FAS - Mathematics

The Graduate Faculty in the Department of Mathematics offers various opportunities for study and research in mathematics which may be pursued by full-time and part-time students. Cooperative programs exist with other departments in the arts and sciences and with other branches of the University, such as a dual master's program with the Department of Computer Science and a graduate training program on Neuroscience in collaboration with Carnegie Mellon University (Center for the Neural Basis of Cognition). The department also accommodates students engaged in graduate studies in other disciplines requiring mathematics, and serves the community by providing mathematics education to those not necessarily pursuing a graduate degree program. Details on graduate programs and departmental regulations are contained in the document, Handbook for Graduate Study in Mathematics at the University of Pittsburgh, obtainable from 309 Thackeray Hall or by telephoning (412) 624-1175.

Degree programs lead to the Master of Arts and Master of Science in Mathematics, Master of Arts and Master of Science in Applied Mathematics, and the Doctor of Philosophy in Mathematics. Within the limitations of course availability, students may study those subjects most suited to their own interests and needs. Successful completion of one of these programs will prepare the student for employment in a wide variety of specialized occupations or for doctoral work in one of these areas. The MA and MS programs in applied mathematics are more structured in their requirements; the interested student can obtain additional information from the department on their nature.

Contact Information

Department Chair: John M. Chadam

Main Office: 301 Thackeray Hall

Phone: (412) 624-1175

Fax: (412) 624-8397

Web site: http://www.math.pitt.edu

Research

The research interests of the department are wide and varied. These include algebra, applied analysis, classical and functional analysis, complex variables, ordinary and partial differential equations, geometry and relativity theory, logic and foundations, mathematical finance, mathematical biology, applied mathematics and numerical analysis, and general topology.

Facilities

The Mathematics Library contains more than 21,000 volumes and 280 research journals. Computer access to databases such as Mathematical Reviews is available to all students and faculty.

In addition to the extensive computing facilities provided by the University, the department maintains several in-house computing sites for use by all departmental graduate students. Available equipment includes several departmental Unix-based servers, and various Macintosh, Windows-based PCs, and Unix-based PCs. All of these machines are connected to the University's Ethernet network. There is also easy and reliable access to the Pittsburgh Supercomputing Center and its state-of-the-art parallel computers.

Admissions

Applicants should have a bachelor's degree in Mathematics or a closely related field, a minimum quality point average (QPA) of 3.00 out of a possible maximum of 4.00 in all undergraduate subjects, and a minimum QPA of 3.25 in the mathematics curriculum. It is desirable that the student's background include courses in calculus, linear and abstract algebra, differential equations, and real and complex analysis. Students lacking preparation in some of these subjects may be required to take the appropriate courses to meet the prerequisites for certain graduate courses. Applications may be submitted at any time, but for Fall Term admission should be received by mid January of that year. Three letters of recommendation are required. The submission of GRE scores (including the math subject exam) is optional, but highly encouraged.

Financial Assistance

The department supports about 50 graduate students through teaching assistantships, teaching fellowships, research assistantships, and Mellon Fellowships. Approximately 15 to 20 teaching assistantships are awarded to first-year students. Details on the nature of these awards can be found under Teaching and Research Appointments in the FAS section of the bulletin and under Fellowships and Traineeships, also in the FAS section of the bulletin.

Degree Requirements

The minimal requirements established by the Graduate Faculty of the University, as described under General Academic Regulations beginning, and any additional requirements of FAS Graduate Studies described under FAS Degree Requirements, should be read in conjunction with program-specific degree requirements described in the following sections.

Requirements for the Master's Degree

Departmental requirements for the Master of Arts (MA) degree in Mathematics are the completion of at least eight mathematics courses and an oral comprehensive examination. Five of the eight courses must be taken at the 2000-3000 level; the remaining ones may be those given by the department at the 1000 level or those cross-listed with other departments. As there are no other course requirements, the student may pursue a highly specialized program of study. Equally possible is a more traditional program providing a broader spectrum of subjects. The well-prepared student carrying a full schedule can complete the degree in a year. A Master of Science (MS) option is available that requires a thesis. Full-time students who are also working for the department as Teaching Assistants may require an additional year. Part-time students are allowed up to four calendar years to complete all requirements.

The programs that lead to the master's degree in Applied Mathematics contain several tracks, each having a selection of required and elective courses. An MS option is available that requires a thesis. The departmental handbook should be consulted for details on these programs. The department also offers a dual-degree program at the master's level with the Department of Computer Science. The degree objective in such programs is the master's degree in Mathematics and a master's degree in some selected other area.

Requirements for the PhD Degree

The main requirement for the Doctor of Philosophy (PhD) degree in Mathematics is the successful completion and defense of a dissertation embodying a substantial piece of original mathematical research. Prior to embarking upon this research, candidates are expected to pass a comprehensive examination demonstrating their competence in their chosen area of mathematics. Additionally, they must pass a written preliminary examination on advanced linear algebra and multivariable calculus. The preliminary examination must be passed within the first two years of full-time study.

