fa17

Fall 2017

Archived: 

Foundations of Mathematical Proof

An introduction to proofs in advanced mathematics, intended as a transition to upper division courses including MATH 4107, 4150 and 4317. Fundamentals of mathematical abstraction including sets, logic, equivalence relations, and functions. Thorough development of the basic proof techniques: direct, contrapositive, existence, contradiction, and induction. Introduction to proofs in analysis and algebra.

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 Graduate Mathematics

This course includes topics on professional development and responsible conduct of research. The course satisfies the GT RCR Academic Policy for Doctoral Students to complete in-person RCR training.

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

Partial Differential Equations I

Method of characteristics for first and second order partial differential equations, conservation laws and shocks, classification of second order systems and applications.

Complex Analysis

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

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