requirements for phd in mathematics

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Requirements for the Ph.D. Degree

Prospective students with questions, please start  here .

The Ph.D. degree in Mathematics requires a minimum of 72 hours of study, which must include at least 48 hours of approved graduate level courses and at least 12 hours of dissertation credit (MTH 6V99).

Other requirements include  two qualifying examinations , a  preliminary examination , and a  defense of the dissertation . There is no foreign language requirement for the Ph.D. degree. For further information on requirements, click on  Graduate FAQs .

Required Core Courses

Twenty-one hours from the following:

• MTH 5310 Advanced Abstract Algebra I
• MTH 5311 Advanced Abstract Algebra II
• MTH 5323 Theory of Functions of Real Variables I
• MTH 5324 Theory of Functions of Real Variables II
• MTH 5330 Topology
• MTH 5331 Algebraic Topology I
• MTH 5350 Complex Analysis
• MTH 5360 Applied Mathematics I
• MTH 5361 Applied Mathematics II

Students must earn a grade of B or better in each of the seven core courses. Furthermore, the seven core courses must include MTH 5310, 5323, 5330, and 5350.

Any course approved for the Master of Science degree in Mathematics, any MTH or STA course at the 6000 level or other electives only as approved by the Department of Mathematics

Dissertation

• MTH 6V99 (12 hours)

Department of Mathematics

Sid Richardson Science Building 1410 S.4th Street Waco, TX 76706

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Applied ph.d. program requirements (fall 2024).

This plan requires a total of 60 units. Students will enroll for 12 units per quarter including research, academic, and seminar units. Before advancing to Candidacy for a doctoral degree, a student must have satisfied all requirements set by the graduate program, maintained a minimum GPA of 3.0 in all course work undertaken (except those courses graded S or U), passed the PhD Preliminary Examination, and passed the Qualifying Examination. A dissertation and an exit seminar are required.

Course Requirements

• Area A (12 units in one of the series) : (i) Analysis Series MAT 201AB/MAT 201C/MAT 205/MAT206 (Analysis) or (ii) Methods of Applied Mathematics MAT 207ABC.  
• Area B (8 units in one of the series): (i) Data Science series: Numerical Optimization (MAT 258A), Discrete and Mixed-Integer Optimization (MAT258B), Mathematics of Data Science (MAT 270); or (ii) Numerical Methods series: Numerical Methods: Fundamentals (MAT 226A), Numerical Methods: Large-Scale Matrix Computations (MAT 226B), Numerical Methods: Ordinary Differential Equations (MAT226C), Numerical Solutions of Differential Equations A, B and C (MAT 228ABC); or (iii) Probability series: Probability Theory A and B (MAT235AB), Mathematical Statistics III (STA231C); or (iv) Theoretical Computer Science series: Theoretical Computer Science (ECS220), Design and Analysis of Algorithms (ECS222).  
• Graduate Advanced Mathematics: 12 units of 200-level Mathematics courses whose course numbers are 279 or less. These include courses from areas A or B not selected as core courses. One mathematics-oriented graduate course outside of Mathematics, could be substituted but only with prior approval by GGAM Chair.  
• Field of Specialization (FOS): Minimum of 15 units in a field of specialization, such as, any courses in Area A or B not taken to satisfy the core requirements, optimization, and control, differential equations, probability and statistics, discrete mathematics, mathematical physics, mathematical biology, harmonic analysis and signal processing, etc. Out of this minimum of 15 units, at least one course of 3 or more units must be outside of Mathematics. Courses outside of the mathematics department have to be approved by the Chair of the graduate group. For a list of preapproved courses, see the GGAM webpage and consult with the potential thesis advisor. An updated list of courses can be found in https://appliedmath.ucdavis.edu/graduate/sample-depth-courses  
• Advanced Mathematics: Maximum of 12 units, in three 100 level (i.e.upper division) math courses.  
• GGAM miniconference: Attendance at the annual GGAM mini-conference, which takes place during winter quarter graduate welcome and consists of faculty talks and a student poster session showcasing the research being done at GGAM, is required in the first or second year, for which 1 unit of 290 will be given in order to document compliance.  
• MAT 290 seminars  
• MAT 390 and Teaching: Each student who accepts a TAship in the Department of Mathematics is required to complete MAT390, which is taught every Fall quarter. Most students take this in their first year, even if they are supported by a fellowship. MAT 390 does not count toward degree units (but does count for the 12-unit minimum required for registration each quarter). All PhD students are required to be teaching assistants for at least one quarter. Exceptions require approval of the GGAMEXEC. Students beyond their first year are encouraged to apply for positions as Associate-Instructors to develop and improve their lecturing skills.  
• Research Units: Students can register for research units but these units cannot substitute course requirements unless previously reviewed and approved by the chair of the graduate group.

