- You are here:
- Home

Fall 2020

Archived:

## Classical Mathematical Methods in Engineering

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

## Dynamics and Bifurcations I

A broad introduction to the local and global behavior of nonlinear dynamical systems arising from maps and ordinary differential equations.

## Differential Geometry

The theory of curves, surfaces, and more generally, manifolds. Curvature, parallel transport, covariant differentiation, Gauss-Bonet theorem

## Introduction to Topology

Point set topology, topological spaces and metric spaces, continuity and compactness, homotopy and covering spaces

## Complex Analysis

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

## 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.

## Mathematical Statistics I

Sampling distributions, Normal, t, chi-square and F distributions. Moment generating function methods, Bayesian estimation and introduction to hypothesis testing

## Introduction to Graph Theory

The fundamentals of graph theory: trees, connectivity, Euler torus, Hamilton cycles, matchings, colorings and Ramsey theory.

## 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.

## Applied Combinatorics

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