Tailored for advanced high school students, undergraduates, graduate students, mathematics educators, and enthusiasts of mathematical challenges, this two-volume collection presents a diverse array of intricate problems, spanning from relatively straightforward to exceedingly complex. Indeed, some of these problems stand as notable accomplishments by renowned mathematicians.
Derived from a renowned Russian source titled “Non-Elementary Problems in an Elementary Exposition,” the primary objective of the book is to familiarize readers with an assortment of new mathematical facts, ideas, and methodologies. Although the majority of the problems delve into higher (“non-elementary”) mathematics, most can be tackled using elementary mathematical principles. In essence, no knowledge beyond a solid high school mathematics course is required.
Volume One encompasses 100 problems, complete with detailed solutions, all centered around probability theory and combinatorial analysis. Topics range from integer representations as sums and products, combinatorial challenges on the chessboard, geometric issues in combinatorial analysis, problems associated with binomial coefficients, to computations of probabilities, experiments involving infinitely many potential outcomes, and experiments featuring a continuum of possible outcomes.
Volume Two includes 74 problems from various mathematical branches, covering subjects like points and lines, lattices of points in the plane, topology, convex polygons, object distribution, nondecimal counting, theory of primes, and more. In both volumes, the problems are presented first, followed by comprehensive solution sections. Answers and hints are conveniently located at the end of each volume.
Whether used as a textbook, for independent study, or as a valuable resource for a mathematics club, this extensive compilation offers 174 thoughtfully selected problems designed to challenge the mathematical acumen and problem-solving abilities of nearly any student, educator, or mathematician.
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