Mathematics

The Mathematics program at Purdue University – West Lafayette offers a comprehensive and rigorous education designed to develop critical thinking, problem-solving skills, and a deep understanding of mathematical concepts essential for various scientific, technological, and academic pursuits. This undergraduate Bachelor of Science degree provides students with a strong foundation in pure and applied mathematics, including calculus, algebra, analysis, differential equations, linear algebra, and discrete mathematics. The curriculum emphasizes both theoretical understanding and practical application, preparing students for diverse career paths such as data analysis, actuarial science, computer science, engineering, education, research, and graduate studies. Throughout the program, students have opportunities to engage in cutting-edge research, participate in internships, and collaborate with faculty on innovative projects. The program aims to equip graduates with quantitative reasoning skills, analytical capabilities, and an appreciation for the beauty and utility of mathematics. With a dedicated team of experienced faculty members and state-of-the-art facilities, students receive personalized mentorship and guidance to support their academic and professional goals. Purdue’s Mathematics program is also designed to foster a strong sense of community, encouraging collaboration and intellectual growth among students, while providing numerous extracurricular activities and organizations to enrich the educational experience. Graduates of the program are well-prepared to contribute to scientific advancements, solve complex real-world problems, and succeed in a wide range of careers that require mathematical expertise. Whether students are interested in pursuing advanced degrees or entering the workforce directly, Purdue Mathematics offers a stimulating environment that challenges and inspires future mathematicians and innovators.

Besides satisfying the general regulations of the Graduate School for the degree of Doctor of Philosophy, the student must comply with the following requirements.

(A) Qualifying Examinations. The student must pass four written examinations chosen as described below. The exams are based on material that is covered in the courses listed and on material from undergraduate prerequisites. Credit for passing a similar examination at another university cannot be transferred.

The Qualifying Examinations are written examinations offered twice a year during week long Qualifier Exam Sessions the week before classes start in August and January. Each examination is written and graded by a faculty member or a committee of faculty members chosen by the Graduate Committee.

The following four subject areas are called the Core 4 Areas

• Complex Analysis (MA 530)
• Real Analysis (MA 544)
• Abstract Algebra (MA 553)
• Linear Algebra (MA 554)

The qualifier exam subject areas are the Core 4 Areas plus the following Area Exams.

• Numerical Analysis (MA 514)
• Probability (MA 519)
• Partial Differential Equations (MA 523)
• Differential Geometry (MA 562)
• Topology (MA 571)

The student must pass at least two exams from the Core 4 Areas, including at least one of 544 or 553. They must also pass two more exams from the Area Exams and the unused two exams from the Core 4.

The Qualifier Deadline for students who enter the program with a master's degree is the January Qualifier Exam Session of their second year. The Qualifier Deadline for students without a master's degree is the January Qualifier Exam Session of their third year. Students who have not passed the four exams on or before the session of their Qualifier Deadline will have their privileges to continue in the Mathematics PhD program terminated.

Each Qualifier Exam can be attempted a maximum of three times and students may attempt as many Qualifier Exams as they wish at any Qualifier Session on or before their Qualifier Deadline. Qualifying exam grades will not be part of your transcript.  

(B) Language. The student must satisfy the foreign language requirement in one of French, German, or Russian. Any of the five options approved by the Graduate School may be used to meet this requirement. They are listed below:

1. By satisfying the foreign language requirement at another grad school and transferring the record to Purdue.
2. By passing four semesters of Purdue’s undergraduate course sequence in an acceptable language with at least a grade of a C- in the last course, or with an equivalent of this requirement transferred from another institution.
3. By examination from one of the department listed above.
4. By graduate coursework. This option is only available in French, German, and Russian. Math will only accept the courses of 603 or 603 and you should take them P/F.
5. If your native language is one of the above languages then you can be exempted from this requirement. See the Graduate Coordinator for more information.

This foreign language requirement is to be met by the student’s Advanced Topics Exam deadline as described in (C) below. In special cases, The Graduate Committee may grant an extension of this deadline.

(C) Advanced Topics Examinations. A student becomes eligible to take the Advanced Topics Examination after passing the Qualifying Examinations. The Advanced Topics Examination serves as the Preliminary Examination in the Department of Mathematics Ph.D. program.

Before taking the Advanced Topics Exam the student must have already passed all of their Core 4 courses with a B- or better( or have passed the corresponding qualifying exam in lieu of taking the course). The Core 4 courses are: MA 530, 544, 553, 554.