Most candidates will require from three to five years of full-time study to complete the degree. Part-time students may be allowed as many as 10 years to finish all requirements.

Additional information and details concerning examinations, requirements, and the advising system can be found in the departmental handbook.

Course Listings

Courses in the 1000 series are advanced undergraduate courses that are frequently suitable for graduate credit. Those in the 3000 series are advanced graduate courses. Course content, prerequisites, frequency of offering, and requirements may change from year to year. Detailed information can be found in the Arts and Sciences Course Descriptions, which is published each term prior to registration.

Selected 1000-level Undergraduate Courses

MATH 1020 Applied Number Theory

MATH 1050 Combinatorial Mathematics

MATH 1070 Classical Numerical Analysis

MATH 1080 Numerical Linear Algebra

MATH 1100 Numerical Optimization Method

MATH 1110 Industrial Numerical Analysis

MATH 1180, 1240 Linear Algebra 1, 2

MATH 1250 Abstract Algebra

MATH 1270, 1280 Ordinary Differential Equations 1, 2

MATH 1310 Graph Theory

MATH 1330 Projective Geometry

MATH 1350 Introduction to Differential Geometry

MATH 1360, 1370 Modeling in Applied Mathematics 1, 2

MATH 1410, 1420 Introduction to the Foundations of Mathematics 1, 2

MATH 1470, 1480 Partial Differential Equations 1, 2

MATH 1530, 1540 Advanced Calculus 1, 2

MATH 1550 Vector Analysis and Applications

MATH 1560 Complex Variables and Applications

MATH 1570 Transformation Methods in Applied Mathematics

MATH 1700 Introduction to Topology

MATH 1730, 1740 Honors Algebra 1, 2

MATH 1750, 1760 Honors Analysis 1, 2

Graduate-level Courses

MATH 2000 Research and Thesis for the Master's Degree

MATH 2030 Numerical Linear Algebra

MATH 2050 Graph Theory

MATH 2060 Combinatorics

MATH 2070, 2071 Numerical Methods in Scientific Computing 1, 2

MATH 2090 Numerical Solution of Ordinary Differential Equations

MATH 2160 Set Theory

MATH 2170 Logic and Foundations

MATH 2180 Introduction to Fractal Geometry

MATH 2200, 2201 Real Analysis 1, 2

MATH 2210, 2211 Complex Analysis 1, 2

MATH 2240 Analytic Number Theory

MATH 2245 Algebraic Number Theory

MATH 2260 Potential Theory

MATH 2280 Hardy Spaces

MATH 2370, 2371 Matrices and Linear Operators 1, 2

MATH 2400, 2401 Functional Analysis 1, 2

MATH 2410, 2411 Harmonic Analysis 1, 2

MATH 2480 Computational Approximation Theory

MATH 2500, 2501 Algebra 1, 2

MATH 2700, 2701 Topology 1, 2

MATH 2750 General Topology 

MATH 2800, 2801 Differential Geometry 1, 2

MATH 2810 Algebraic Geometry

MATH 2900, 2901 Partial Differential Equations 1, 2

MATH 2920, 2921 Ordinary Differential Equations 1, 2

MATH 2930 Asymptotics and Special Functions

MATH 2950 Methods of Applied Math

MATH 2960 Computational Fluid Mechanics

MATH 2990 Independent Study

MATH 3000 Research and Dissertation for the PhD Degree

MATH 3031 Network Theory

MATH 3055 Chromatic Polynomials and Graph Structure

MATH 3060 Combinatorics and Finite Fields

MATH 3070 Numerical Solution of Nonlinear Systems

MATH 3071 Numerical Solution of Partial Differential Equations

MATH 3072 The Finite Element Method

MATH 3075 Parallel Finite Element Method

MATH 3090 Directed Study

MATH 3211 Riemann Surfaces

MATH 3215, 3216 Quasiconformal Maps 1, 2

MATH 3220, 3221 Several Complex Variables 1, 2

MATH 3250, 3251 Singular Integral Theory 1, 2

MATH 3260-3262 Topics in Fractal Geometry 1, 2, 3

MATH 3270, 3271 Iteration of Rational Maps 1, 2

MATH 3370 Computational Models in Neurobiology

MATH 3375 Computational Neuroscience

MATH 3410, 3411 Hilbert Spaces of Entire Functions 1, 2

MATH 3450 Theory of Distributions

MATH 3480 Topics in Spline Approximation

MATH 3550 Lie Groups and Lie Algebras

MATH 3750 General Topology 2

MATH 3920 Nonlinear Methods in Differential Equations

MATH 3921 Pseudodifferential Operators

MATH 3930 Fixed Point Theory

MATH 3940, 3941 Applied Analysis 1, 2

MATH 3950 Nonlinear Dynamics, Chaos, and Oscillation

MATH 3951 Physical Methods in Mathematics

MATH 3960 Mathematics of Phase Boundaries