Graduate Course Descriptions

MATH 8806 Algebra I (Fall: 3)
MATH 8807 Algebra II (Spring: 3)

The Math 8806-8807 sequence will cover the following topics: Group Theory (Group actions, Sylow, Nilpotent/Solvable, simple groups, Jordan-Holder series, presentations); commutative algebra (uniqueness of factorization, Jordan decomposition, Dedekind rings, class groups, local rings, Spec); finite fields; algebraic numbers; Galois theory; Homological algebra; Semisimple algebra.

MATH 8808 Geometry/Topology I (Fall: 3)
MATH 8809 Geometry/Topology II (Spring: 3)

The MATH 8808-8809 sequence will cover the following topics: Point-set topology, fundamental group and covering spaces, smooth manifolds, smooth maps, partitions of unity, tangent and general vector bundles, (co)homology, tensors, differential forms, integration and Stokes' theorem, de Rham cohomology.

MATH 8810 Real Analysis (Fall: 3)
Topics include: Measure Theory, Hilbert Space and Fourier Theory. Possible topics from: Lebesgue measure starting on R, convergence and Fubini theorems, generalizing to locally compact spaces and groups.

MATH 8811 Complex Analysis (Spring: 3)
Topics include: Local and global theory of analytic functions of one variable.

MATH 8820 Introduction to Representation Theory (Fall: 3)
Introduction of a broad range of representation theory, including representations of finite and compact Lie groups, and finite dimensional representations of complex semisimple Lie groups and Lie algebras, and quantum groups.

MATH 8821 Number Theory I (Fall: 3)
MATH 8822 Number Theory II (Spring: 3)

Possible topics include: Factorization of ideals, local fields, local-vs-global Galois theory, Brauer group, adèles and idèles, class field theory, Dirichlet L-functions, Chebotarev density theorem, class number formula, Tate's thesis.

MATH 8831 Geometry/Topology III (Fall: 3)
MATH 8832 Geometry/Topology IV (Spring: 3)

Possible topics include: differential geometry, hyperbolic geometry, three-dimensional manifolds, knot theory.

MATH 8845 Topics in Algebra and Number Theory (Fall: 3)
Selected topics in Algebra and Number Theory.

MATH 8855 Topics in Geometry and Topology  (Fall: 3)
Selected topics in Geometry and Topology.

MATH 8890 Graduate Teaching Seminar I
This seminar is directed at building the teaching skills of beginning graduate students, who will typically be serving as Teaching Assistants. Topics include: use of blackboard, explaining problems, assigning points in grading exams and homework, classroom management. The seminar will include both practice and case-studies based discussion.

MATH 8891 Graduate Teaching Seminar II
This seminar is directed at building the teaching skills of advanced graduate students, who are teaching their own classes for the first time. Topics include: preparation of a syllabus, preparation of an examination, assigning course grades, lecture organization and preparation, lecture delivery, classroom management. The seminar will include both practice and case-studies based discussion.

MATH 8892 Graduate Research Seminar
This seminar is directed at building the research skills of graduate students.

MATH 8899 Readings and Research (Offered by arrangement with individual faculty members)
Department permission is required.

This is an independent study course, taken under the supervision of a Mathematics Department faculty member. Interested students should see the Assistant Chair for Graduates.