Ph.D. Preliminary Examination

The Ph.D. Preliminary Examination is a written examination covering materials from the student’s chosen tracks Area A (MAT 201AB or MAT 207ABC) and Area B: Data Science: (MAT 168, MAT170); Numerical Methods (MAT128ABC); Probability (MAT 135AB); and Theoretical Computer Science (ECS220, ECS222). The exam is offered in June and September every year. PhD students are required to pass this examination before the end of their second year.  They may take the examination multiple times; what matters is when they pass, not how many attempts.

Qualifying Examination

Students must complete the course requirements before taking their Qualifying Examination (QE). The QE will consist of a written research proposal, a syllabus of materials relevant to the research proposal covered in the chosen tracks in Areas A and B, and oral examination. Approximately six weeks before the date of the proposed QE, the research proposal, along with the QE Application, is submitted to GGAMEXEC for approval. Once approved and required signatures obtained, the QE Application will be forwarded to the Office of Graduate Studies for final approval. The QE should be taken by the sixth quarter and no later than the end of the ninth quarter after admission to the Ph.D. program. Passing the QE makes the student eligible for advancement to candidacy.

Dissertation

The doctoral dissertation is an essential part of the Ph.D. program. A topic will be selected by the student, under the guidance of the Dissertation Advisor. Students are encouraged to begin their research activity as early as possible. The dissertation must contain an original contribution of publishable quality to the knowledge of applied mathematics. Acceptance of the dissertation by the dissertation committee must follow Graduate Studies guidelines (Plan B). The program does not have any program-specific requirements, such as length or presentation format. Instructions on preparation of the dissertation and a schedule of dates for filing the thesis in final form are available from Graduate Studies; the dates are also printed in the UC Davis General Catalog.

Exit Seminar

Ph.D. students are required to give a 60-minute seminar presentation, open to the public, on their dissertation subject.

Optional Final Oral Examination (at the discretion of the Dissertation Committee)

After the exit seminar, the student’s dissertation committee may meet privately with the student to discuss the contents of the dissertation and ask additional questions. Satisfaction of this requirement must be verified by the Dissertation Committee Chair.

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

PhD Requirements

The purpose of the Doctor of Philosophy program is to prepare the student for research and teaching.

It is expected that each graduate student who is a U.S. citizen or permanent resident should begin the process of establishing North Carolina residency during the first semester of graduate study. Detailed information can be found here.

Time and residency requirements

First year courses.

Courses taken during the first year are usually chosen from the following list, which is designed to prepare students for the PhD qualifying examinations. Master’s students will typically take these courses as well in the first year before focusing in the second year on the requirements for a Master’s degree.

Qualifying Exam Requirements

There are five qualifying exams:

• Algebra: Math 676 and 677
• Analysis: Math 653 and 656
• Geometry-Topology: Math 680 and 681
• Methods of Applied Mathematics: Math 668 and 669
• Scientific Computation: Math 661 and 662

PhD qualifying exams are given twice each year, near the beginning of classes in August and January. PhD students are encouraged to take the PhD qualifying exams early and in principle would be ready to take them in August after the first year. The qualifying exams, sometimes called comps, are subject to the following rules:

• A PhD student can pass either the Pure Math option for the for the qualifying examination or the Applied Math option.
• To pass the Pure Math Option, a student is required to pass three of the five qualifying exams by the beginning of the sixth semester. Any three of the five can be passed.
• To pass the Applied Math option, a student is required to pass Methods of Applied Math and Scientific Computation by the beginning of the sixth semester.
• In each examination period a student can take any number of qualifying examinations, from one to five.
• A graduate student who passes a PhD qualifying examination, as determined by the Graduate Committee, will receive credit for that examination toward the PhD requirements.
• If a student does not pass at least one PhD exam by the beginning of the fourth semester, the department will not guarantee financial support past the end of the fourth semester. However, if such a student passes one exam by the beginning of the fifth semester, then reinstatement of financial support will be considered.
• To remain in the PhD program, a graduate student must pass the written qualifying exam, with either the Pure Math or the Applied Math option, by the beginning of the sixth semester. A student who does not do this will be out of the PhD program.
• Any exceptional cases will be decided by the graduate committee.

