Challenging Mathematical Problems with Elementary Solutions, Vol. II: Volume 2 (Dover Books on Mathematics #2)

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 p
XI. The Calculation of Areas of Regions Bounded by Curves
XII. Some Remarkable Limits
XIII. The Theory of Primes
Solutions
Hints and Answers
Bibliography


Publisher Marketing:

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.