Summer 2017

Archived:

## Introduction to Discrete Mathematics

Mathematical logic and proof, mathematical induction, counting methods, recurrence relations, algorithms and complexity, graph theory and graph algorithms.

## Probability and Statistics with Applications

Introduction to probability, probability distributions, point estimation, confidence intervals, hypothesis testing, linear regression and analysis of variance.

## Introduction to Probability and Statistics

This course is a problem oriented introduction to the basic concepts of probability and statistics, providing a foundation for applications and further study.

## Classical Mathematical Methods in Engineering

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

## 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

## Applied Combinatorics

Elementary combinatorial techniques used in discrete problem solving: counting methods, solving linear recurrences, graph and network models, related algorithms, and combinatorial designs.

## Math Methods of Applied Sciences I

Review of linear algebra and ordinary differential equations, brief introduction to functions of a complex variable.

## Integral Equations and Transforms

Volterra and Fredholm linear integral equations, relation to differential equations, solution methods, Fourier, Laplace and Mellin transforms, applications to boundary value problems and integral equations.

## Introduction to Hilbert Spaces

Geometry, convergence, and structure of linear operators in infinite dimensional spaces. Applications to science and engineering, including integral equations and ordinary and partial differential equations.

## Real Analysis II

Topics include L^p, Banach and Hilbert spaces, basic functional analysis.