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  • Mathematics
    Department Chair: John M. Chadam
    Main Office: 301 Thackeray Hall
    (412) 624-1175 (phone) (412) 624-8397 (fax)
    http://www.math.pitt.edu

    Primary Faculty: Professors ASENJO, BEATROUS, BURBEA, CAGINALP, CHADAM (Chair), CHAO, CONSTANTINE (Joint, Statistics), ERMENTROUT, HASTINGS, HEATH, LAU, LAYTON, MANFREDI, McLEOD (University Professor), PORSCHING (Director of Graduate Studies), RABIER, TROY; Associate Professors CHEN, COHEN, HEBERT, LENNARD, MARSDEN, METZGER, PAN, SPARLING, THOMPSON (Undergraduate Chair), WHITEHEAD; Assistant Professors ANITESCU, CHOW, YOTOV; Instructor ELDER; Senior Lecturers ARRINGTON, MICHAEL

    Emeritus Faculty: Professors BENEDICTY, DESKINS (Dean Emeritus), HALL, KNIPP, LAUSH, LEHNER (Andrew Mellon Professor), MacBEATH, MASANI (University Professor), MYERS, RHEINBOLDT (Andrew Mellon Professor); Associate Professors CULLEN, KOVACS, PORTER, SACKS, SLAUGHTER, TEATS

    The Graduate Faculty 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 joint master’s program with the School of Engineering. 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 301 Thackeray Hall or by telephoning (412) 624-1175.

  • Admission to Graduate Studies
    Applicants should have a bachelor's degree in Mathematics or a closely related field, a minimum quality point average (QPA) of 3.00 relative to 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 admission should be received by the beginning of February of that year. Three letters of recommendation are required.

  • Graduate Student Support
    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 elsewhere in this bulletin.

  • Master’s Degree Requirements
    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 (see Statute of Limitations and Leaves of Absence in the first section of this bulletin).

    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 dual-degree programs at the master's level, which enable a student to coordinate studies in mathematics with those in a discipline exploiting their application. The degree objective in such programs is the master’s degree in Mathematics and a master's degree in some selected other area.

  • Doctoral Degree Requirements
    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 (see Statute of Limitations and Leaves of Absence in the first section of this bulletin).

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

  • Programs
    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. For any of these degrees the minimal requirements established by the Graduate Faculty of the University and by FAS Graduate Studies, as described elsewhere in this bulletin, should be consulted along with the specific departmental requirements.

  • 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 a departmental Unix-based server and various Macintosh, Windows-based PCs, and Unix- based PCs. Most 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, the CRAY C90 and massively parallel T3E.

