Georgia Institute of Technology College of Sciences

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.

Overview of integral calculus, multivariable calculus, and differential equations for biological sciences.

Problems from the life sciences and the mathematical methods for solving them are presented. The underlying biological and mathematical principles and the interrelationships are emphasized.

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

A study of the linear programming problem, including the simplex method, duality, and sensitivity analysis with applications to matrix games, integer programming and networks.

Introduction to algebraic methods in topology. Includes homotopy, the fundamental group, covering spaces, simplicial complexes. Applications to fixed point theory and group theory.

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