This article explores diverse heuristics and strategies for non-standard mathematical problem solving, highlighting invariants, symmetry, and extremal principles as crucial tools that foster deeper insight and highly flexible, creative reasoning.
Methods of Solving Some Non-Standard Problems in Mathematics
DOI:
Keywords:
Non-standard problems
problem-solving heuristics
invariants
Abstract
References
Pólya, G. How to Solve It: A New Aspect of Mathematical Method. – Princeton: Princeton University Press, 1973. – 253 p.
Engel, A. Problem-Solving Strategies. – 3rd ed. – New York: Springer, 1998. – 403 p.
Zeitz, P. The Art and Craft of Problem Solving. – 2nd ed. – Hoboken, NJ: John Wiley & Sons, 2007. – 464 p.
Andreescu, T.; Gelca, R. Mathematical Olympiad Challenges. – 2nd ed. – New York: Birkhäuser, 2008. – 280 p.
Titu Andreescu; Krusemeyer, M.; Lerescu, B. Mathematical Miniatures. – Washington, DC: The Mathematical Association of America, 2013. – 204 p.
Rosen, K. Discrete Mathematics and Its Applications. – 8th ed. – New York: McGraw-Hill, 2019. – 944 p.