Graduate Programs in Mathematics at Lehigh University

Department of Mathematics
Christmas-Saucon Hall
Lehigh University
14 East Packer Ave.
Bethlehem, PA 18015

Application forms for admission and financial aid may be obtained from the graduate advisor. Applicants requesting financial aid should apply by February 1. The TOEFL is required of all students whose native language is not English, and the TSE is required for teaching assistants from non-English-speaking countries. The GRE General Test and Subject Test in mathematics are recommended for all applicants.

The mathematics department currently has 22 teaching assistants. They receive a stipend of approximately $9600 for the academic year, and tuition is covered. Usually one or two of our graduate students are supported by fellowships from the university, which give the stipend and tuition without the teaching duties.

M.S. in Mathematics

The master's program demands 30 credit hours of graduate courses with at least 18 hours at the 400 level. With the permission of the chairman, up to six hours of these courses can be replaced by a thesis. All students in the master's program must also pass a comprehensive examination. This exam is given during the first year, and covers calculus, differential equations, and linear algebra.

With a judicious choice of courses, a student in the master's program can specialize in pure mathematics, applied mathematics, or statistics. The M.S. degree can serve both as a final degree in mathematics or as an appropriate background for the PhD.

PhD in Mathematics

The plan of work for the PhD degree includes the Comprehensive Exam described above, and qualifying examinations. The student must pass exams in three of the following areas: analysis, algebra, differential geometry, topology, logic and set theory, probability, statistics, numerical analysis, and differential equations. A general exam, in which the candidate describes the thesis program, a foreign language examination, and the doctoral dissertation and its defense complete the work for the PhD degree. To see a list of recent theses granted, click here .

Graduate courses

The following courses can be taken by graduate students. (Some 200-level courses are occasionally taken by students whose background is a bit weak.) Not all of these courses are offered in any single academic year.

303 Mathematical Logic
304 Axiomatic Set Theory
307 General Topology
309 Theory of Probability
310 Probability and its Applications
312 Applied Statistics
316 Complex Analysis
320 Ordinary Differential Equations
322-3 Methods of Applied Analysis, I-II
327 Groups and Rings
329 Recursive Functions and the Theory of Computation
334 Mathematical Statistics
338 Regression Analysis
340 Design and Analysis of Algorithms
341 Mathematical Models and their Formulation
342 Number Theory
374 Statistical Project
401-2 Real Analyis, I-II
404 Mathematical Logic
405-6 Partial Differential Equations, I-II
407 Theory and Technique of Optimization
408 Algebraic Topology I
Stat 410 Random Processes and their Applications
Stat 412 Applied Statistics
414 Topics in Ordinary Differential Equations
416 Complex Function Theory
419 Linear Operators in Hilbert Space
423-4 Differential Geometry, I-II
428 Fields and Modules
430 Numerical Analysis
431 Calculus of Variations
435-6 Functional Analysis, I-II
Stat 438 Linear Models
443 General Topology II
444 Algebraic Topology II
445 Topics in Algebraic Topology
449 Topics in Algebra
453 Function Theory
455 Topics in Number Theory
461 Topics in Mathematical Statistics
462 Nonparametric Statistics
463 Advanced Probability
464 Advanced Stochastic Processes
471 Homological Algebra
472 Group Representations

Applied Mathematics Program

There is also an interdisciplinary graduate program in applied mathematics, offered by the Department of Mathematics and the Department of Mechanical Engineering and Mechanics. These are the Divisions of Applied Mathematics and Statistics and of Engineering Mathematics, respectively. Students apply to the whole program, but then are admitted to one of the divisions. Both M.S. and PhD degrees are offered. For application forms, contact Mary Ann Dent (Math Dept, 14 East Packer Ave., mad8@lehigh.edu).