideration please apply by the following deadlines:

Note for PhD applicants:

We will accept applications for an October start up until the general University deadline in May, but your chances of obtaining funding are significantly reduced. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).

Only in exceptional circumstances will we consider admission to a later start date in the academic year (i.e., January or April). If you intend to apply for a later start date please contact us at [email protected] so we can advise you on the feasibility of your plan.

Note for MPhil applicants:

We will accept applications until the general University deadline in February, but you will not be considered for funding. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).

Most interviews are expected to take place in the second half of January.

The purpose of the interview is to try to ascertain the extent of the applicant's relevant knowledge and experience, and to gauge whether their interests and abilities align with the research of the potential supervisor and/or research group. It will most likely consist of a discussion of your background and motivations for applying to the course, as well as some questions on relevant topics.

Not all applicants will be selected for interview.

If you are selected for interview, you will be contacted by email at the address you provided on your application. The email should confirm:

  • the location of the interview (it may be in-person or on-line dependent upon interviewer availability, your distance from Cambridge, as well as individual preferences),
  • the interview format and whether you should prepare anything specific in advance,
  • the approximate duration of the interview,
  • who you will be meeting.

Prior to interview you may declare a disability, serious health problem or caring responsibility which may require reasonable adjustments for the interview to be made.

Due to interviewer availability and the tight admissions timetable, we can usually only rearrange the time and date of your interview under exceptional circumstances.

Decision timeline

Both DAMTP and DPMMS make most of their PhD/MPhil admissions decisions for October entry in January and early February, and you should not expect to receive a decision on your application before mid-February (even if you apply much earlier). We expect to have made decisions on all applications by mid-July. The Department makes every effort to take decisions on applications at the earliest opportunity. In some cases, however, it may take some time for a decision to be made. Applications may need to be viewed by several potential supervisors before a final decision can be reached.

To consider your application formally we must receive a complete application form, together with all supporting documents, by the deadline.

Communication of outcomes

You will be notified of the formal outcome of your application via the Applicant Portal.

Following an interview, you can normally expect to receive notification of the outcome within a week or two.

If you are successful, the University’s Postgraduate Admissions Office will issue a formal offer of admission which will outline all your conditions. As processing times can vary, we may also contact you informally to notify you of our decision.

We do not provide formal feedback to applicants who are unsuccessful at either the application or interview stage.

Take a look at our frequently asked questions for PhD applicants.

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IMSc offers PhD and integrated PhD programmes in Mathematics. Applicants for the PhD programme should have completed a Masters degree in Mathematics or Statistics by the time they actually join the programme. Applicants for the integrated PhD programme should have completed a Bachelors degree in Mathematics or Statistics by the time they actually join the programme. Exceptional candidates with a Bachelors or Masters degree in other fields will also be considered for admission to the integrated PhD programme. How to apply Candidates aspiring for admission to the IMSc Ph.D/Integ. Ph.D programmes in Mathematics must appear for the National Board for Higher Mathematics (NBHM) Ph.D scholarships Screening Test. The IMSc academic year starts in the month of August. To apply for August of a given year, candidates must write the NBHM exam held in January of that year. Candidates must apply directly to the NBHM in order to write the screening test. They need not send a separate application to IMSc. IMSc (and HRI) will get the test scores and copies of the applications directly from the NBHM and will independently send interview call letters to candidates who have passed their screening criteria. Interviews are held in March/April. Final selection of candidates is based on their performance in the interview.

Information about the NBHM Ph.D scholarships test This test is held around the third week of January each year, and is advertised in leading national newspapers the previous November. The announcement will also appear on the websites of NBHM , IMSc , HRI among others. Sample exams from past years are available here and here .

Updated Nov 2014: This year's exam has been announced. It will be held on January 24, 2015. The announcement can be found here .

Exceptional cases: While the NBHM Ph.D. Scholarship examination is the advertised and accepted entrance examination for JRF (Mathematics) positions at IMSc, the Mathematics Faculty of IMSc may, in the case of exceptionally good candidates, under exceptional circumstances, waive the requirement of the entrance examination and directly call them for an interview. Such candidates are required to have passed the CSIR-UGC (JRF) or GATE examinations in that year, Please click here for more information on requesting this waiver.