Course Requirements

All Ph.D. students must take and receive a grade of P or higher in at least six courses from the following two lists:

• Comprehensive courses that are not basic courses for any of the three comprehensive exams passed by the student
• Algebra: Math 641, 643, 771, 774, 775
• Analysis: Math 657, 751, 753, 754, 857
• Applied Mathematics: Math 635, 761, 762, 768, 769, 892
• Geometry-Topology: Math 781, 782, 773, 775, 776

Furthermore, of these six courses every PhD student must take and receive a grade of P or higher in three courses numbered over 700 from the second tier list

A student taking a pure math option, respectively an applied math option, may replace one, respectively one or more, course/s in the second tier requirement with other graduate level courses inside or outside of the department. For each replacement course, the student must obtain permission, prior to registration, from both the adviser and the graduate director.

Any incomplete grades must be resolved within one year (ideally within one semester).

Oral Examination Requirement

When the student is prepared and has selected a direction for the PhD dissertation, the PhD candidate must pass an oral examination on material basic to the proposed dissertation area. The examination will be conducted by the PhD committee of the student, which consists of five faculty members and is chaired by the student’s adviser. The committee will recommend action to correct any deficiencies noted during the oral examination.

After passing the oral examination the candidate continues working in the area of concentration to complete the PhD dissertation.

Dissertation Defense

Computer language requirement.

A Master’s or PhD student must pass a computer language requirement by demonstrating a certain level of programming ability. Please note the following guidelines:

• Computer language requirements are the same for PhD and Master’s students.
• Passing the following courses at UNC will be sufficient to satisfy the computer language requirement: MATH 565, MATH 566, MATH 661, MATH 662, MATH 761, MATH 762, COMP 110, COMP 116, COMP 121, COMP 401
• Any computer science course which lists one of these courses as a prerequisite is also acceptable.
• A Master’s or PhD student may also satisfy the computer language requirement by passing an approved one semester undergraduate course on computer programming at any university.
• If the course title title on the transcript is not self-explanatory, then a syllabus, text or other information may be required. In all cases where there is some question about whether a course fulfills the requirement the Graduate Director will decide in consultation with the Graduate Committee.

Teaching Requirement

Students are required to take and successfully pass the TA Teaching Seminar, a special section of Math 920, during their first fall semester of their program. Students are also required to perform a minimum of two semesters of instructional service.

A semester of instructional service can be satisfied by any of the following:

• Teach one course: 12 hours
• Lead 4 recitations (includes 110L and 231L): 3 hours each
• Lead 2 labs (383L, 528L, 529L): 6 hours each

For Additional Information Contact

Ann Van Elsue Graduate Student Services Manager Phillips Hall 331A 919-962-4178 [email protected]

Graduate Degree Requirements

Graduate Handbook

The following information is a snapshot of all Master of Arts, Master of Science, and Ph.D. in Mathematics requirements from the University of Arizona Catalog. For full details on these requirements, please see the Mathematics Graduate Program handbook.

Master of Arts vs Master of Science in Mathematics

The Master of Science in Mathematics program requires a plan of study, professional development requirement, a thesis and examinations, and 30 units of approved graduate credit with differing parameters. 

See the Mathematics Graduate Handbook for more specific details.

Admission Requirements

Master of Arts (M.A.)

While both degrees require a Master's thesis, the Master of Arts degree requires more courses outside mathematics and has a teaching option intended for secondary school teachers. This degree often serves as a stepping stone towards the PhD but not as strongly as the Master of Science. 

Master of Science (M.S.)

While this degree also requires a thesis, the Master of Science degree requires a greater number of more advanced mathematics courses (technically those which are not co-convened). This degree often serves as a stepping stone towards the PhD but not as strongly as the Master of Science. The M.A. but especially the Master of Science often serve as a stepping stone towards the PhD.

Doctor of Philosophy (PhD) in Mathematics

The Doctor of Philosophy degree usually requires about five years to complete. Ph.D. requirements are far more in depth than those of the Masters programs. You can find more detailed information in the Graduate Handbook. Aside from generalized course requirements, all Ph.D. students are required to select a supporting minor, find a graduate faculty advisor, complete professional development requirements, complete a dissertation, and successfully defend the dissertation. Course requirements include 36 units of graduate credit in the major with an additional 18 units of dissertation ( MATH920 ).

Catalog Requirements

Doctor of Philosophy (PhD)

This is the degree for you if you plan to pursue a career in academic research, university teaching, or high-level research in industry or a government laboratory. The most important requirement is a dissertation which represents a substantial new contribution, of publishable quality, to the mathematical sciences. In fact, the point of the PhD degree is to prepare you to make and publish exactly this sort of contribution.

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Doctor of Philosophy in Mathematics

Department of Mathematics

Note: Students in this program can choose to receive the Doctor of Philosophy or the Doctor of Science in Mathematics. Students receiving veterans benefits must select the degree they wish to receive prior to program certification with the Veterans Administration. 

