Mathematics


Elements of Modern Algebra Seventh Edition By Linda Gilbert and Jimmie Gilbert

Contents Preface ……………….. xi 1 Fundamentals ……………….. 1 1.1 Sets ……………….. 1 1.2 Mappings ……………….. 12 1.3 Properties of Composite Mappings (Optional) ……………….. 25 1.4 Binary Operations ……………….. 30 1.5 Permutations and Inverses ……………….. 37 1.6 Matrices ……………….. 42 1.7 Relations ……………….. 55 Key Words and Phrases ……………….. 62 A Pioneer in Mathematics: Arthur Cayley ……………….. 62 2 The Integers ……………….. 65 2.1 Postulates for the Integers (Optional) ……………….. 65 2.2 Mathematical Induction ……………….. 71 2.3 Divisibility ……………….. 81 2.4 Prime Factors and Greatest Common Divisor ……………….. 86 2.5 Congruence…