NBHM Coursework at IMSc: Students who have been selected for the NBHM PhD scholarship can opt for an extra year of course work at an institution of repute before joining an institution for the doctoral programme. NBHM will pay this extra year's scholarship through the host institution. More information is available here .

Students selected for the NBHM PhD scholarship, but not selected at IMSc, may seek permission to do this first year course work at IMSc. For more details on how to apply for NBHM coursework at IMSc, please click here .

IMSc offers PhD and integrated PhD programmes in Physics.

Applicants for the PhD programme should have completed a Masters degree in the Physics by the time they actually join the programme.

Applicants for the integrated PhD programme should have completed a Bachelors degree in Physics by the time they actually join the programme.

Exceptional candidates with a Bachelors or Masters degree in other areas will also be considered for admission to the integrated PhD programme.

A monthly stipend of Rs. 12,000 for the first two years and Rs. 14,000 in subsequent years (subject to satisfactory performance), together with an annual contingency grant of Rs. 10,000, housing and medical facilities will be provided.

Further details of our academic programme can be found here .

Admission to both of these programmes is based on the candidate's performance in Joint Entrance Screening Test (JEST) and interview.

The advertisement of the JEST examination is expected to appear in national newspapers in the last quarter of each year.

Those who have qualified for  Junior Research Fellowship (JRF)   of UGC-CSIR NET examination or Graduate Aptitude Test in Engineering ( GATE ) may apply for direct interview. Further details of direct interview can be found here

The normal route to the IMSc graduate research program is through an interview, and JEST ( Joint Entrance Screening Test )  is one of the means by which we screen students and select them for interview. JEST is conducted for the PhD and Integrated PhD programmes for Theoretical Computer Science in IMSc.

What is JEST ?

The  Joint Entrance Screening Test in Theoretical Computer Science is a test conducted across the country each year, usually on one day in the month of February. For JEST 2011 TCS on 20 February 2011 there were approximately  2000 applicants.

Who is eligible?

M.Sc./ M.E. / M.Tech. / M.C.A. in Computer Science and related disciplines, interested in the mathematical aspects of computer science, will be considered for the Ph.D. programme. Students who expect to complete their final examination by the following July are also eligible to apply.

Talented graduates with Bachelor's degree in science/ mathematics/ statistics/ computer science/ information technology/ Engineering will be considered for the Integrated M.Sc.-Ph.D. programme. This means that they pick up a Masters' degree and a PhD degree on completion of the integrated programme.

Where can I write the JEST exam?

JEST will be conducted at major cities across the country.  JEST 2010 was conducted at Ahmedabad, Aligarh, Allahabad, Bangalore, Bardhaman, Bhopal, Bhubaneswar, Chandigarh, Chennai, Delhi, Goa, Guwahati, Hyderabad, Indore, Jaipur, Kanpur, Kharagpur, Kochi, Kolkata, Madurai, Mumbai, Nagpur, Nainital, Patna, Pune, Raipur, Roorkee, Sambalpur, Silchar, Siliguri, Thiruvananthapuram, Udaipur and Visakhapatnam.

Can I do a PhD part-time with my job?

No, we only admit full-time students at IMSc. However, if you register for PhD with some university, there are possibilities of research collaboration with IMSc. Please see our page on the Graduate Visitor Programme .

Can I use a GATE score instead of writing JEST in Theoretical Computer Science?

No. We use the GATE score as additional information.

Are past JEST question papers for TCS available?

See JEST FAQ

Are sample JEST questions for TCS available?

See JEST FAQ .

What material is covered by the JEST questions for TCS?

What is the structure of the JEST examination for TCS?

It is a three-hour written test. The question paper consists of two parts:

  • Part A is multiple-choice to be marked on the answer card provided.
  • Part B requires short answers to be written on the space provided in the paper.

How is the evaluation done?