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The PDF includes all information on this page and its related tabs. Subject (course) information includes any changes approved for the current academic year.

College of Arts & Sciences

Prerequisites for Admission

To enter the program, students need the following:

• A Bachelor’s degree and/or a Master’s degree in Mathematics (completed by the start of the PhD program) with a minimum grade point average of 3.0.
• A strong background in theory and applied mathematics courses including at least three proof based courses (eg. real analysis, complex analysis, abstract algebra, etc).

Applications from students who do not satisfy all of the prerequisites but have a strong academic background in a field that draws significantly from mathematics (eg, statistics, economics, computer science, etc.) and have taken several mathematics courses may be considered under special circumstances. Applications from prospective students who are in the process of taking relevant prerequisite courses will be accepted and evaluated. It is important to understand that satisfying the prerequisites does not alone guarantee admission. Admission is highly competitive and is the result of a number of factors including academic record, letters of recommendation, breadth and depth of academic background and experience, and strength of academic institutions attended.

PhD in Mathematics

The PhD in Mathematics provides training in mathematics and its applications to a broad range of disciplines and prepares students for careers in academia or industry. It offers students the opportunity to work with faculty on research over a wide range of theoretical and applied topics.

Degree Requirements

The requirements for obtaining an PhD in Mathematics can be found on the associated page of the BU Bulletin .

• Courses : The courses mentioned on the BU Bulletin page can be chosen from the graduate courses we offer here . Half may be at the MA 500 level or above, but the rest must be at the MA 700 level or above. Students can also request to use courses from other departments to satisfy some of these requirements. Please contact your advisor for more information about which courses can be used in this way. All courses must be passed with a grade of B- or higher.
• Analysis (examples include MA 711, MA 713, and MA 717)
• PDEs and Dynamical Systems (examples include MA 771, MA 775, and MA 776)
• Algebra and Number Theory (examples include MA 741, MA 742, and MA 743)
• Topology (examples include MA 721, MA 722, and MA 727)
• Geometry (examples include MA 725, MA 731, and MA 745)
• Probability and Stochastic Processes (examples include MA 779, MA 780, and MA 783)
• Applied Mathematics (examples include MA 750, MA 751, and MA 770)
• Comprehensive Examination : This exam has both a written and an oral component. The written component consists of an expository paper of typically fifteen to twenty-five pages on which the student works over a period of a few months under the guidance of the advisor. The topic of the expository paper is chosen by the student in consultation with the advisor. On completion of the paper, the student takes an oral exam given by a three-person committee, one of whom is the student’s advisor. The oral exam consists of a presentation by the student on the expository paper followed by questioning by the committee members. A student who does not pass the MA Comprehensive Examination may make a second attempt, but all students are expected to pass the exam no later than the end of the summer following their second year.
• Oral Qualifying Examination: The topics for the PhD oral qualifying exam correspond to the two semester courses taken by the student from one of the 3 subject areas and one semester course each taken by the student from the other two subject areas. In addition, the exam begins with a presentation by the student on some specialized topic relevant to the proposed thesis research. A student who does not pass the qualifying exam may make a second attempt, but all PhD students are expected to pass the exam no later than the end of the summer following their third year.
• Dissertation and Final Oral Examination: This follows the GRS General Requirements for the Doctor of Philosophy Degree .

Admissions information can be found on the BU Arts and Sciences PhD Admissions website .

Financial Aid

Our department funds our PhD students through a combination of University fellowships, teaching fellowships, and faculty research grants. More information will be provided to admitted students.

More Information

Please reach out to us directly at [email protected] if you have further questions.

School of Science

Mathematical sciences, ph.d in mathematics.

Exploring New Theories at the Forefront of Mathematics and its Applications

Doctoral studies form our core graduate program.  The faculty in the department excel in numerous areas of applied mathematics and are well versed in many related disciplinary fields, thus they are highly qualified to train graduate students and mentor them in producing high-quality research and dissertations at the intersection of mathematics and the sciences or engineering.  Our Ph.D. training opens doors to research careers in academia, government laboratories, and industry and our department has a strong record of placing Ph.D. students in prestigious postdoctoral positions at top-tier universities and labs, and in industrial positions.

Students working for the doctorate must demonstrate high achievement both in scholarship and in independent research. All programs must follow the general rules of the Office of Graduate Education .

Program of Study

The Ph.D. degree results from following a program of study in mathematics or in applied mathematics.

Requirements

Students working for the doctorate must demonstrate high achievement both in scholarship and in independent research. All programs must follow the general rules of the Office or Graduate Education .

