Courses

Surveys classical mathematical physics, starting with complex variable theory and finite dimensional vector spaces. Discusses topics in ordinary and partial differential equations, the special functions, boundary value problems, potential theory, and Fourier analysis. Prereqs., MATH 4001 and 4320. Undergraduates must have approval of the instructor. Same as PHYS 5030. Prerequisites: Restricted to Graduate Students only.

Surveys classical mathematical physics, starting with complex variable theory and finite dimensional vector spaces. Discusses topics in ordinary and partial differential equations, the special functions, boundary value problems, potential theory, and Fourier analysis. Prereq., MATH 5030. Undergraduates must have approval of the instructor. Same as PHYS 5040.

Prereq., MATH 3130 or APPM 3310. Undergraduates must have approval of the instructor. Same as MATH 4120, APPM 5120.

Highlights vector spaces, linear transformations, eigenvalues and eigenvectors, and canonical forms. Prereq., MATH 3130. Undergraduates must have approval of the instructor.

Undergraduates must have approval of the instructor. Prereq., MATH 4001. Same as MATH 4330. Prerequisites: Restricted to Graduate Students only.

Introduces theory and applications of ordinary differential equations, including existence and uniqueness theorems, qualitative behavior, series solutions, and numerical methods, for scalar equations and systems. Prereqs., MATH 3130 and 4310. Undergraduates must have approval of the instructor. Prerequisites: Restricted to Graduate Students only.

Undergraduates must have approval of the instructor. Prereq., MATH 3130. Recommended prereqs., MATH 3110 and 3140. Same as MATH 4440. Prerequisites: Restricted to Graduate Students only.

Prereq., MATH 4430 or APPM 2360. Undergraduates need instructor consent. Same as MATH 4470. Prerequisites: Restricted to Graduate Students only.

Prereq., MATH 4510 or APPM 3570. Undergraduates must have approval of the instructor. Same as MATH 4520 and APPM 5520. Prerequisites: Restricted to Graduate Students only.

Prereqs., MATH 4510/APPM 3570 and MATH 4520/APPM 4520. Undergraduates must have approval of the instructor. Same as MATH 4540/APPM 5540.

Solution of nonlinear algebraic equations, interpolation, approximation theory, and numerical integration. Prereqs., APPM 3130 or MATH 3130, and experience with a scientific programming language. Undergraduates must have approval of the instructor. Prerequisites: Restricted to Graduate Students only.

Solution of linear systems, eigenvalue problems, optimization problems, and ordinary and partial differential equations. Prereq., MATH 5600 or APPM 5600. Undergraduates must have approval of the instructor.

Designed to train students to become effective teachers. Students teach a mathematics course, meeting weekly with faculty to discuss problems particular to the teaching of mathematics. Prereqs., graduate standing and experience as a teaching assistant. Prerequisites: Restricted to Graduate Students only.

Proves the compactness theorem, showing the essential finiteness of logical implication. Proves many basic properties of theories, showing how the syntactic form of statements influences their behavior w.r.t, different models. Finally, studies properties of elements that cannot be stated by a single formula (the type of the element) and shows it can be used to characterize certain models. Prerequisites: Restricted to Graduate Students only.

Studies the computable and uncomputable. Shows that there are undecidable problems, and from there builds up the theory of sets of natural numbers under Turing reducibility. We will study Turing reducibility, the arithmetical hierarchy, oracle constructions, and end with the finite injury priority method. Recommended prereq., MATH 6000. Prerequisites: Restricted to Graduate Students only.

Examines divisibility properties of integers, congruencies, diophantine equations, arithmetic functions, quadratic residues, distribution of primes, and algebraic number fields. Prereq., MATH 3140. Undergraduates must have approval of the instructor. Prerequisites: Restricted to Graduate Students only.

Studies group theory and ring theory. Prereq., MATH 3140. Undergraduates need instructor consent. Prerequisites: Restricted to Graduate Students only.

Studies modules, fields, and Galois theory. Prereq., MATH 6130. Undergraduates need instructor consent.

Introduces topics used in number theory and algebraic geometry, including radicals of ideals, exact sequences of modules, tensor products, Ext, Tor, localization, primary decomposition of ideals, and Noetherian rings. Prereq., MATH 6140. Undergraduates must have approval of the instructor. Prerequisites: Restricted to Graduate Students only.

Introduces algebraic geometry, including affine and projective varieties, rational maps and morphisms, and differentials and divisors. Additional topics might include Bezout's Theorem, the Riemann-Roch Theorem, elliptic curves, and sheaves and schemes. Prereq., MATH 6140. Undergraduates must have approval of the instructor.

Introduces number fields and completions, norms, discriminants and differents, finiteness of the ideal class group, Dirichlet's unit theorem, decomposition of prime ideals in extension fields, decomposition, and ramification groups. Prereqs., MATH 6110 and 6140. Undergraduates must have approval of the instructor.

Acquaints students with the Riemann Zeta-function and its meromorphic continuation, characters and Dirichlet series, Dirichlet's theorem on primes in arithmetic progressions, zero-free regions of the zeta function, and the prime number theorem. Prereqs., MATH 6110 and 6350. Undergraduates must have approval of the instructor.

Introduces elements of general topology, algebraic topology, and differentiable manifolds. See also MATH 6220. Prereqs., MATH 3130, 3140 and 4320. Undergraduates must have approval of the instructor. Prerequisites: Restricted to Graduate Students only.

Introduces elements of general topology, algebraic topology, and differentiable manifolds. See also MATH 6210. Prereq., MATH 6210. Undergraduates must have approval of the instructor.

Instructs students on fundamental concepts such as manifolds, differential forms, de Rham cohomology, Riemannian metrics, connections and curvatures, fiber bundles, complex manifolds, characteristic classes, and applications to physics. Prereqs., MATH 3130 and 4320. Undergraduates must have instructor consent. Prerequisites: Restricted to Graduate Students only.