MAT 4605 - THEORY OF NUMBERS

credits: 3.0
An investigation of the properties of integers. Topics include divisibility, unique prime factorization, the Euclidean Algorithm, linear congruences and linear Diophantine equations, multiplicative number theoretical functions and primitive roots. Objectives: A) To define and use important properties of integers such as divisibility; B) Find and use congruences on the set of integers; C) Be able to generate multiple representations of integers; D) Use a number of important theorems such as the Division Algorithm, the Fundamental Theorey of Arithmetic, Fermat’s Little Theorem and the Chinese Remainder Theorem; E) Define and use multiplicative functions such as Euler’s Function; F) Have improved their ability to work with, understand and communicate higher level mathematics; G) Define mathematical concepts precisely and use these definitions in writing proofs; H) Construct their own original proofs and write these proofs in a logically correct and clear way. Method of Instruction: In-class lecture and discussion, group problem solving, and computer exercises as appropriate. Method of Evaluation: Grades will be based on homework assignments, activities, one midterm exam and a comprehensive final exam.

Prerequisite(s): MAT 2020 - CALCULUS II and MAT 2100 - DISCRETE MATHEMATICS