  • Part A is evaluated mechanically. Part A scores will be available at the JEST website . IMSc decides a first cutoff. Only for students who meet this first cutoff, Part B of the answerbook will be evaluated.
  • The Part B scores are not declared. IMSc decides a second cutoff based on the performance in both parts.
  • Students meeting this second cutoff are called for an interview to Chennai.
  • Interview dates are usually during the last week of April and the first week of May.

What should I do to increase my chances of getting selected?

Here are some criteria which were followed by the TCS JEST examiners in recent years.

The first cutoff selects the top students among the Part A scores. IMSc chooses the cutoff depending on the number of students taking the examination and the number of answerbooks for which Part B is to be evaluated (manually). In 2010 we chose this cutoff to get the top 250 in Part A.

  • Among the top students with Part A scores,  those who get low Part B scores are rejected.
  • The top few among the Part B scores are selected. IMSc chooses this second cutoff depending on the number of students to be called to the interviews (to be done in a limited amount of time).
  • Apart from this, we look at answers of candidates who top-score on individual questions in Part B (if very few candidates overall do well on a question they have an advantage), or if the answers are ingenious or meticulous enough to deserve extra credit. In 2010 we were able to call around 30 students for TCS interviews.

For students interested in frontier research at the interface of biology, computation, physics and applied mathematics

IMSc is a leader in India in fundamental research in theoretical physics, mathematics and theoretical computer science, with several members actively pursuing research in interdisciplinary areas including computational biology.   In 2013 IMSc started a unique Ph.D. programme in this subject, training students to apply cutting-edge computational and mathematical techniques to problems in modern biology, in collaboration with leading biology departments and institutions in India and abroad.  

IMSc  is an autonomous national research institute under the Department of Atomic Energy, Government of India, and a constituent institution of the Homi Bhabha National Institute (HBNI), Mumbai (a deemed university).   Ph.D. degrees will be awarded by HBNI.

STRUCTURE OF PROGRAMME

Before embarking on their research, students have three semesters of coursework, which consists of seven core courses, to be carried out at IMSc; elective courses, which may be taken at IMSc or at other institutions by mutual consent; and lab rotations, at collaborating labs in other institutions. The core coursework covers essentials of modern biology, essential techniques from physics, mathematics, statistics and computer science, physics of proteins and biomolecules, biological sequence analysis and algorithms, and systems biology. Elective coursework covers various topics in greater depth. Following the coursework and a comprehensive examination, students will embark on research leading to a Ph.D. degree.

Selected candidates will be research fellows at IMSc and will receive fellowships, housing or house rent allowance, and contingency grants.

Click here for course syllabus.

Biology at IMSc

Current areas of interest include:

  • Biophysics and mechanobiology
  • Systems and network biology
  • Pattern formation and dynamics
  • Biomolecular modelling
  • Regulatory genomics
  • Evolutionary biology
  • Computational neuroscience
  • Infectious disease modelling

We expect to expand into more areas in coming years. See here for more details.

Eligibility

Masters degree in any branch of science or engineering

Valid test score from any national research entrance examination (UGC-CSIR NET, JEST, GATE, NBHM, DBT BINC, etc).  Test scores must be valid as of June 2015.

IMPORTANT DATES :

Application deadline: March 31, 2015

Interview dates: May/June, 2015 (to be announced)

Offers of admission: June/July, 2015

HOW TO APPLY:

Please send applications on plain paper to:

The Registrar The Institute of Mathematical Sciences CIT Campus, Taramani Chennai 600 113, India

Include with your application:

  • A covering letter
  • A statement of interest
  • A curriculum vitae including university grades/marks
  • Results of relevant national test (JEST, NBHM, GATE, NET, BINC or other)

Incomplete applications will not be considered.

Last date for applications March 31, 2015

Department of Mathematics

Indian institute of science, the ph.d. programme.

See also: The Integrated Ph.D.Degree_Programme

The Department of Mathematics offers excellent opportunities for research in both pure and applied mathematics. Visit the Research Areas page to get a sense of the research interests of the faculty in the department. The written test conducted by IISc for entrance to the Ph.D. programme has been discontinued as of 2013. Students will be selected through the examinations listed below, followed by an interview at IISc.

Eligibility

Minimum second-class or equivalent grade in the qualifying examination/degree (which is relaxed to a “pass class” for SC/ST candidates). See below for degrees that qualify.