The student’s program of study must include:

• At least six, 4-credit (nonthesis) graduate mathematics courses (i.e., those with numbers MATH 6XXX or MATP 6XXX).
• At least one 3- or 4-credit course at the graduate (6000) level outside the department (i.e., not coded MATH or MATP and not cross-listed with any department course), selected in consultation with the math adviser.
• All doctoral students must pass a written preliminary exam as well as an oral qualifying examination and complete an oral candidacy presentation.

In addition, the course MATH 6591 Research in Mathematics is strongly suggested. Any deviations from these requirements must have the approval of the Department’s Graduate Committee.

The program catalog can be found here .

Resources frequently used by graduate students in Mathematics can be found here .

Program Outcome

Students who successfully complete this program will be able to:

• Demonstrate mastery of graduate-level courses covering a range of topics, including mathematical analysis, mathematical methods and modeling, computational mathematics, and operations research.
• Demonstrate mastery of graduate-level courses in at least one area outside of mathematics.
• Conduct high-quality original research on a topic in mathematics or applied mathematics with results suitable for journal publications and technical presentations.
• Read and interpret research level articles in mathematics and develop new mathematical concepts.
• Develop mathematical formulation and solution of scientific problems from a range of disciplines.
• Communicate sophisticated mathematical ideas and concepts concisely and effectively in both oral and written form.

Financial Aid

There are several potential ways that a Math Sciences graduate student can get financial support while enrolled at RPI. The most common methods are:

Fellowships

There are many opportunities for students to obtain fellowships to support their graduate studies.  These fellowships can come from inside or outside the department or the Institute.  For example, recent fellowships have been available from the Department of Education, and there are competitive fellowships available from the National Science Foundation. The specifics of fellowships vary from year to year, and the  Graduate Student Coordinator has information on available fellowships and application procedures.  Your academic advisor in the department is another good source of information about fellowships. You should be sure to consider that the Math Sciences Department has guidelines for continuation of support for doctoral students. Graduate students who receive full support from the Department should plan to complete their doctoral programs within four or five years. Students can expect that their support will continue through this period, provided that they continue to make satisfactory progress toward their degree and they continue to perform well in their teaching assignments. "Satisfactory progress" means completing courses, required examinations (preliminary, qualifying, and candidacy), selecting a research area, and making progress toward completing a thesis. If a student requires support beyond the fifth year, each situation will be considered individually.

Teaching Assistantship

Teaching Assistant (TA) assignments vary significantly throughout Rensselaer Polytechnic Institute. In the Department of Mathematical Sciences, TA-ships are typically one-year appointments that cannot be extended for more than two years. They tend to be of two types. TA-ships can take the form of independent classroom teaching (often called recitations), which may include small lectures, problem solving, computer labs, grading, office hours, etc. The TA works with a TA Supervisor, who is the faculty member teaching the course. The vast majority of TA-ships are of this form. A few teaching assistantships take the form of grading and office hours only. All TA’s are required to participate in RPI’s TA Training Program as well as the Department’s TA Orientation prior to their first semester of teaching. In addition, all TA’s must attend the TA Seminar before or during their first semester of teaching at RPI. A graduate student, the Math Sciences Department Master TA, typically teaches this one-credit course (graded as Satisfactory/Unsatisfactory). The topics of this course vary according to the needs of the participants. In the past they have included: Maple, Grading, Laptops, Composing Quizzes, Campus Resources, Academic Honesty, Proctoring Exams, Extra Help, Office Hours, Latex, Making a Syllabus, etc.  In addition, each TA has their class visited and feedback is provided.

Research Assistantship

Many faculty in the Math Sciences Department have research funding that can be used to support graduate students who are interested in doing research in their field. The Research Assistantships (RA’s) do not typically have any teaching component. This allows a graduate student to have more time to work on Master’s or Ph. D. research. This is a topic you may want to talk to your advisor about.

Academic Opportunities

Graduate Academic Awards

Academic awards for graduate students who demonstrated outstanding ability in his or her academic work.

SIAM Student Chapter at RPI

SIAM exists to ensure the strongest interactions between mathematics and other scientific and technological communities through membership activities, publication of journals and books, and conferences.

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University of Louisiana at Lafayette

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Requirements.

A student working towards a PhD in mathematics is expected to major in one of the areas of mathematics in which there is active faculty research interest. The areas are divided into three concentrations:

• Applied Mathematics (including Mathematical Biology, Numerical Analysis, Ordinary Differential Equations, and Partial Differential Equations);
• Pure Mathematics (including Algebra, Analysis, and Topology); and,
• Statistics.

The requirements for the PhD in Mathematics are described below.

