| From the Preface to the First Printing |
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| From the Preface to the Seventh Printing |
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viii | |
| Preface to the Second Edition |
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ix | |
| "How to Solve It" list |
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xvi | |
| Introduction |
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xix | |
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1 | (1) |
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Questions, recommendations, mental operations |
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1 | (1) |
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2 | (1) |
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3 | (1) |
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Teacher and student. Imitation and practice |
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3 | (2) |
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Main divisions, main questions |
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5 | (1) |
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Understanding the problem |
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6 | (1) |
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7 | (1) |
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8 | (2) |
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10 | (2) |
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12 | (1) |
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13 | (1) |
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14 | (2) |
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16 | (3) |
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19 | (1) |
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The teacher's method of questioning |
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20 | (2) |
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Good questions and bad questions |
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22 | (1) |
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A problem of construction |
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23 | (2) |
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25 | (4) |
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29 | (213) |
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33 | (4) |
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PART III. SHORT DICTIONARY OF HEURISTIC |
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37 | (9) |
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46 | (4) |
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50 | (7) |
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57 | (1) |
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58 | (1) |
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Can you check the result? |
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59 | (2) |
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Can you derive the result differently? |
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61 | (3) |
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64 | (4) |
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68 | (4) |
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72 | (1) |
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73 | (1) |
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73 | (1) |
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Could you derive something useful from the data? |
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73 | (2) |
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Could you restate the problem?† |
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75 | (1) |
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Decomposing and recombining |
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75 | (10) |
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85 | (7) |
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92 | (1) |
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Determination, hope, success |
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93 | (1) |
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94 | (1) |
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Did you use all the data? |
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95 | (3) |
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Do you know a related problem? |
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98 | (1) |
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99 | (1) |
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99 | (4) |
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103 | (5) |
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108 | (2) |
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110 | (1) |
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Here is a problem related to yours and solved before |
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110 | (2) |
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112 | (1) |
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113 | (1) |
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If you cannot solve the proposed problem |
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114 | (1) |
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Induction and mathematical induction |
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114 | (7) |
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121 | (1) |
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Is it possible to satisfy the condition? |
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122 | (1) |
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123 | (1) |
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123 | (1) |
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123 | (6) |
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129 | (5) |
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134 | (7) |
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141 | (7) |
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148 | (1) |
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149 | (5) |
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Problems to find, problems to prove |
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154 | (3) |
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157 | (3) |
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160 | (2) |
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Reductio ad absurdum and indirect proof |
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162 | (9) |
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171 | (1) |
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171 | (1) |
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172 | (1) |
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172 | (1) |
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173 | (1) |
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Separate the various parts of the condition |
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173 | (1) |
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174 | (4) |
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178 | (12) |
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190 | (7) |
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197 | (2) |
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199 | (1) |
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200 | (2) |
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202 | (3) |
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205 | (1) |
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The intelligent problem-solver |
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206 | (1) |
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207 | (1) |
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The traditional mathematics professor |
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208 | (1) |
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209 | (5) |
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214 | (1) |
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215 | (6) |
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221 | (4) |
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225 | (9) |
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PART IV. PROBLEMS, HINTS, SOLUTIONS |
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234 | (4) |
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238 | (4) |
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242 | |