Master’s degree in the Mathematical or Physical Sciences, or B.E./B.Tech. (or equivalent degree) in an appropriate field of Engineering or Technology.

The candidate should also have passed one of the following entrance tests: CSIR-UGC NET for JRF, or UGC-NET for JRF, or GATE (all of these to be valid as of August 1, 2018), or the NBHM 2018 Screening Test; or must hold an INSPIRE Ph.D. fellowship.

Concerning candidates who have passed one of the above examinations: only eligible candidates who have been short-listed on the basis of their scores in one of the above examinations will be called for the interview. Note: the short-list for NBHM 2018 will be based only on the NBHM 2018 screening test. Selection to the Ph.D. programme will be based on performance in the interview.

Candidates who are yet to complete their examinations for the eligible degree and expect to complete all the requirements for their degree (including all examinations, project dissertations, viva voce, etc.) before July 31, 2018, are eligible to apply.

How to Apply

Please visit the IISc admissions page for information and instructions on how to access the online admission portal.

Students admitted to the Ph.D. programme need to take a minimum of 12 credits to complete the course requirement. Each course carries 3 credits. (View the webpage Courses for more information.)

Employment Opportunities after Ph.D.

Visit the webpage Careers in Mathematics .

Other relevant material

Nbhm ph.d. screening test: past question papers & answer keys.

June 2005: Question Paper , Answer Key

February 2006: Question Paper , Answer Key

January 2007: Question Paper , Answer Key

February 2008: Question Paper ,

January 2009: Question Paper , Answer Key

January 2010: Question Paper , Answer Key

January 2011: Question Paper

January 2012: Question Paper

January 2013: Question Paper , Answer Key

IMAGES

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COMMENTS

  1. The Qualifying Exam

    The exam consists of three, three-hour papers held on consecutive afternoons. Each paper has six questions, one each on the subjects: Algebra, Algebraic Geometry, Algebraic Topology, Differential Geometry, Real Analysis and Complex Analysis. Each question carries 10 points.

  2. Admissions

    Ph.D. Program in Pure Mathematics The department does not grant a terminal Master's degree, but the Master's can be obtained "on the way" to the Ph.D. by fulfilling certain course and language exam requirements.

  3. Prospective Ph.D. Students

    Admission to our PhD program includes at least five years of guaranteed funding, including stipend, tuition, health services fee, and health insurance, for students who maintain good standing in the program. Are GREs required? For the PhD program, the GRE general test is required and the GRE (mathematics) subject test is highly recommended ...

  4. PhD Qualifying Exams

    Requirement for students starting in Autumn 2023 and later: To qualify for the Ph.D. in Mathematics, students must choose and pass examinations in two of the following four areas: (i) algebra, (ii) real analysis, (iii) geometry and topology, (iv) applied mathematics. The exams each consist of two parts. Students are given three hours for each part.

  5. Admission

    Welcome to the MIT Mathematics Graduate Admissions page. This page explains the application process in general. For complete details, go to the on-line application which is available mid-September to December. These instructions are repeated there. MIT admits students starting in the Fall term of each year only.

  6. Ph.D. Admissions

    Ph.D. Admissions. Three Letters of Recommendation (May submit up to 5 letters, but only 3 are required.) TOEFL iBT Special Home Edition and IELTS Indicator online test are accepted. GRE General Test scores are no longer included in the admission process in accordance with a policy of the Rackham Graduate School.

  7. Ph.D. in Mathematics

    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 ...

  8. Ph.D. Program

    In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements. During the first year of the Ph.D. program: Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics. Pass the six-hour written Preliminary Examination covering calculus ...

  9. Department of Mathematics at Columbia University

    The PhD program is an intensive course of study designed for the full-time student planning a career in research and teaching at the university level or in quantitative research and development in industry or government. Admission is limited and highly selective. Successful applicants have typically pursued an undergraduate major in mathematics.

  10. Graduate Preliminary Exam

    This exam is no longer required of PhD students starting in 2023 and beyond. The prelim exam focuses on the key material from undergraduate mathematics that is most important to those entering a mathematics graduate program. It is given in two parts (I & II), in the morning and afternoon of the same day. Each of these two parts consists of six ...

