Integers, polynomials, and rings: a course in algebra

Abstract

Introduction: The McNugget Problem.- Introduction: The McNugget Problem.- Integers.- Induction and the Division Theorem.- The Euclidean Algorithm.- Congruences.- Prime Numbers.- Rings.- Euler' Theorem.- Binomial Coefficients.- Polynomials.- Polynomials and Roots.- Polynomials with Real Coefficients.- Polynomials with Rational Coefficients.- Polynomial Rings.- Quadratic Polynomials.- Polynomial Congruence Rings.- All Together Now.- Euclidean Rings.- The Ring of Gaussian Integers.- Finite Fields.