Ebook Challenging Mathematical Problems with Elementary Solutions, Vol. I: 001 (Dover Books on Mathematics), by A. M. Yaglom, I. M. Yaglom
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Challenging Mathematical Problems with Elementary Solutions, Vol. I: 001 (Dover Books on Mathematics), by A. M. Yaglom, I. M. Yaglom
Ebook Challenging Mathematical Problems with Elementary Solutions, Vol. I: 001 (Dover Books on Mathematics), by A. M. Yaglom, I. M. Yaglom
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Designed for advanced high school students, undergraduates, graduate students, mathematics teachers, and any lover of mathematical challenges, this two-volume set offers a broad spectrum of challenging problems — ranging from relatively simple to extremely difficult. Indeed, some rank among the finest achievements of outstanding mathematicians.
Translated from a well-known Russian work entitled Non-Elementary Problems in an Elementary Exposition, the chief aim of the book is to acquaint the readers with a variety of new mathematical facts, ideas, and methods. And while the majority of the problems represent questions in higher ("non-elementary") mathematics, most can be solved with elementary mathematics. In fact, for the most part, no knowledge of mathematics beyond a good high school course is required.
Volume One contains 100 problems, with detailed solutions, all dealing with probability theory and combinatorial analysis. Topics include the representation of integers as sums and products, combinatorial problems on the chessboard, geometric problems on combinatorial analysis, problems on the binomial coefficients, problems on computing probabilities, experiments with infinitely many possible outcomes, and experiments with a continuum of possible outcomes.
Volume Two contains 74 problems from various branches of mathematics, dealing with such topics as points and lines, lattices of points in the plane, topology, convex polygons, distribution of objects, nondecimal counting, theory of primes, and more. In both volumes the statements of the problems are given first, followed by a section giving complete solutions. Answers and hints are given at the end of the book.
Ideal as a text, for self-study, or as a working resource for a mathematics club, this wide-ranging compilation offers 174 carefully chosen problems that will test the mathematical acuity and problem-solving skills of almost any student, teacher, or mathematician.
- Sales Rank: #1348060 in eBooks
- Published on: 2013-04-26
- Released on: 2013-04-26
- Format: Kindle eBook
Language Notes
Text: English, Russian (translation)
About the Author
Yaglom, Institute of Atmospheric Physics, Academy of Sciences, USSR.
I. M. Yaglom authored many books which have since become academic standards of reference. These include Complex Numbers in Geometry, Geometric Transformations, A Simple Non-Euclidean Geometry and its Physical Basis, and Probability and Information. He was Professor of Mathematics at Yaroslavl State University from 1974 83 and a technical consultant at the Academy of Pedagogical Sciences from 1984 88.
Most helpful customer reviews
32 of 32 people found the following review helpful.
One of a few
By Max
I've read the Russian original of this book. It is wonderful. I really enjoyed it, and often used the ideas I found there to solve other problems. Highly recommended, espesially for the high school students unterested in mathematics, but extremely interesting for anybody who likes math.
32 of 33 people found the following review helpful.
Simply excellent
By UNPINGCO
It's amazing that so many results that you may have seen in more advanced books proven with more advanced techniques can also be proven with elementary methods. Some of the constructions are amazingly clever. Additionally, the authors take time to highlight the important results in elementary mathematics that are often used in more advanced areas without qualification.
20 of 20 people found the following review helpful.
Difficult, but fun, problems.
By Sebastien Gilmour
The reviewer below seems rather confused. This book has problems which COULD be solved in a mechanical way, but almost all the solutions given are simple and creative. Futhermore, there are often two solutions given. I find the problems hard, but maybe I am just not very smart. How could this book alter your perception of truth? By giving you knowledge?
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