After passing the Qualifying Examinations, a student must find a faculty member willing to serve as the Advanced Topics Examination Coordinator. This Coordinator, once identified, begins to serve as the student's academic advisor, counseling the student and signing course registration forms. Usually the Coordinator becomes the student's thesis advisor, provided the student passes the Advanced Topics Examination. The student must meet with the Coordinator to prepare an Advanced Topics Examination Proposal Form, which is to be filed in the Graduate Office at least one month prior to the examination date. Once this form has been filed the student must then file their Plan of Study with the Graduate School.

The Advanced Topics Proposal form lists the Coordinator, two courses beyond the qualifying level on which the student is to be examined (or a body of mathematics roughly equivalent to this), and one other faculty member who, with the Coordinator, administers the Advanced Topics Examination. At the discretion of the Coordinator, the examination may also cover a third subject, possibly with a third examiner. The examinations may be oral or written, and may be given separately or together. The conditions of the examination are specified on the Advanced Topics Examination Proposal Form, which must be approved and signed by the Coordinator, the student, and the Graduate Committee Chair at least one month prior to the exam date. To pass the examination requires agreement of all members of the committee and the consent of one to serve as the student's thesis advisor. While this is usually the Coordinator it need not be.

A student may take the Advanced Topics Examination at most twice; however, the examination should be passed within one and one half years of passing the Qualifying Examinations. In special cases the Graduate Committee may grant an extension of this time limit. Each time the examination is taken, a new Advanced Topics Examination Proposal Form must be filed in the Graduate Office. 

(D) Plan of Study. The plan of study should be submitted electronically to the Graduate School through MyPurdue by each student at least one month before passing the Advanced Topics Examinations. The student must arrange for an advisory committee to approve the plan of study, with the chair being the supervisor of thesis research. If you select a chair from outside the Mathematics Department then you must select a Mathematics faculty member to serve as a co-chair on your committee. This advisory committee must have at least half of its members with a faculty appointment over 50% in the Department of Mathematics. Substitutions in course requirements and the transfer of master’s degree credits from other universities may be permitted with the approval of the advisory committee and the Graduate Committee. The Plan of Study Generator (POSG) may be accessed via the MyPurdue portal at http://mypurdue.purdue.edu (see section X).

The plan of study must include:

1. At least a total of 42 hours of Purdue graduate course work. However, all applicable courses (only those graduate courses with a letter grade) should be listed on the plan of study with the exception of any courses used for a Purdue Master's degree. A completed plan of study must list courses with at most two grades of C and all other grades of A or B. (A total of 90 credit hours are required for the Ph.D. degree, but this total includes thesis research MA 699, which is not included on the plan of study.)
2. At least three courses (nine credit hours) at an advanced level in the field of specialty or closely related to it. Reading courses and seminars may be included.
3. The courses MA 530, 544, 553, and 554 and two courses from among MA 514, 519, 523, 562, 571, 572, and 585. A student can avoid taking any of these courses by passing the qualifier exam in the subject.
4. For students in applied mathematics, at least two courses selected from CS 514, 515, 614, 615, and one course that uses advanced mathematics, taken outside the mathematical sciences.
5. For students in numerical analysis, at least two courses selected from MA 523, 543, 611, 642, 643.

(E) Preliminary Examination. The Advanced Topics Exam serves as the Preliminary Examination in the Math Ph.D. program. Graduate School regulations require that at least two sessions (including summer sessions) must elapse between the preliminary examination and the thesis defense. A request form must be submitted to the Graduate Office at least one month prior to the examination date. The Graduate office will fill this form out for you after you have submitted your Advanced Topics Proposal Form to the Graduate Office and your Plan of Study is on file with the Graduate School. If a student has an advisor who is not in the Department of Mathematics then an advisory committee must be approved by the Graduate Committee of the Department of Mathematics. (For example, this could be the case for a student in the CS&E program.) This advisory committee must have at least half of its members with a faculty appointment over 50% in the Department of Mathematics. In this case, a preliminary examination may be required. The purpose of this exam is to ensure that the proposed thesis problem(s) is chiefly mathematical in nature, and that a thesis on this topic is appropriate as a thesis in the Department of Mathematics. A report on the preliminary examination shall be made in writing to the Graduate Committee of Mathematics discussing the proposed project, with particular emphasis on the mathematical content. The Graduate Committee will then make the final decision whether the thesis topic is acceptable.

(F) Admission to Candidacy. To be admitted to candidacy for the Ph.D. degree, the student must fulfill the preceding requirements.

(G) Dissertation. A thesis must be submitted in final form presenting new results of sufficient importance to merit publication. The student must distribute copies of their thesis to their committee for review at least two weeks before their defense is scheduled, or at the discretion of the students’ advisor, the thesis defense can be postponed to a later date. The student must present the contents of the thesis before an examining committee consisting of a minimum of four faculty members in an open colloquium or seminar. At least half of the examining committee must have a faculty appointment over 50% in the Department of Mathematics. The thesis must be acceptable to this committee. A request form for the appointment of the final examining committee must be received by the Graduate School not later than one month before the examination. The thesis must meet departmental and University format requirements. The Graduate Office will provide the necessary information.

