Mathematics syllabuses in modern secondary schools contain a wide range of notions and basic facts from various mathematical disciplines. This study aims to assist readers (pupils and teachers) in extending their knowledge about these topics and to learn about connections between them. The material is presented in the form of problems. The book is intended as a sequel to "What to Solve?".
Mathematics syllabuses in modern secondary schools contain a wide range of notions and basic facts from various mathematical disciplines. This study aims to assist readers (pupils and teachers) in extending their knowledge about these topics and to learn about connections between them. The material is presented in the form of problems. The book is intended as a sequel to "What to Solve?".
1: The Fibonacci sequence, generalized Fibonacci sequences, and
related topics
2: Patterns of dots and partitions of integers
3: Patterns, related to rational numbers: periodic decimal
fractions, repunits, and visible lattice points
4: Reflected light rays and real numbers: a theorem of
Kronecker
5: The Chinese remainder theorem and invisible lattice points
6: Two famous inequalities and some related problems
7: "Mysteries" of the their dimension: on cubes, pyramids, and
spheres
8: A Glimpse of higher-dimensional spaces: hypercubes, lattice
paths, and related number patterns
9: Do it with groups
10: From puzzles to research topics: selected problems of
combinatorics
`comprises 10 really interesting extended exercises in problem
solving, with solutions, ranging from the Chinese remainder theorem
to geometry in four dimensions'
Ian Stewart, New Scientist, September 1995
`Excellent resource for independent study or problem-solving
seminars.'
American Mathematical Monthly
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