Georgia Institute of Technology College of Sciences

This course will cover important topics in linear algebra not usually discussed in a first-semester course, featuring a mixture of theory and applications.

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

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.

Elementary combinatorial techniques and proof methods used in discrete problem solving.

Introduction to numerical algorithms for some basic problems in computational mathematics. Discussion of both implementation issues and error analysis. Crosslisted with CX 4640 (formerly CS 4642).

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

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

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

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

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.