(H) Recommendation for the Ph.D. Degree. If the above requirements are met within the time limits stated below, the candidate will be recommended to the faculty to receive the degree of Doctor of Philosophy.

(I) Time Limits for Completion of the Ph.D. Degree. Seven years from entry into the graduate program (i.e., 14 semesters plus the intervening summers - plus one additional summer to finish if necessary) is the maximum time allowed to complete the Ph.D. in the Mathematics Department. An additional year may be allowed if requested by the student's Thesis Committee and approved by the department's Graduate Committee. Any exceptions to this policy will require approval by the Department Head.

(J) Financial Support. Continued financial support by the Mathematics Department will depend on satisfactory academic progress and satisfactory performance in teaching and/or research duties. The Graduate Committee urges students to complete the Ph.D. within seven years since financial support will be terminated after that time. The Mathematics Department requires that their students always maintain full-time enrollment, in fall and spring that is at least 8 credit hours and in summer at least 6 credit hours.

(K) Research in Absentia. Research in absentia is possible only for students who have fulfilled the requirements (A) through (E) in section IV and are well into a research program. A request for permission from the Mathematics Department to do research in absentia requires the approval of the major professor, the Graduate Committee Chair, and the Graduate School. This form must be filed one month prior to the start of the session in which research in absentia registration is requested.

The Graduate School application fee is $60 (U.S. dollars) for domestic applicants and $75 (U.S. dollars) for international applicants. The deadline for applications is January 15.

Applicants should arrange to take the GRE General Test and the GRE Math Subject Test (Institution Code: 1631, Department Code 0703) enough in advance so that scores are received by the department before January 15.

Non-native English speakers need to obtain a minimum score of 570 on the paper-based TOEFL exam or 230 on the computer-based exam. The following minimum scores are required for the iBT: Reading 19, Listening 14, Speaking 18, Writing 18 and an overall score of at least 77. An official score report not more than two years old must be submitted (Institution Code 1631, Department Code 72).

Scholarships

Fellowships

Beginning graduate students who intend to work toward the Ph.D. degree will be considered for fellowships. Some of these fellowships include the Andrews, Ross, Lynn, Knox, Purdue Doctoral, and Puskas Fellowships. These fellowships provide a stipend of $21,000-$23,000 or more for twelve months with all tuition remitted. An additional stipend is provided to cover insurance costs. These fellowships have tenures ranging from 1 to 2 years, after which the student will be supported with a departmental teaching assistantship or research assistantship up to a total of seven years provided satisfactory academic progress towards the Ph.D. is made.

Research fellowships are available for advanced students for both the summer and the academic year.

Purdue University is a tenable school under the provisions set forth by the Fannie and John Hertz Foundation. Hertz Fellowships cover tuition and all fees plus a $25,000 annual stipend. Students apply directly for this fellowship.

Teaching Assistantships

Students who do not receive fellowships will be given graduate teaching assistantships with stipends ranging from $14,670 to $16,020 per academic year with a minimum of $16,020 for most successful applicants who can be assigned to classroom teaching. Half-time assistants usually teach four hours per week. Fees are remitted to several hundred dollars a semester and reduced insurance costs. Teaching assistant training and mentoring is provided by the Assistant to the Head.

The Mathematics program at Purdue University - West Lafayette offers students a comprehensive education in pure and applied mathematics, preparing them for diverse career paths in academia, industry, and government. The curriculum is designed to develop strong analytical, problem-solving, and quantitative reasoning skills, essential for tackling complex challenges across various fields. Students have the opportunity to explore fundamental areas such as algebra, calculus, geometry, discrete mathematics, probability, and statistics. Advanced courses allow for specialization in areas like pure mathematics, applied mathematics, and mathematical modeling, enabling students to tailor their educational experience to their interests and career goals. The program emphasizes both theoretical understanding and practical application, often incorporating research projects, internships, and collaborative work to foster real-world experience. The university's faculty includes renowned mathematicians who guide students through innovative research and mentorship programs. Purdue University also provides resources such as state-of-the-art computational labs, tutoring centers, and student organizations dedicated to mathematics. Graduates of the program are well-equipped for graduate studies or employment in fields such as data science, finance, software development, engineering, and education. The program's rigorous coursework and vibrant academic community aim to cultivate critical thinking, creativity, and intellectual curiosity. Overall, Purdue's Mathematics program strives to produce graduates who are capable of contributing significantly to scientific and technological advancements, equipped with a strong foundation in mathematical theory and its applications in the modern world.