A Concrete Approach to Abstract Algebra: From the Integers to the Insolvability of the QuinticA 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. Ancillary list: * Online ISM http://textbooks.elsevier.com/web/manuals.aspx?isbn=9780123749413 * Online SSM http://www.elsevierdirect.com/product.jsp?isbn=9780123749413 * Ebook http://www.elsevierdirect.com/product.jsp?isbn=9780123749413

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Contents
1  
19  
61  
Chapter 4 The Rational Numbers and the Real Numbers  97 
Chapter 5 The Complex Numbers  137 
Chapter 6 The Fundamental Theorem of Algebra  189 
Chapter 7 The Integers Modulo n  227 
Chapter 8 Group Theory  265 
Chapter 11 Rational Values of Trigonometric Functions  423 
Chapter 12 Polynomials over Arbitrary Fields  437 
Chapter 13 Difference Functions and Partial Fractions  487 
Chapter 14 An Introduction to Linear Algebra and Vector Spaces  527 
Chapter 15 Degrees and Galois Groups of Field Extensions  573 
Chapter 16 Geometric Constructions  623 
Chapter 17 Insolvability of the Quintic  645 
685  
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A Concrete Approach to Abstract Algebra: From the Integers to the ... Jeffrey Bergen No preview available  2010 