How to Solve It: Modern Heuristics'I will tel! you' the hermit said to Lancelot 'the right of the matter.' Anonymous, The Quest of the Holy Grail Gyorgy Polya's How to Solve It [287] stands as one of the most important contributions to the problem-solving literatme in the twentieth century. Even now, as we move into the new millennium, the book continues tobe a favorite among teachers and students for its instructive heuristics. The first edition of the book appeared in 1945, near the end of the Second World War and a few years before the invention of the transistor. The book was a quick success, and a second edition came out in 1957. How to Solve It is a compendium of approaches for tackling problems as we find them in mathematics. That is, the book provides not only examples of techniques and procedures, but also instruction on how to make analogies, use auxiliary devices, work backwards from the goal to the given, and so forth. Es sentially, the book is an encyclopedia of problem-solving methods to be carried out by hand, but more than that, it is a treatise on how to think about framing and attacking problems. |
Contents
| 1 | |
| 9 | |
What Are the Numbers? | 16 |
How Important Is a Model? | 31 |
What Are the Prices in 711? | 49 |
Traditional Methods | 60 |
Whats the Color of the Bear? | 110 |
How Good Is Your Intuition? | 135 |
Can You Tune to the Problem? | 271 |
Tuning the Algorithm to the Problem | 277 |
Can You Mate in Two Moves? | 303 |
Day of the Week of January 1st | 331 |
What Was the Length of the Rope? | 359 |
Do You Like Simple Solutions? | 385 |
Summary | 403 |
Problems and Projects | 435 |
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Common terms and phrases
adaptive applied approach best solution better binary strings branch and bound chapter choice choose cluster component consider constraints converge cost crossover defined determine deterministic digit edges eval evaluation function evolution evolutionary algorithm evolutionary computation example feasible region feasible solution figure flip fuzzy set Gaussian Genetic Algorithms GENOCOP global greedy greedy algorithm heuristic hill-climbing infeasible individuals infeasible solutions initial input iteration layer length linear matrix membership function memory method minimize move mutation neighborhood neural network neuron node nonlinear offspring optimization problems optimum output parameters parents path penalty permutation population possible probability problem solving procedure programming random variable randomly real-world problems recombination representation requires sample search space selection self-adaptation simple simulated annealing step structure subtours swap tabu search techniques there's tion tour traveling salesman problem variation operators vector weights zero