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The Penn Math Department maintains a wide list of courses, basic and advanced, from which it chooses its course offerings for each year. These offerings are chosen with regard to faculty and student interest as well as with an eye to balance among subfields represented in the Department. The actual list of offerings is generally ready by February 15 for the academic year beginning that Fall.

Description of Graduate Courses

The following is the standard list from which grad courses are normally chosen:

Masters Level Courses:

  • Math 500 - Geometry-Topology
  • Math 502/503 - Abstract Algebra
  • Math 508/509 - Advanced Analysis
  • Math 520/521 - Selections from Algebra
  • Math 524/525 - Topics in Modern Applied Algebra
  • Math 530(480)- Mathematics of Finance
  • Math 540/541 - Selections from Classical and Functional Analysis
  • Math 542 - Calculus of Variations
  • Math 548/549 - Topics in Analysis
  • Math 560/561 - Selections from Geometry and Topology
  • Math 570/571(Phil506) - Introduction to Logic and Computability
  • Math 574/575 - Mathematical Theory of Computation
  • Math 580/581 - Combinatorial Analysis and Graph Theory
  • Math 582/583 - Applied Mathematics and Computation
  • Math 584/585 - The Mathematics of Medical Imaging and Measurement
  • Math 590/591 - Advanced Applied Mathematics
  • Math 594(Phys500) - Advanced Methods in Applied Mathematics
  • Math 599 - Independent Study

Basic Courses - required for the Ph.D. (offered every year):

  • Math 504/505 - Graduate Proseminar in Mathematics
  • Math 600/601 - Topology and Geometric Analysis
  • Math 602/603 - Algebra
  • Math 608/609 - Analysis
  • Math 618 - Algebraic Topology, first semester (fall)

More Advanced Courses:

  • Math 619 - Algebraic Topology, second semester (spring)
  • Math 620/621 - Algebraic Number Theory
  • Math 622/623 - Complex Algebraic Geometry
  • Math 624/625 - Algebraic Geometry
  • Math 626/627 - Commutative Algebra
  • Math 628/629 - Homological Algebra
  • Math 630/631 - Differential Topology
  • Math 632/633 - Topological Groups
  • Math 638/639 - Algebraic Topology, Part II
  • Math 640/641 - Ordinary Differential Equations
  • Math 644/645 - Partial Differential Equations
  • Math 646/647 - Several Complex Variables
  • Math 650/651 - Lie Algebras
  • Math 652/653 - Operator Theory
  • Math 654/655 - Lie Groups
  • Math 656/657 - Representation of Continuous Groups
  • Math 660/661 - Differential Geometry
  • Math 670/671 - Topics in Logic
  • Math 676 - Advanced Geometric Methods in Computer Science
  • Math 680/681 - Applied Linear Analysis
  • Math 690/691 - Topics in Mathematical Foundations of Program Semantics
  • Math 692/693 - Numerical Analysis
  • Math 694/695(Phys654/655) - Mathematical Foundations of Theoretical Physics
  • Math 702/703 - Topics in Algebra
  • Math 720/721 - Advanced Number Theory
  • Math 724/725 - Topics in Algebraic Geometry
  • Math 730/731 - Topics in Algebraic and Differential Topology
  • Math 748/749 - Topics in Classical Analysis
  • Math 750/751 - Topics in Functional Analysis
  • Math 752/753 - Topics in Operator Theory
  • Math 760/761 - Topics in Differential Geometry
  • Math 794 - Physics for Mathematicians
  • Math 820/821 - Algebra Seminar
  • Math 824/825 - Seminar in Algebra, Algebraic Geometry, Number Theory
  • Math 830/831 - Geometry-Topology Seminar
  • Math 840/841 - Analysis Seminar
  • Math 844/845 - Seminar in Partial Differential Equations
  • Math 850/851 - Seminar in Functional Analysis
  • Math 860/861 - Seminar in Reimannian Geometry
  • Math 870/871 - Logic Seminar
  • Math 872/873 - Seminar in Logic and Computation
  • Math 880/881 - Combinatorics Seminar
  • Math 999 - Independent Study
  • Math 995 - Dissertation