Agebra (Google eBook)

ISRAEL M AUTOR GELFAND

Springer, 1993 - Mathematics - 153 pages

This text has been adopted at: Holyoke Community College, Holyoke, MA University of Illinois in Chicago, Chicago, IL University of Chicago, Chicago, IL California State University, Hayward, CA Georgia Southwestern College, Americus, GA Carey Col

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Contents

• 1 Introduction: 1
• 4 Addition in the decimal number system: 2
• 5 The multiplication table and the multiplication algorithm: 5
• 6 The division algorithm: 6
• 7 The binary system: 8
• 8 The commutative law: 11
• 10 The use of parentheses: 13
• 11 The distributive law: 14
• 12 Letters in algebra: 15
• 13 The addition of negative numbers: 17
• 14 The multiplication of negative numbers: 18
• 15 Dealing with fractions: 21
• 16 Powers: 25
• 17 Big numbers around us: 26
• 18 Negative powers: 27
• 19 Small numbers around us: 29
• 20 How to multiply am by an or why our definition is convenient: 30
• 21 The rule of multiplication for powers: 32
• The square of a sum: 33
• 23 How to explain the square of the sum formula to your younger brother or sister: 34
• 24 The difference of squares: 36
• 25 The cube of the sum formula: 39
• 26 The formula for a + 64: 40
• 27 Formulas for a + 65 a + 66 and Pascals triangle: 42
• 28 Polynomials: 44
• When are polynomials equal?: 46
• 30 How many monomials do we get?: 48
• 31 Coefficients and values: 49
• 32 Factoring: 51
• 33 Rational expressions: 56
• 35 Polynomial and rational fractions in one variable: 61
• 36 Division of polynomials in one variable the remainder: 62
• 37 The remainder when dividing by x a: 68
• 38 Values of polynomials and interpolation: 72
• 39 Arithmetic progressions: 77
• 40 The sum of an arithmetic progression: 79
• 41 Geometric progressions 41 Geometric progressions: 81
• 42 The sum of a geometric progression: 83
• 43 Different problems about progressions: 85
• 44 The welltempered clavier: 87
• 45 The sum of an infinite geometric progression: 91
• 46 Equations: 94
• 47 A short glossary: 95
• 49 The case p 0 Square roots: 96
• 50 Rules for square roots: 99
• 51 The equation x2 + px + q 0 Problem 235 Solve the equation: 100
• 52 Vietas theorem: 102
• 53 Factoring ax2 f bx + c: 106
• 54 A formula for ax2 + bx + c 0 where a 0: 107
• 55 One more formula concerning quadratic equations: 108
• 57 The graph of the quadratic polynomial: 110
• 58 Quadratic inequalities: 114
• 60 Biquadratic equations: 116
• 61 Symmetric equations: 117
• 62 How to confuse students on an exam: 118
• 63 Roots: 120
• 64 Noninteger powers: 123
• 65 Proving inequalities: 127
• 66 Arithmetic and geometric means: 130
• 67 The geometric mean does not exceed the arithmetic mean: 132
• 69 Geometric illustrations: 134
• 70 The arithmetic and geometric means of several numbers: 136
• 71 The quadratic mean: 144
• 72 The harmonic mean: 147

Bibliographic information

• Title: Agebra
• Author: ISRAEL M AUTOR GELFAND
• Contributor: ALEXANDER AUTOR SHEN
• Edition: 6, illustrated
• Publisher: Springer, 1993
• ISBN: 0817636773, 9780817636777
• Length: 153 pages
• Subjects: Mathematics / Algebra / General