Time and residency

A PhD student must successfully complete a minimum of two semesters of full-time consecutive graduate study, not including summer sessions. All degree requirements must be completed within six calendar years following advancement to candidacy in the PhD program.

A PhD student must complete a minimum of seventy-two semester hours of credit beyond the Bachelor's degree. At least forty-eight of these semester hours must be in regular course work. At least twenty-four of these semester hours must be in dissertation research (MATH 699). More information...

Comprehensive examinations

Written comprehensive exams.

One of the milestones on your progress toward the PhD is successful completion of your written comprehensive exams. More information...

Oral comprehensive examination

Another milestone on your progress toward the PhD is successful completion of your oral examination. More information...

Language requirement

A PhD student must demonstrate knowledge in two languages other than English and the student's native language (if different from English). More information...

PhD dissertation

A PhD student must complete a dissertation. The dissertation must represent an original contribution to applied mathematics, pure mathematics, or statistics, and must be of such quality as to be publishable in an appropriate professional journal. More information...

MS for PhD candidates

A PhD student who has completed all the requirements for the MS degree may petition the Graduate School for the MS degree. The student will need to complete and submit the appropriate forms and pay the relevant fees. The department does not require PhD students to obtain an MS before obtaining the PhD. They may do so if they so desire and have fulfilled the relevant requirements from both the department and the Graduate School, and it is something that is well worth considering.

Regular status

Some students are admitted in "conditional status"; this includes all international students who do not have a degree from an American university, and students who were admitted with low GPA and/or low GRE test scores. Students who are admitted in conditional status must file a Petition for Regular Status with the Graduate School as soon as they successfully complete 12 hours of graduate credit with a 3.0 GPA or better and no more than one grade of C; and/or they submit satisfactory standardized test results. The Petition for Regular Status form is available under the Current Graduate Students Forms tab at the Graduate School forms and resources web page .

After a PhD student has completed the oral comprehensive exam, he or she may apply for PhD candidacy early in that semester. This is done by filing an Application for Doctoral Candidacy form.  The form must be filed before the student can obtain the degree. The Application Doctoral Candidacy form is available under the PhD Student Forms tab at the Graduate School forms and resources web page .

Eligibility

A student may become "ineligible to continue in Graduate School" should the student receive two grades of C, a grade lower than a C, or if his or her GPA drops below 3.0. A student will also become ineligible if, after having successfully appealed ineligible status once, he or she receives one more grade of C or below. If this occurs, the student will be unable to enroll in courses, and will not be able to receive financial assistance from the department or university. More information...

The Graduate School has a Doctor of Philosophy Degree Checklist that the student should consult; it includes the steps required for graduation. The Doctor of Philosophy Degree Checklist is available at the Graduate School "Staying on Track" Checklist web page .

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PhD Degree Requirements

Updated on August 15, 2023

A PhD candidate must satisfy the requirements for a doctoral degree as laid out by the UW Graduate School.  Some of the key Graduate School requirements and additional requirements from the Mathematics Department are listed below.  If you have questions about the requirements, please contact your preliminary advisor, Student Services or the Graduate Program Chair.  

Three years of full time study, two of which must be at the University of Washington.

All PhD students must take twelve 500-level numerically graded courses in Mathematics, Applied Mathematics, or Statistics in their first two years of study.  Students are expected to take seven quarters of core courses; at least five of them in their first year. The current list of core courses consists of MATH 504, MATH 505, MATH 506; MATH 524, MATH 525, MATH 534; MATH 544, MATH 545, MATH 546.  Courses from other departments may be included in the twelve with approval of the Graduate Program Coordinator.  Students who have already met their core course requirement may take additional core courses for a grade of S/NS. It is the student’s responsibility to select S/NS credit if they w ish to use this option . 

The seven quarters of core courses requirement only applies to students who are entering our PhD Program in September 2023 or later.  

Writing Milestone :

By the end of the second year, each student must produce a carefully written mathematical document. This could be in any area, not just a presumed area of specialization, with any faculty member, not just a potential advisor. Such a document can be an expository paper coming from deep study of material in a reading course with a faculty member, a write-up of a project done under the supervision of a faculty member, an existing research paper that the student has done could also count, if a faculty member agrees. In general, this is flexible but the resulting document must be substantial .  

The writing milestone requirement only applies to students who are entering our PhD Program in September 2023 or later.  

General Examination:

The General Examination is an oral examination on a special area of intended research, given by a committee after the student has passed the preliminary exams. This exam can be given only after two years of graduate study, to students who have formally declared an advisor, and have formed their thesis committee with the Graduate School. Normally, it should be taken by the middle of the student's fourth year. In extenuating circumstances, the exam can be postponed if approved by the Graduate Committee. In addition, the students must prepare a written General Paper and distribute it to the committee at least two weeks before the date of the General Exam. The content of this paper is decided upon in consultation with the committee. For example, this might be a 10-20 page expository account of the student's research area, culminating in a problem or list of problems to be studied, together with a discussion of some of the relevant literature.

