sp19

Spring 2019

Archived: 

Classical Mathematical Methods in Engineering

Fourier series, Fourier integrals, boundary value problems for partial differential equations, eigenvalue problems

Linear Programming

A study of the linear programming problem, including the simplex method, duality, and sensitivity analysis with applications to matrix games, integer programming and networks.

Introduction to Algebraic Topology

Introduction to algebraic methods in topology. Includes homotopy, the fundamental group, covering spaces, simplicial complexes. Applications to fixed point theory and group theory.

Complex Analysis

Topics from complex function theory, including contour integration and conformal mapping

Analysis II

Differentiation of functions of one real variable, Riemann-Stieltjes integral, the derivative in R^n and integration in R^n

Analysis I

Real numbers, topology of Euclidean spaces, Cauchy sequences, completeness, continuity and compactness, uniform continuity, series of functions, Fourier series

Topics in Linear Algebra

Linear algebra in R^n, standard Euclidean inner product in R^n, general linear spaces, general inner product spaces, least squares, determinants, eigenvalues and eigenvectors, symmetric matrices

Introduction to Information Theory

The measurement and quantification of information. These ideas are applied to the probabilistic analysis of the transmission of information over a channel along which random distortion of the message occurs.

Mathematical Statistics II

Hypothesis testing, likelihood ratio tests, nonparametric tests, bivariate and multivariate normal distributions

Stochastic Processes II

Renewal theory, Poisson processes and continuous time Markov processes, including an introduction to Brownian motion and martingales

Pages

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