Skip to main content

Secondary navigation:

College of Arts and Sciences

Graduate Course Descriptions

department of mathematics

MT 806 Algebra I (Fall: 3)
MT 807 Algebra II (Spring: 3)

The MT 806-807 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.

MT 808 Geometry/Topology I (Fall: 3)
MT 809 Geometry/Topology II (Spring: 3)

The MT 808-809 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.

MT 810 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.

MT 811 Complex Analysis (Spring: 3)
Topics include: Local and global theory of analytic functions of one variable.

MT 821 Number Theory I (Fall: 3)
MT 822 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.

MT 831Geometry/Topology III (Fall: 3)
MT 832 Geometry/Topology IV (Spring: 3)

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

MT 890 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.

MT 891 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.

MT 892 Graduate Research Seminar
This seminar is directed at building the research skills of graduate students.

MT 899 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.

MT 903 Seminar (Spring: 3)
This seminar is required of all candidates for the M.A. degree who are not in the joint M.A./M.B.A. program. It is intended for second-year graduate students.

View descriptions of courses offered prior to the 2010-2011 academic year.