Descriptions of 500-level Mathematics Courses for 2012-2013
- MATH
504/5/6 Modern Algebra
(Aut/Win/Spr)
Three-quarter sequence covering group theory; field theory and Galois
theory; commutative rings and modules, linear algebra, theory of forms;
representation theory, associative rings and modules; commutative algebra
and elementary algebraic geometry. Prerequisite: MATH 404 or equivalent.
- MATH
514 Networks and Combinatorial
Optimization (Aut)
Networks and directed graphs. Paths and trees. Feasible and optimal flows
and potentials. Transportation problems, matching and assignment problems.
Algorithms and applications. Prerequisite: MATH 308 or AMATH 352 and MATH
324. Offered: jointly with AMATH 514.
- MATH 516 Numerical Optimization (Win)
Methods of solving optimization problems in finitely many variables, with
or without constraints. Steepest descent, quasi-Newton methods. Quadratic
programming and complementarity. Exact penalty methods, multiplier
methods. Sequential quadratic programming. Cutting planes and nonsmooth
optimization. Prerequisite: MATH 515. Offered: jointly with AMATH 516.
- MATH 524/5/6 Real Analysis (Aut/Win/Spr)
Three-quarter sequence covering the theory of measure and integration,
point set topology, Banach spaces, Lp spaces, applications to
the theory of functions of one and several real variables. Additional
topics to be chosen by instructor. Prerequisite: MATH 426 or equivalent.
- MATH 534/5/6 Complex Analysis (Aut/Win/Spr)
Three-quarter sequence covering complex numbers, analytic functions,
contour integration, power series, analytic continuation, sequences of
analytic functions, conformal mapping of simply connected regions, and
related topics. Prerequisite: MATH 426.
- MATH
544/5/6 Topology and
Geometry of Manifolds (Aut/Win/Spr)
Three-quarter sequence covering general topology, the fundamental group,
covering spaces, topological and differentiable manifolds, vector fields,
flows, the Frobenius theorem, Lie groups, homogeneous spaces, tensor
fields, differential forms, Stokes's theorem, deRham cohomology.
Prerequisite: MATH 404 and MATH 426 or equivalent.
- MATH
554/5/6 Linear Analysis
(Aut/Win/Spr)
Three-quarter sequence covering advanced linear algebra and matrix analysis,
ordinary differential equations (existence and uniqueness theory, linear
systems, numerical approximations), Fourier analysis, introductions to
functional analysis and partial differential equations, distribution
theory. Prerequisite: MATH 426 and familiarity with complex analysis at
the level of 427 (the latter may be obtained concurrently).
- MATH 581/582/583 Special Topics in
Mathematics(Aut/Win/Spr)
Advanced topics in various areas of mathematics.