  11. Doctor of Philosophy (PhD) in Mathematics Education

    The program is individualized to meet the needs of graduate students. The student must develop, with the guidance from the major professor and committee, a program that is applicable to their background and interest. The average Ph.D. program requires 4-6 years beyond a master's degree. The program is comprised of coursework in four major areas.

  12. Ph.D. Mathematics Course, Eligibility, Entrance Exams, Syllabus

    01 December, 2023 : IIM Jammu PhD (Working Professionals) Admission 2024 Open; Apply till March 31, 2024 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.

  13. Ph.D and Integrated Ph.D programmes in Mathematics: Eligibility

    1. The NBHM scholarship written test which will be held in January 2024. While applying for this test, the candidate may choose either the "Doctoral Scholarship" option or the "Master's Scholarship" option or "Both". 2. The CSIR UGC NET exam of June 2023 or December 2023 - the top 30 ranks in Mathematics are eligible to apply.

  14. Ph.D Admission

    Admissions Ph.D Admission to Ph.D programme in Mathematics and Statistics A special welcome to all who wish to pursue a career in Mathematics and Statistics research. The Department of Mathematics, IITB offers Ph.D. program in the areas of Mathematics and Statistics. Admission to the PhD program is based on a written test and interview.

  15. Chennai Mathematical Institute

    The entrance exam for 2024-25 admissions will be held on Sunday, 19 May, 2024 at 14:00. Here is the schedule for applications for the session starting in August, 2024 (academic year 2024-2025). Applications ... Qualify for PhD Mathematics via NBHM.

  16. PhD Syllabus 2024: Subjects, Entrance Exam Syllabus, List of PhD Courses

    The syllabus for PhD entrance exams includes common topics from 10+2, graduation and postgraduation level i.e. technology, life sciences, mathematics, sciences, and general aptitude. The subjects and topics included in PhD Syllabus vary based on the PhD Specialization and sub-stream one chooses.

  17. PhD Written Entrance Exam

    PhD Written Entrance Exam List of examination subjects for applicants to the PhD program The test for subject 0 (BMA) consists of 10 multiple choice questions. No explanation is needed in this part. Tests for subjects 1-11 consist of 4-5 questions. Each subject will be marked out of 100.

  18. Research Programmes

    The Faculty of Mathematics offers three doctoral (PhD) and one MPhil research programmes. Select a course below to visit the University's Course Directory where you can read about the structure of the programmes, fees and maintenance costs, entry requirements and key deadlines. Research Areas and Potential Supervisors

  19. Admissions

    How to apply. Candidates aspiring for admission to the IMSc Ph.D/Integ. Ph.D programmes in Mathematics must appear for the National Board for Higher Mathematics (NBHM) Ph.D scholarships Screening Test. The IMSc academic year starts in the month of August. To apply for August of a given year, candidates must write the NBHM exam held in January ...

  20. Ph.D. programme: Mathematics@IISc

    The Ph.D. Programme. The Department of Mathematics offers excellent opportunities for research in both pure and applied mathematics. Visit the Research Areas page to get a sense of the research interests of the faculty in the department. The written test conducted by IISc for entrance to the Ph.D. programme has been discontinued as of 2013.

  21. PhD Admission 2024: Important Dates, Selection Process, Last Date to

    NTA conducts the UGC NET to offer PhD Admission 2024 in top central universities such as JNU, DU, etc. NTA also conducts a PhD Entrance Exam to offer PhD Admission for DU/JNU/BHU/BBAU for candidates who have not qualified for the UGC NET and JRF. IIT Madras has released the IIT JAM 2024 Answer Key.

  22. Ph.D Entrance Exam

    Published on 18/10/2023. Intimation of Date of Examination and Correction in the particulars of the online Application Form of Ph.D. Entrance Test for DU, JNU, BHU and BBAU - 2023 - Reg. Published on 21/09/2023. Extension of Date of Registration in respect of Ph.D. Entrance Test for DU, JNU, BHU and BBAU - 2023. Published on 13/09/2023.