Mathematics

The Princeton University Mathematics program offers a comprehensive and rigorous education in pure and applied mathematics, designed to develop students' analytical skills, problem-solving abilities, and critical thinking. The curriculum is tailored to provide a thorough grounding in fundamental mathematical concepts, including algebra, calculus, geometry, topology, number theory, and mathematical analysis, while also offering opportunities to explore advanced topics such as mathematical logic, combinatorics, and differential equations. Students benefit from close interactions with distinguished faculty members who are leaders in their fields, engaging in original research projects, seminars, and collaborative problem-solving exercises that foster a deep understanding of mathematical theories and their real-world applications. The program emphasizes both theoretical understanding and practical application, preparing students for careers in academia, industry, finance, data science, cryptography, and technology. Students are encouraged to participate in internships, research assistantships, and summer programs that enhance their learning experience and professional development. Princeton's state-of-the-art facilities, resource-rich environment, and vibrant intellectual community support innovative exploration and discovery across all levels of study. Whether pursuing an undergraduate major or engaging in advanced graduate research, students are equipped with the mathematical tools necessary to address complex problems and contribute to scientific advancements. The program also benefits from Princeton’s interdisciplinary approach, enabling students to integrate mathematical techniques with fields such as physics, computer science, economics, and engineering. Graduates of the Princeton Mathematics program are well-prepared for doctoral studies, influential research careers, or leadership positions in industry and government agencies, where quantitative analysis and logical reasoning are invaluable. Overall, Princeton’s Mathematics program offers an inspiring academic journey that challenges students to think deeply, innovate, and excel in diverse and evolving disciplines.

Courses:

The department offers a broad variety of research related courses as well as introductory (or “bridge”) courses in several areas, which help first-year students strengthen their mathematical background. Students also acquire standard beginning graduate material primarily through independent study, and consultations with the faculty and fellow students.

Language(s):

Students must satisfy the language requirement by demonstrating to a member of the mathematics faculty a reasonable ability to read ordinary mathematical texts in one of the following three languages: French, German or Russian. The language test must be passed before the end of the first year, and before standing for the general examination.

Pre-Generals Requirements(s):

Seminars

The department offers numerous seminars on diverse topics in mathematics. Some seminars consist of systematic lectures in a specialized topic; others present reports by students or faculty on recent developments within broader areas. There are regular seminars on topics in algebra, algebraic geometry, analysis, combinatorial group theory, dynamical systems, fluid mechanics, logic, mathematical physics, number theory, topology and other applied and computational mathematics. Students may also attend, without fees or formalities, seminars in the School of Mathematics at the IAS.

The department also facilitates several informal seminars specifically geared toward graduate students: (1) Colloquium Lunch Talk, where experts who have been invited to present at the department colloquium will give introductory talks, which allows graduate students to understand the afternoon colloquium more easily; (2) Graduate Student Seminar (GSS), which is organized and presented by graduate students and helps in creating a vibrant mathematical interaction among the graduate students; and, (3) What’s Happening in Fine Hall (WHIFH) seminar, where faculty members present talks in their own research areas specifically geared towards graduate students. Reading seminars are also organized and run by graduate students.

General Exam:

First-year students are set on the fast track of research by choosing two advanced topics of research, beyond needing a strong knowledge of three more general subjects – algebra, and real and complex analysis, as part of the required general exam. Depending upon individual preparation, a student may take the general exam in the first or second year of study.  The two advanced topics are expected to come from distinct major areas of mathematics, and the student’s choice is subject to the approval of the department. Usually by the second year, students will begin investigations of their own that lead to the doctoral dissertation.

General Exam in Mathematical Physics

For a mathematics student interested in mathematical physics, the general exam is adjusted to include mathematical physics as one of the two special topics.

Qualifying for the M.A.:

The Master of Arts (M.A.) degree is considered an incidental degree on the way to full Ph.D. candidacy and is earned after a student successfully passes the language requirement as well as the general exam, and is recommended by the faculty. It may also be awarded to students who, for various reasons, may leave the Ph.D. program, provided that these requirements have been met.

Teaching:

During the second, third and fourth years, graduate students are expected to either grade or teach two sections of an undergraduate course, or the equivalent, each semester. Although students are not required to teach in order to fulfill department Ph.D. requirements, they are strongly encouraged to do so at least once before graduating. Teaching letters of recommendation are necessary for most postdoctoral applications.

Post-Generals Requirement(s):

Selection of a Research Adviser

Upon completion of the general examination, the student is expected to choose a thesis adviser.

Dissertation and FPO:

Two to three years is usually necessary for completion of a suitable dissertation. Upon completion and acceptance of the dissertation by the department and Graduate School, the candidate is admitted to the final public oral examination, in which the dissertation is presented and defended by the candidate.

The Ph.D. is awarded after the candidate’s doctoral dissertation has been accepted and the final public oral examination sustained.

• Application Fee: $90
• Statement of Academic Purpose
• Resume/Curriculum Vitae
• Recommendation Letters
• Transcripts
• Fall Semester Grades
• Prerequisite Tests
• English Language Tests
• GRE : General and mathematics subject tests.

For Ph.D. candidates, tuition and fees during a student’s regular period of enrollment are provided in full from a student’s graduate student financial support, in the form of tuition support from fellowships, assistantships, or external sources.

The annual stipend amount provided to Ph.D. candidates during their regular enrollment is intended to support a single graduate student based on estimated costs. Master’s students or students with spouses and/or dependents may require additional resources to support their living expenses 

The Mathematics program at Princeton University is one of the most prestigious and comprehensive undergraduate and graduate programs in the world. It offers students the opportunity to engage deeply with pure mathematics, applied mathematics, and interdisciplinary areas that involve mathematical methods. The undergraduate curriculum covers a broad spectrum of mathematical disciplines, including algebra, analysis, geometry, topology, and number theory, along with advanced courses in mathematical logic, combinatorics, and mathematical physics. Students are encouraged to develop their problem-solving skills through problem sets, research projects, and participation in seminars and mathematical competitions.

At the graduate level, Princeton's Department of Mathematics provides rigorous coursework and research opportunities across various fields, including differential geometry, algebraic geometry, mathematical physics, and number theory. The program fosters close collaboration between students and faculty, many of whom are leaders in their fields, and promotes original research leading to the Ph.D. degree. The university's distinctive approach emphasizes both theoretical understanding and practical application, preparing students for careers in academia, industry, finance, data science, and beyond.

Princeton's Mathematics Department is known for its strong community, rich history of mathematical discoveries, and contributions to both pure and applied mathematics. The university offers various resources, including seminars, colloquia, workshops, and a vibrant math club, to enrich students' academic experience. Additionally, students have access to interdisciplinary initiatives and research centers, facilitating exploration at the intersection of mathematics with physics, computer science, economics, and other fields.

Research at Princeton often involves cutting-edge projects supported by grants, collaborations with other departments and institutions, and numerous opportunities for independent study. The department encourages an environment of curiosity, innovation, and intellectual rigor. Faculty members are actively involved in mentoring students and guiding their academic and research pursuits, enabling them to contribute meaningful work to the mathematical sciences.

Overall, Princeton’s Mathematics program combines a rigorous academic curriculum, innovative research, and a vibrant community to foster the development of highly skilled mathematicians who are prepared to excel in diverse fields and contribute to scientific progress and technological advancement. The program’s distinguished reputation attracts talented students and faculty from around the world, making it a leading hub for mathematical education and research.