Graduate Brochure
Table of Contents
The Mathematics Department
The Department has about twenty faculty members actively involved in research and graduate education. With a graduate student body of about the same size, we are a program of moderate size with a high faculty/student ratio providing students with unique opportunities for flexible program design and ample interaction with faculty. Classes are small and are held in an informal atmosphere enabling students and faculty to work closely together.
There is a weekly colloquium featuring invited talks by prominent visitors covering the full spectrum of mathematical disciplines. In addition, the faculty and advanced graduate students organize several weekly seminars to explore topics of current research interest. The department also sponsors the Grosswald Lectures, an annual series of lectures given by leading mathematicians.
The Department shares physical facilities with the Department of Computer and Information Sciences in Wachman Hall, a modern 12-story structure. The facilities include the Department Office, faculty and graduate student offices, departmental computer facilities, and several seminar rooms and lounges. The departmental computer facilities are primarily Mac OS desktops coupled with Liux servers.
Some Aspects of the Program
For new students the Graduate Program in Mathematics offers a repertoire of courses that ease the transition from undergraduate to graduate studies. These courses provide a sound mathematical background, while helping beginning students to mature mathematically. Naturally, individuals with enough maturity and knowledge need not take these more basic courses. This introductory curriculum is an example of Temple University's general philosophy. In our department this philosophy takes shape as a commitment to actively participate in our students' development as future mathematicians. We take pride in caring for our students. Our faculty is very accessible, and quite willing to talk mathematics with any inquiring student. It is this attitude towards our students that most distinguishes our program from other graduate programs in mathematics. While requiring excellence, we work hard at providing the environment for achieving it.
Our department offers a great variety of possible choices for areas of specialization, areas in which we have a strong research presence. Numerical analysis, and numerical resolution of evolution equations, as well as some aspects of mathematical physics related to statistical mechanics, are well represented as areas of active research in applied mathematics. Within pure mathematics, algebra, algebraic and analytic number theory, several complex variables, harmonic analysis, differential geometry and topology, and global geometry are areas in which we have good research activity. Straddling pure and applied disciplines, probability and statistics are areas in which research is also carried out in our department.
The Graduate Program in Mathematics admits students for the Fall and the Spring semesters, although the former is the recommended time for starting studies. Incoming classes usually consist of about ten students. Most PhD students are supported by teaching assistantships. MA students are awarded teaching assistantships on the basis of availability of funds, performance and special teaching abilities. The teaching assistantships entail a stipend, a book allowance and full tuition remission, and are awarded on a yearly basis for up to five years. A small number of research assistantships are also awarded each year, funded by faculty grants. Our best applicants are often recommended for a university fellowship; these are awarded on a competitive basis, and consist of two years (the first and the fourth year) of stipend and full tuition remission.
Degree Programs and Requirements
The department offers both M.A. and Ph.D. degrees.
The M.A. Degree
The M.A. is available in two tracks: pure and applied. The pure mathematics track is built around a core of algebra, real and complex analysis, topology, and probability. The applied track has a core of numerical analysis, operations research, probability, statistics, and differential equations.
Students enrolled in the M.A. program must complete satisfactorily ten courses (30 semester hours). Each of the two tracks has its own core of courses which must be included among the ten courses taken. At least seven of these ten must be regular graduate mathematics courses; at most three may be approved graduate courses in other departments or appropriate advanced undergraduate mathematics courses.
After fulfilling the course requirements, all students must pass a written comprehensive examination. The examination for students in the pure track is based on material from core courses in algebra, real and complex analysis, topology, and probability. The applied mathematics comprehensive examination is based on core courses in numerical analysis, probability, statistics, operations research, and differential equations. For both tracks a satisfactory performance on the Ph.D. written exam may be substituted for the M.A. comprehensive exam. A thesis option is available as an alternative to the M.A. comprehensive examination.
The Graduate School Bulletin contains additional university requirements of a general nature such as residency, continuous enrollment, and transfer credits.
Promising M.A. students are encouraged to continue on to the Ph.D. program. The work done for the M.A. degree can be used towards partial fulfillment of the Ph.D. requirements.
The Ph.D. Degree
Students enrolled in the Ph.D. program must complete sixteen semester graduate courses beyond the baccalaureate.
Before being admitted to candidacy for the Ph.D. degree a student must pass a written comprehensive qualifying exam and an oral preliminary exam and demonstrate a reading knowledge in one of the following three languages: French, German, and Russian. The requirement is the same for both foreign and domestic students; however, a student whose native language is one of these three will be given credit for it without examination. The written comprehensive exam covers real analysis, complex analysis, and algebra. This exam must be passed before the oral exam can be administered. The oral exam is given by a faculty committee and covers advanced topics chosen in consultation with the student's adviser.