- Print ISBN 9780123749413
- Electronic ISBN 9780080958620
A Concrete Approach to Abstract Algebra begins with a concrete and thorough examination of familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials, in this unique approach, the author builds upon these familar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. The text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics wich arise in courses in algebra, geometry, trigonometry, precalculus and calculus. The final four chapters present the more theoretical material needed for graduate study.
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Introduction; What This Book Is about and Who This Book Is for; Proof and Intuition; The Integers; Rational Numbers and the Real Numbers; The Complex Numbers; The fundamental Theorem of Algebra; The Integers Modulo n; Group Theory; Polynomials over the Integers and Rationals; Roots of Polynomials of Degree Less than 5; Rational Values of Trigonometric Functions; Polynomials over Arbitrary Fields; Difference Functions and Partial Fractions; An Introduction to Linear Algebra and Vector Spaces; Degrees and Galois Groups of Field Extensions; Geometric Constructions; The Insolvability of the Quintic; Bibliography; Index