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

  • Courses
    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
    1020 APPLIED NUMBER THEORY 3 CR.
    1050 COMBINATORIAL MATHEMATICS 3 CR.
    1070 CLASSICAL NUMERICAL ANALYSIS 3 CR.
    1080 NUMERICAL LINEAR ALGEBRA 3 CR.
    1100 NUMERICAL OPTIMIZATION METHOD 3 CR.
    1110 INDUSTRIAL NUMERICAL ANALYSIS 3 CR.
    1180, 1240 LINEAR ALGEBRA 1, 2 3 CR. EA
    1250 ABSTRACT ALGEBRA 3 CR.
    1270, 1280 ORDINARY DIFFERENTIAL EQUATIONS 1, 2 3 CR. EA.
    1310 GRAPH THEORY 3 CR.
    1330 PROJECTIVE GEOMETRY 3 CR.
    1350 INTRODUCTION TO DIFFERENTIAL GEOMETRY 3 CR.
    1360, 1370 MODELING IN APPLIED MATHEMATICS 1, 2 3 CR. EA.
    1410, 1420 INTRODUCTION TO THE FOUNDATIONS OF MATHEMATICS 1, 2 3 CR. EA.
    1470, 1480 PARTIAL DIFFERENTIAL EQUATIONS 1, 2 3 CR. EA.
    1530, 1540 ADVANCED CALCULUS 1, 2 3 CR. EA.
    1550 VECTOR ANALYSIS AND APPLICATIONS 3 CR.
    1560 COMPLEX VARIABLES AND APPLICATIONS 3 CR.
    1570 TRANSFORMATION METHODS IN APPLIED MATHEMATICS 3 CR.
    1700 INTRODUCTION TO TOPOLOGY 3 CR.
    1730, 1740 HONORS ALGEBRA 1, 2 3 CR. EA.
    1750, 1760 HONORS ANALYSIS 1, 2 3 CR. EA.
    Graduate-level Courses
    2000 RESEARCH AND THESIS FOR THE MASTER'S DEGREE VAR. CR.
    2030 NUMERICAL LINEAR ALGEBRA 3 CR.
    2050 GRAPH THEORY 3 CR.
    2060 COMBINATORICS 3 CR.
    2070, 2071 NUMERICAL METHODS IN SCIENTIFIC COMPUTING 1, 2 3 CR. EA.
    2090 NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS 3 CR.
    2160 SET THEORY 3 CR.
    2170 LOGIC AND FOUNDATIONS 3 CR.
    2180 INTRODUCTION TO FRACTAL GEOMETRY 3 CR.
    2200, 2201 REAL ANALYSIS 1, 2 3 CR. EA.
    2210, 2211 COMPLEX ANALYSIS 1, 2 3 CR. EA.
    2240 ANALYTIC NUMBER THEORY 3 CR.
    2245 ALGEBRAIC NUMBER THEORY 3 CR.
    2260 POTENTIAL THEORY 3 CR.
    2280 HARDY SPACES 3 CR.
    2370, 2371 MATRICES AND LINEAR OPERATORS 1, 2 3 CR. EA.
    2400, 2401 FUNCTIONAL ANALYSIS 1, 2 3 CR. EA.
    2410, 2411 HARMONIC ANALYSIS 1, 2 3 CR. EA.
    2480 COMPUTATIONAL APPROXIMATION THEORY 3 CR.
    2500, 2501 ALGEBRA 1, 2 3 CR. EA.
    2700, 2701 TOPOLOGY 1, 2 3 CR. EA.
    2750 GENERAL TOPOLOGY 3 CR.
    2800, 2801 DIFFERENTIAL GEOMETRY 1, 2 3 CR. EA.
    2810 ALGEBRAIC GEOMETRY 3 CR.
    2900, 2901 PARTIAL DIFFERENTIAL EQUATIONS 1, 2 3 CR. EA.
    2920, 2921 ORDINARY DIFFERENTIAL EQUATIONS 1, 2 3 CR. EA.
    2930 ASYMPTOTICS AND SPECIAL FUNCTIONS 3 CR.
    2950 METHODS OF APPLIED MATH 3 CR.
    2960 COMPUTATIONAL FLUID MECHANICS 3 CR.
    2990 INDEPENDENT STUDY VAR. CR.
    3000 RESEARCH AND DISSERTATION FOR THE PHD DEGREE VAR. CR.
    3031 NETWORK THEORY 3 CR.
    3055 CHROMATIC POLYNOMIALS AND GRAPH STRUCTURE 3 CR.
    3060 COMBINATORICS AND FINITE FIELDS 3 CR.
    3070 NUMERICAL SOLUTION OF NONLINEAR SYSTEMS 3 CR.
    3071 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS 3 CR.
    3072 THE FINITE ELEMENT METHOD 3 CR.
    3075 PARALLEL FINITE ELEMENT METHOD 3 CR.
    3090 DIRECTED STUDY VAR. CR.
    3211 RIEMANN SURFACES 3 CR.
    3215, 3216 QUASICONFORMAL MAPS 1, 2 3 CR. EA.
    3220, 3221 SEVERAL COMPLEX VARIABLES 1, 2 3 CR. EA.
    3250, 3251 SINGULAR INTEGRAL THEORY 1, 2 3 CR. EA.
    3260-3262 TOPICS IN FRACTAL GEOMETRY 1, 2, 3 3 CR. EA.
    3270, 3271 ITERATION OF RATIONAL MAPS 1, 2 3 CR. EA.
    3370 COMPUTATIONAL MODELS IN NEUROBIOLOGY 3 CR.
    3375 COMPUTATIONAL NEUROSCIENCE 3 CR.
    3410, 3411 HILBERT SPACES OF ENTIRE FUNCTIONS 1, 2 3 CR. EA.
    3450 THEORY OF DISTRIBUTIONS 3 CR.
    3480 TOPICS IN SPLINE APPROXIMATION 3 CR.
    3550 LIE GROUPS AND LIE ALGEBRAS 3 CR.
    3750 GENERAL TOPOLOGY 2 3 CR.
    3920 NONLINEAR METHODS IN DIFFERENTIAL EQUATIONS 3 CR.
    3921 PSEUDODIFFERENTIAL OPERATORS 3 CR.
    3930 FIXED POINT THEORY 3 CR.
    3940, 3941 APPLIED ANALYSIS 1, 2 3 CR. EA.
    3950 NONLINEAR DYNAMICS, CHAOS AND OSCILLATION 3 CR.
    3951 PHYSICAL METHODS IN MATHEMATICS 3 CR.
    3960 MATHEMATICS OF PHASE BOUNDARIES 3 CR.

                  

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