Integers, Polynomials, and Rings A Course in Algebra /

• Main Author: Irving, Ronald S. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2004.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Algebra.; Associative rings.; Rings (Algebra).; Field theory (Physics).; Associative Rings and Algebras.; Field Theory and Polynomials.

Mathematics is often regarded as the study of calculation, but in fact, mathematics is much more. It combines creativity and logic in order to arrive at abstract truths. This book is intended to illustrate how calculation, creativity, and logic can be combined to solve a range of problems in algebra...

Table of Contents:

• 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.