To The Reader |
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ix | |
Introduction |
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xi | |
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1 | (14) |
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1 Arithmetic in the Integers, Part I |
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2 | (5) |
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2 Roll Back, A Number Game of Chance |
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7 | (1) |
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8 | (1) |
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4 Arithmetic in the Integers, Part II |
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9 | (6) |
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Seminar 2 Divisibility and Order in the Integers |
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15 | (16) |
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15 | (1) |
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2 Properties of Divisibility |
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16 | (4) |
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3 Divisibility and Arithmetic in Z. |
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20 | (1) |
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4 An Activity on Secret Codes, I |
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21 | (2) |
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23 | (5) |
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6 Divisibility and Order in Z. |
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28 | (3) |
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Seminar 3 GCD's and The Division Algorithm |
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31 | (20) |
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31 | (2) |
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33 | (2) |
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35 | (3) |
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4 Return to Euclid's Game |
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38 | (2) |
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5 The Euclidean Algorithm |
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40 | (3) |
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6 GCD's as Linear Combinations |
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43 | (8) |
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Seminar 4 Prime Numbers and Factorization Into Primes |
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51 | (14) |
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51 | (7) |
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2 Factorization Into Primes |
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58 | (7) |
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Seminar 5 Applications of Prime Power Factorization |
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65 | (16) |
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1 Finding All Positive Divisors of n |
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65 | (4) |
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69 | (2) |
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3 The Greatest Common Divisor, the Least Common Multiple and the Least Common Denominator |
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71 | (6) |
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4 Secret Codes, a Game of Integer Divisors, II |
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77 | (4) |
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Seminar 6 Modular Arithmetic and Divisibility Tests |
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81 | (18) |
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81 | (1) |
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81 | (1) |
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81 | (4) |
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85 | (7) |
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5 Congruence and Tests for Divisibility |
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92 | (7) |
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Seminar 7 More Modular Arithmetic |
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99 | (16) |
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99 | (4) |
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2 The Arithmetic of Congruence Classes |
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103 | (6) |
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3 What is a Linear Congruence? |
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109 | (1) |
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4 Solving Linear Congruences |
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109 | (4) |
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113 | (2) |
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Seminar 8 The Arithmetic of Fractions |
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115 | (16) |
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115 | (1) |
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2 Fractions and Why We Need Them |
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115 | (2) |
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3 Multiplication of Fractions and Common Denominators |
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117 | (6) |
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4 Equivalence of Fractions |
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123 | (8) |
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Seminar 9 Properties of Multiplication of Fractions |
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131 | (14) |
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1 Reducing a Fraction to Lowest Terms |
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131 | (3) |
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2 Multiplication and Equivalence |
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134 | (2) |
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3 Properties of Multiplication of Fractions |
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136 | (1) |
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4 Equality and Equivalence |
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137 | (1) |
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5 Fractions and Mixed Numbers |
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138 | (1) |
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139 | (2) |
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7 Word Problems with Fractions |
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141 | (4) |
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Seminar 10 Addition of Fractions |
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145 | (16) |
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1 Addition of Fractions with the Same Denominator |
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145 | (1) |
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2 The Rule for Addition of Fractions |
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146 | (3) |
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3 Comparison of Methods for Addition of Fractions |
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149 | (4) |
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4 The Properties of Addition of Fractions |
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153 | (3) |
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5 The Distributive Property |
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156 | (1) |
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6 Addition and Equivalence |
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157 | (4) |
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Seminar 11 The Decimal Expansion of a Fraction |
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161 | (18) |
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1 Definitions of Decimal Fraction, Decimal Expansion and Decimal |
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161 | (3) |
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2 Constructing the Decimal Expansion of a Fraction |
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164 | (6) |
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3 Fractions with Terminating Decimals |
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170 | (4) |
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4 Fractions with Nonterminating Decimals |
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174 | (5) |
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Seminar 12 Order and the Number Line |
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179 | (20) |
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1 Positive Fractions and Negative Fractions |
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179 | (2) |
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2 Comparison of Fractions |
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181 | (3) |
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3 Properties of Order in the Set of Fractions |
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184 | (4) |
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188 | (2) |
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5 Representing Fractions on the Number Line |
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190 | (6) |
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6 Decimals on the Number Line |
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196 | (3) |
Appendix A The Mysterious Long Division Algorithm |
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199 | (6) |
Appendix B The Pigeonhole Principle |
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205 | (2) |
Index |
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207 | |