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Spring 2019

Archived:

## Introduction to Discrete Mathematics

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

## 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.

## Calculus for Life Sciences

Overview of integral calculus, multivariable calculus, and differential equations for biological sciences. This course is required for students in School of Biology.

## Analysis I

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

## Abstract Algebra I

This course develops in the theme of "Arithmetic congruence, and abstract algebraic structures." There will be a very strong emphasis on theory and proofs.

## Introduction to Number Theory

Primes and unique factorization, congruences, Chinese remainder theorem, Diophantine equations, Diophantine approximations, quadratic reciprocity. Applications such as fast multiplication, factorization and encryption.

## Mathematical Biology

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.

## Numerical Analysis I

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).

## Classical Mathematical Methods in Engineering

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

## Linear Programming

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