It is incredibly powerful, although, at first sight, often appears innocuous.
Tags: Why Are Chores Important EssayDeeds Of AssignmentJohnson Cornell EssaysEssay On Television Effects OnHow Do You Write A Literature ReviewHow To Write A Business EssayWisp Business PlanResearch Concept PaperSuccess in solving special cases may be reassuring of the validity of the original claim, while failure to solve a special case may prompt the solver to look for a counterexample which will also serve to disprove the larger problem.
Specialization is opposite to generalization; it is wonderful that both are valuable tools in the arsenal of a problem solver. Polya's thesis that quite often more general or more strict problems are easier to solve than the more special ones.
Further reading I highly recommend the 1981 article The heuristic of George Polya and its relation to artificial intelligence by Alan Newell that offers penetrating analysis of Polya's problem solving heuristics prior to the discussion on its applicability to AI.
Specializaton, i.e., considering special cases, or introducing additional restrictions, while trying to solve a problem may highlight aspects of the original problem that have perhaps been missed at first glance.
Enjoyment of having a problem solved is more a result of detecting and exploiting the problem's peculiarities.
As a rule, those peculiarities once observed define a refined class of problems which succumb to the same method of solution.
Whereas an example may be used to support or illustrate a claim, a counterexample is used to refute an assertion.
How an example is being used often depends on the purpose or the formulation.
Try one of the tactics, force yourself to speak aloud - something will come out.
Ray Bradbury, when short on ideas, taught himself to work with a dictionary picking random words and trying to put them together into something meaningful and relevant. Also, note that some of the tactics was previously mentioned - with additional advice - in a short assay of what constitutes a proof.
Comments Problem Solving Strategies Engel
Problem-Solving Strategies
Jul 11, 2013. Engel, Arthur. Problem-solving strategies/Arthur Engel. p. cm. — Problem books in mathematics. Includes index. ISBN 0-387-98219-1.…
Problem-solving-strategiesBOOK 9- Problem Books in.
Angel Engel Institut f¨ur Didaktik der Mathematik Johann Wolfgang Goethe–Universit¨at Frankfurt am Main Senckenberganlage 9–11 60054 Frankfurt am Main.…
Strategy and Tactics in Problem Solving - Cut the Knot
One of the best problem solving strategies is do something; do not get and stay. Springer, 2007; A. Engel, Problem-Solving Strategies, Springer Verlag, 1998.…
Good books on problem solving / math olympiad - MathOverflow
Polya's "How to Solve It" is a good one. When prepping for the Putnam, I used "Problem Solving Through Problems".…
Problem-Solving Strategies - Arthur Engel Importado
Problem-Solving Strategies is a unique collection of competition problems over twenty major national and international mathematical competitions for high.…
Putnam at UCLA
The William Lowell Putnam Mathematical Competition Problems and Solutions 1938-1964, by A. M. Gleason. Problem-Solving Strategies, by Arthur Engel.…
Recommended Mathematics Literature
Problem-Solving Strategies. Arthur Engel. Springer, 1998. See this book at Amazon.com. A good initial preparation for IMO-style problem solving A Primer for.…
Arthur Engel mathematician - Wikipedia
Arthur Engel born 1928 is a German mathematics teacher, educationalist and prolific author. Engel's 1998 Problem-Solving Strategies has been described as the "most complete training book available for secondary and collegiate.…
Math books - Art of Problem Solving
Problems in Algebra from the Training of the US IMO Team by Titu Andreescu. Problem Solving Strategies by Arthur Engel contains significant material on.…