A PhD thesis must be a well-written original contribution to the scientific literature.  This document will be archived by the University of Washington Library.   During the preparation of the thesis, a student must take 27 credits of Math 800 required over a period of at least three quarters.

Final examination:.

The PhD thesis defense is the Final Examination.  The defense is an oral exam given by the thesis committee consisting of the advisor as the chair of the committee, two additional members of the department who have been appointed to the Graduate School, plus one member of the committee from outside the Math Department called the Graduate School Representative (GSR).  Successful completion of the exam is required for the PhD.

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Phd in mathematics: requirements, salary, jobs, & career growth, what is phd in mathematics.

A PhD in Mathematics is a highly specialized degree that entails completing original research in a specific area of mathematics and making a significant contribution to the field.

Students in a PhD program generally take advanced mathematics courses to expand their understanding of the subject and to obtain the abilities needed to undertake research.

They collaborate extensively with faculty mentors and other researchers to create a research project that takes several years to finish.

A PhD in Mathematics study typically results in the discovery of new mathematical theories, proofs, or algorithms that can be applied in a variety of domains such as computer science, physics, finance, and engineering.

A PhD in Mathematics is a tough and rigorous curriculum that needs great mathematical competence, strong analytical skills, and endurance.

Graduates of mathematics PhD programs frequently move on to positions in academia, research, or business, where they can use their mathematical skills to solve challenging issues and make substantial contributions to their field.

How much money do people make with a PhD in Mathematics?

Individuals with a PhD in Mathematics can expect to earn more than those with a bachelor’s or master’s degree in the subject.

As of May 2020, the median annual income for mathematicians and statisticians, which includes individuals with a PhD in Mathematics, was $96,660, according to the US Bureau of Labor Statistics.

However, depending on the field and region, earnings might range from $59,500 to more than $160,000 per year.

I ndividuals with a PhD in Mathematics are frequently employed in academia, where salaries vary according to the type of institution, rank, and years of experience.

For the 2021-2022 academic year, the median income for full-time faculty members in the mathematical sciences was $92,000, according to the American Mathematical Society.

What is expected job growth with PhD in Mathematics?

According to the U.S. Bureau of Labor Statistics, employment of mathematicians and statisticians, which includes people with a PhD in Mathematics, is expected to expand 33 percent from 2020 to 2030, substantially faster than the national average.

The rising use of data and the need for quantitative analysis in a range of areas, including healthcare, finance, and technology, are projected to drive this expansion.

Scientific research and development services, which are expected to grow 48 percent from 2020 to 2030, and management, scientific, and technical consulting services, which are expected to grow 37 percent over the same period, are expected to see the most growth in mathematicians and statisticians’ employment.

What can you do with a PhD in Mathematics?

Individuals holding a PhD in Mathematics have numerous job options. Here are a couple such examples:

1. Academia: Individuals with a PhD in Mathematics can pursue academic careers such as professorships or research positions in universities or research institutions. Graduate students and postdoctoral researchers can also be supervised by them.

2. Data Science: As the amount of data in many businesses grows, there is a great demand for people with extensive mathematical skills who can work as data scientists, data analysts, or statisticians.

3. Financial Services: Individuals with a PhD in Mathematics can work as quantitative analysts, risk managers, or financial analysts in the financial industry.

4. Technology: Individuals with a PhD in Mathematics can work in technology organizations as data scientists or machine learning engineers, thanks to the rising use of artificial intelligence and machine learning.

5. Government Agencies: Individuals with a PhD in Mathematics can work for government organizations such as the National Security Agency (NSA), the Department of Defense, or the National Aeronautics and Space Administration (NASA) in positions such as cryptographers, systems analysts, or aerospace engineers.

6. Consulting: Individuals with a PhD in Mathematics can work for consulting firms, where they can provide analytical and modeling services to clients in a variety of industries.

What are the requirements for a PhD in Mathematics?

The specific requirements for obtaining a PhD in Mathematics can vary depending on the institution and program, but generally, the following are common requirements:

1. Bachelor’s or Master’s Degree: Applicants to most PhD programs in Mathematics must have a Bachelor’s degree from a recognized university. Although it is not usually required, certain schools may accept applicants with a Master’s degree in a related discipline.

2. Academic Transcripts: Applicants are usually expected to present certified transcripts of their undergraduate and graduate education, which demonstrate their academic performance and achievement.

