Topics include: global properties of flows and diffeomorphisms, Invariant sets and dynamics, Bifurcations of fixed and periodic points; stability and...
PREREQUISITES
The classical calculus of variations: the Gateaux variation, necessary conditions, transversality, corner conditions, Euler-Lagrange multiplier...
Optimization of functions of several variables, restricted by equality and inequality constraints, with applications. Linear programming, including...
Quasilinear equations: Cauchy problems, method of characteristics; Cauchy-Kovalevski theorem; generalized solutions; wave equation, Huygens'...
Subject matter to vary from year to year. Given jointly with MATH 837*. PREREQUISITE
Configuration space, generalized coordinates, Euler-Lagrange equations. Forces: dissipative, potential. Simple mechanical control systems: modeling,...
Topological equivalence and topological invariants; homotopy and the fundamental group; covering spaces; homotopy type; Brower
Fundamental principles of communication theory, information measures, entropy, mutual information, divergence; source encoding, Huffman codes,...
Theory and practice of quantization and signal compression systems. PREREQUISITE
An introduction to mathematical logic, including some of the following topics: syntax of first-order theories, Peano arithmetic, G
This course covers performance models for data networking, delay models and loss models; analysis of multiple access systems, routing, and flow...
An important topic in mathematics not covered in any other courses. PREREQUISITE
For a complete description, see MATH 491*. PREREQUISITE
Open to students with a strong interest in some topic not covered in any of the regular courses. The student must find an instructor willing to...
For a complete description, see MATH 500*. PREREQUISITE