• Loren C. Larson
Part of the Problem Books in Mathematics book series (PBM)


Strategy or tactics in problem-solving is called heuristics. In this chapter we will be concerned with the heuristics of solving mathematical problems. Those who have thought about heuristics have described a number of basic ideas that are typically useful. The five classics on problem-solving by George Polya are masterpieces devoted entirely to the practical study of heuristics in mathematics. Among the ideas developed in these books, we shall focus on the following:
  1. (1)

    Search for a pattern.

  2. (2)

    Draw a figure.

  3. (3)

    Formulate an equivalent problem.

  4. (4)

    Modify the problem.

  5. (5)

    Choose effective notation.

  6. (6)

    Exploit symmetry.

  7. (7)

    Divide into cases.

  8. (8)

    Work backward.

  9. (9)

    Argue by contradiction.

  10. (10)

    Pursue parity.

  11. (11)

    Consider extreme cases.

  12. (12)




Positive Integer Lattice Point Equilateral Triangle Equivalent Problem Binomial Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York Inc. 1983

Authors and Affiliations

  • Loren C. Larson
    • 1
  1. 1.Department of MathematicsSt. Olaf CollegeNorthfieldUSA

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