Spring 2016


Classical Mathematical Methods in Engineering

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

Dynamics and Bifurcations II

A continuation of Dynamics and Bifurcations I

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

Introduction to Number Theory

Primes and unique factorization, congruences, Chinese remainder theorem, Diophantine equations, Diophantine approximations, quadratic reciprocity. Applications such as fast multiplication, factorization and encryption.


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