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.

Challenging Mathematical Problems With Elementary Solutions, Vol. 1

Science & Math

A. M. Yaglom

I.M. Yaglom

Mathematics

Dover Publications

Challenging Mathematical Problems With Elementary Solutions (Volume 2)

Challenging Mathematical Problems with Elementary Solutions, Vol. 1: Combinatorial Analysis and Probability Theory.

Holden-Day

YAGLOM, I. FELIX KLEIN AND SOPHUS LIE. EVOLUTION OF THE IDEA OF SYMMETRY IN THE NINETEENTH CENTURY. BASEL, 1988, xii 237 p. figuras.Encuadernacion original. Nuevo.

Felix Klein and Sophus Lie

Birkhauser

Very Good, and not far from Near Fine. First English language edition.  Moscow: Mir Publishers, 1978. The extraordinarily scarce, and aptly titled, I.M. Yaglom treatise, An Unusual Algebra. Translated from the Russian by I.G. Volosova. No ISBN number, despite its 1978 publication in both languages. Small octavo, printed green perfect-bound wraps, 128 pp. Very Good, and quite close to Near Fine, a moderate crease at bottom right of front cover (scan)  being the only truly notable flaw. No writing or marking, inside or out. Bright, stout copy of a true rarity in the genre. See scan. LT20

Unusual Algebra

Mir Publishers

This book is the sequel to Geometric Transformations I which appeared in this series in 1962. Part I treas length-preserving transformations, this volume treats shape-preserving transformations; and Part III treats affine and protective transformations. These classes of transformations play a fundamental role in the group-theoretic approach to geometry. 
As in the previous volume, the treatment is direct and simple. The introduction of each new idea is supplemented by problems whose solutions employ the idea just presented, and whose detailed solutions are given in the second half of the book.

Geometric Transformations II (NEW MATHEMATICAL LIBRARY)

Random House]

The familiar plane geometry of secondary school - figures composed of lines and circles - takes on a new life when viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries. This book is the concluding Part IV of Geometric Transformations, but it can be studied independently of Parts I, II, and III. The present Part IV develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The notion of inversion, or reflection in a circle, is the key tool employed. Applications include ruler-and-compass constructions and the Poincaré model of hyperbolic geometry. The straightforward, direct presentation assumes only some background in elementary geometry and trigonometry.

Geometric Transformations IV (Anneli Lax New Mathematical Library, 44)

American Mathematical Society

See the best price to sell, buy, or rent books by I.M. Yaglom. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by I.M. Yaglom