3. Statement of Purpose: Applicants are typically expected to provide a personal statement or statement of purpose detailing their research interests, academic ambitions, and reason for pursuing a PhD in Mathematics.

4. Standardized Test Scores: Applicants to many PhD programs may be required to submit scores from standardized tests such as the Graduate Record Examination (GRE) or other related assessments.

5. Letters of Recommendation: Applicants to PhD programs in Mathematics are frequently required to provide letters of recommendation from academic or professional sources who may speak to the applicant’s academic talents, research potential, and eligibility for a PhD program.

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How long does it take to get a phd in mathematics.

The length of time it takes to earn a PhD in Mathematics can vary depending on a number of factors, such as the program’s structure, the student’s progress, and the research area. However, in general, it takes around 4-6 years to complete a PhD in Mathematics in the United States.

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Do you need a masters in mathematics to get a phd in mathematics.

In most circumstances, a master’s degree in mathematics is not required to pursue a PhD in mathematics.

Many PhD programs in Mathematics accept students who have a bachelor’s degree in Mathematics or a related field and a strong academic record and research potential.

However, some PhD programs may offer a master’s degree as part of the PhD requirements. This is known as a “master’s on the way to a PhD” program.

In this instance, students would normally complete the master’s degree coursework and research requirements before enrolling in the PhD program.

What are the Best PhD in Mathematics Degree programs?

1. massachusetts institute of technology (mit) 2. university of california, berkeley 3. stanford university 4. harvard university 5. princeton university 6. university of chicago 7. california institute of technology (caltech) 8. university of michigan 9. new york university (courant institute) 10. university of texas at austin, leave a comment cancel reply.

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Study Postgraduate

Phd in mathematics (2022 entry), explore our phd in mathematics.

The PhD in Mathematics offers an intellectually stimulating and dynamic atmosphere research in both pure and applied mathematics. Study at the University of Warwick's Mathematics Institute, ranked 3rd in the UK in REF 2014, an international centre of research excellence.

Course code

3 October 2022

3 to 4 years full-time

Qualification

Mathematics Institute

University of Warwick

About this research graduate course

Course overview.

Mathematics at Warwick covers a full range of both pure and applied areas. The Mathematics Postgraduate Degrees are appropriate for students with a strong and broad mathematical background who wish to continue to focus on primarily mathematical questions 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 aim is to produce excellent PhD students who have undertaken high quality original research and who are well-prepared for a career, either in academia or elsewhere.

Teaching and Learning

Students are required to complete a series of modules in theirs 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 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 integrated MA, MMath or MSc degree in Mathematics or a science degree with high mathematical content.

English language requirements

You can find out more about our English language requirements . 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 .

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.

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.

Taught course fees   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. Information about department specific costs should be considered in conjunction with the more general costs below, such as:

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.

Mathematics Funding Opportunities

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

Living costs

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

Mathematics at Warwick

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

Find out more about us on our website

Our courses

• Interdisciplinary Mathematics (Diploma plus MSc)
• Interdisciplinary Mathematics (MSc)
• Mathematical Sciences (MASt)
• Mathematics (Diploma plus MSc)
• Mathematics (MSc)
• Mathematics of Systems (MSc leading to PhD)
• Mathematics (PhD)
• Mathematics of Systems (PhD)

Taught course applications

Here is our checklist on how to apply for taught postgraduate courses at Warwick.

Research course applications

Here is our checklist on how to apply for research postgraduate degrees at the University of Warwick.

After you’ve applied

Find out how we process your application.

Applicant Portal

Track your application and update your details.

Admissions statement

See Warwick’s postgraduate admissions policy.

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Ask questions and engage with Warwick.

Postgraduate Open Day

Postgraduate fairs.

Throughout the year we attend exhibitions and fairs online and in the UK. These events give you the chance to learn about our Master's and PhD study routes, and the wider context of postgraduate study.

Find out more

Every week, you can connect directly with representatives from Warwick, who will be answering your questions on applying to and studying postgraduate studies at Warwick.

Sign up for Live Chats

Departmental events

Some academic departments hold events for specific postgraduate programmes, these are fantastic opportunities to learn more about Warwick and your chosen department and course.

See our online departmental events

Connect with us

Want to hear more about postgraduate study at Warwick? Register your interest and find out more.

Learn more about Postgraduate study at the University of Warwick.

Why Warwick

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

6th in the UK (The Guardian University Guide 2022) Link opens in a new window

64th in the world (QS World University Rankings 2023) Link opens in a new window

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(The Graduate Market in 2022, High Fliers Research Ltd. Link opens in a new window )

About the information on this page

This information is applicable for 2022 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.