Challenging Mathematical Problems with Elementary Solutions: Volume 2

Challenging Mathematical Problems with Elementary Solutions: Volume 2

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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. "show more

Product details

  • Paperback | 223 pages
  • 136 x 214 x 12mm | 240.4g
  • Dover Publications Inc.
  • New York, United States
  • English
  • black & white illustrations
  • 0486655377
  • 9780486655376
  • 376,367

Table of contents

Preface to the American Edition Suggestions for Using the Book Problems I. Points and Lines II. Lattices of Points in the Plane III. Topology IV. A Property of the Reciprocals of Integers V. Convex polygons VI. Some Properties of Sequences of Integers VII. Distribution of Objects VIII. Nondecimal Counting IX. Polynomials with Minimum Deviation from Zero (Tchebychev Polynomials) X. Four Formulas for pXI. The Calculation of Areas of Regions Bounded by Curves XII. Some Remarkable Limits XIII. The Theory of Primes Solutions Hints and Answers Bibliographyshow more