영문목차
Contents
Preface xi
A User's Guide xv
Acknowledgments xix
Chapter 1 What This Book Is about and Who This Book Is for 1
Chapter 2 Proof and Intuition 19
Chapter 3 The Integers 61
Chapter 4 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 9 Polynomials over the Integers and Rationals 365
Chapter 10 Roots of Polynomials of Degree Less than 5 411
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 The Insolvability of the Quintic 645
Bibliography 685
Index 687