Algebra

Front Cover
Springer Science & Business Media, Jan 1, 1993 - Mathematics - 153 pages
2 Reviews
This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.
  

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This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation. 

Review: Singapore Math Algebra by Gelfand and Shen

User Review  - Li Su - Christianbook.com

it is a very challenging book for youngster. Book is in excellent shape and shipping in on time. Read full review

Selected pages

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
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

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
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
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