The USSR Olympiad Problem Book


Book Description

Over 300 challenging problems in algebra, arithmetic, elementary number theory and trigonometry, selected from Mathematical Olympiads held at Moscow University. Only high school math needed. Includes complete solutions. Features 27 black-and-white illustrations. 1962 edition.




Equations and Inequalities


Book Description

A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.




100 Great Problems of Elementary Mathematics


Book Description

Problems that beset Archimedes, Newton, Euler, Cauchy, Gauss, Monge, Steiner, and other great mathematical minds. Features squaring the circle, pi, and similar problems. No advanced math is required. Includes 100 problems with proofs.




Challenging Problems in Algebra


Book Description

Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.




A Problem Seminar


Book Description

There was once a bumper sticker that read, "Remember the good old days when air was clean and sex was dirty?" Indeed, some of us are old enough to remember not only those good old days, but even the days when Math was/un(!), not the ponderous THEOREM, PROOF, THEOREM, PROOF, . . . , but the whimsical, "I've got a good prob lem. " Why did the mood change? What misguided educational philoso phy transformed graduate mathematics from a passionate activity to a form of passive scholarship? In less sentimental terms, why have the graduate schools dropped the Problem Seminar? We therefore offer "A Problem Seminar" to those students who haven't enjoyed the fun and games of problem solving. CONTENTS Preface v Format I Problems 3 Estimation Theory 11 Generating Functions 17 Limits of Integrals 19 Expectations 21 Prime Factors 23 Category Arguments 25 Convexity 27 Hints 29 Solutions 41 FORMAT This book has three parts: first, the list of problems, briefly punctuated by some descriptive pages; second, a list of hints, which are merely meant as words to the (very) wise; and third, the (almost) complete solutions. Thus, the problems can be viewed on any of three levels: as somewhat difficult challenges (without the hints), as more routine problems (with the hints), or as a textbook on "how to solve it" (when the solutions are read). Of course it is our hope that the book can be enjoyed on any of these three levels.




Inequalities


Book Description

This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving inequalities. It is written for all middle and high-school students, as well as for graduate and undergraduate students. School teachers and trainers for mathematical competitions will also gain benefit from this book.




Problems and Theorems in Classical Set Theory


Book Description

This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.




The Stanford Mathematics Problem Book


Book Description

Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.




Essays in Constructive Mathematics


Book Description

Contents and treatment are fresh and very different from the standard treatments Presents a fully constructive version of what it means to do algebra The exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader