COURSE AIMS AND OBJECTIVES: The course aim is to train students to use heuristic strategies and methods when solving problems related to high school mathematics, in independent, individual and/or teamwork. The topics have been chosen so that they enable the training of students, prospective mathematics teachers, to affirm the problem-solving and interest as fundamental principles of mathematics teaching at all educational levels.
COURSE DESCRIPTION AND SYLLABUS:
1. Mathematical problem. Heuristics, strategies and methods. Spotting patterns. Backward solving method. Graphical method. Algebraic method.
2. Proofs (direct proof, proof by contraposition, proof by contradiction). Examples of proofs in school mathematics. Construction of examples and counterexamples. Mathematical induction. Reading and constructing of proofs.
3. Divisibility. The fundamental theorem of arithmetic. Problems with prime numbers. Diophantine equations. Proofs of irrationality. Polynomials with integer coefficients.
4. Logical-combinatorial problems. Basic principles of counting. Binomial theorem. Method of invariants. Dirichlet's principle.
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Kako ću riješiti matematički zadatak, G. Polya, Školska knjiga, Zagreb, 1966.
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Matematičko otkriće, G. Polya, Hrvatsko matematičko društvo, Zagreb, 2003.
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Posebne metode rješavanja matematičkih problema, Z. Kurnik, Element, Zagreb, 2010.
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Dirichletovo pravilo, M. Krnić, HMD, Zagreb, 2011.
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Elementarna matematika 1, Pavković, Veljan, Školska knjiga, Zagreb, 2004.
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Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12, A. Posamentier, S. Krulik, Corvin Press, 2008.
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Techniques of Problem Solving, S.G. Krantz, American Mathematical Society, 1997.
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Aha! Putovanje u središte problema, M. Bašić, Hrvatsko matematičko društvo, Zagreb, 2021.
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Elementarna teorija brojeva, Pavković,Dakić,Mladinić, HMD, Element, Zagreb, 1994.
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Male teme iz matematike, Pavković et al., HMD, Zagreb, 1994.
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Poučci elementarne matematike, A.Marić, Element, Zagreb, 2006.
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