Applied and Computational Math

The Program in Applied and Computational Mathematics offers a select group of highly qualified students the opportunity to obtain a thorough knowledge of branches of mathematics indispensable to science and engineering applications, including numerical analysis and other computational methods.

Courses:

Students must choose three areas in which to be examined out of a list of six possibilities specified below. The student should choose their specific topics by the end of October. The director of graduate studies, in consultation with the student, appoints a set of advisers from among the faculty and associated faculty. The adviser in each topic meets regularly with the student, monitors progress and assigns additional reading material. Advisers are traditionally members of the Princeton University faculty within the department, but members of the faculty from other departments may serve as advisers with approval. They can be any member of the University faculty, but are normally either program or associated faculty. The first-year student should choose three topics from among the following six applied mathematics categories:

Asymptotics, analysis, numerical analysis and signal processing; Discrete mathematics, combinatorics, algorithms, computational geometry and graphics; Mechanics and field theories (including computational physics/chemistry/biology); Optimization (including linear and nonlinear programming and control theory); Partial differential equations and ordinary differential equations (including dynamical systems); and Stochastic modeling, probability, statistics and information theory.

Additional topics may be considered with prior approval by the director of graduate studies. Typically, students take regular or reading courses with their advisers in each of the three areas, completing the regular exams and course work for these courses.

Pre-Generals Requirements(s):

At the end of the first year, students will also take a preliminary exam, consisting of a joint interview by their three first-year advisers. Each student should decide with their first-year advisers which of these courses are relevant for their areas.

Students should access their level of preparation for the preliminary examination by reviewing homework and examinations from the previous year’s work.  Students who fail the preliminary examination, may with support of the first-year advisers take the examination a second time.

General Exam:

Students will not be admitted to the third year of enrollment unless they have successfully completed the general examination. The general examination, or generals, is designed as a sequence of interviews with assigned professors.  The examination takes place during the first year and covers three areas of applied mathematics. The generals culminate in a seminar on a research topic, usually delivered toward the end of the fourth term or second year of enrollment.

A student who completes all departmental requirements (coursework, preliminary exams, with no incompletes) but fails the general examination may take it a second time. Students who fail the general examination a second time, will have their degree candidacy terminated.

Qualifying for the M.A.:

The Master of Arts degree is normally an incidental degree on the way to full Ph.D. candidacy, but may also be awarded to students who for various reasons leave the Ph.D. program. Students who have satisfactorily passed required coursework including the resolution of any incompletes and have passed the preliminary exam, may be awarded an M.A. degree.  Upon learning the department’s determination of their candidacy to receive the M.A., students apply for the master's degree online through the advanced degree application system. 

Dissertation and FPO:

The doctoral dissertation must consist of either a mathematical contribution to some field of science or engineering, or the development or analysis of mathematical or computational methods useful for, inspired by, or relevant to science or engineering.

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 test required and subject tests in mathematics, physics, engineering or a related field recommended.

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