The present book is rare, even unique of its kind, at least among mathematics texts published in Russian. You have before you neither a textbook nor a monograph, although these selected chapters from elementary mathematics certainly constitute a fine educational tool. It is my opinion that this is more than just another book about mathematics and the art of teaching that subject. Without considering the actual topics treated the author himself has described these in sufficient detail in of the book as a whole, the Introduction , I shall attempt to convey a general idea and describe the impressions it makes on the reader.

Almost every chapter begins by considering well-known problems of elementary mathematics. Now, every worthwhile elementary problem has hidden behind its diverting formulation what might be called "higher mathematics," or, more simply, mathematics, and it is this that the author demonstrates to the reader in this book. It is thus to be expected that every chapter should contain subject matter that is far from elementary. The end result of reading the book is that the material treated has become for the reader "three-dimensional" as it were, as in a hologram, capable of being viewed from all sides.

Similar ebooks. Mathematical Olympiad Challenges. Titu Andreescu. Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals.

## Putnam and Beyond - AbeBooks - Razvan Gelca:

An important feature of the work is the comprehensive background material provided with each grouping of problems. Problems and Theorems in Classical Set Theory. Peter Komjath. Although the? The invention of forcing produced a powerful, technically sophisticated tool for solving unsolvable problems. Still, most results of the pre-Cohen era can be digested with just the knowledge of a commonsense introduction to the topic. And it is a worthy e?

In this volume we o? Most of classical set theory is covered, classical in the sense that independence methods are not used, but classical also in the sense that most results come fromtheperiod,say,— Challenging Problems in Geometry. Alfred S.

Designed for high school students and teachers with an interest in mathematical problem-solving, this volume offers a wealth of nonroutine problems in geometry that stimulate students to explore unfamiliar or little-known aspects of mathematics. Included are nearly problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency, and many other subjects.

Within each topic, the problems are arranged in approximate order of difficulty.

Detailed solutions as well as hints are provided for all problems, and specific answers for most. Invaluable as a supplement to a basic geometry textbook, this volume offers both further explorations on specific topics and practice in developing problem-solving techniques. Rooted in a pedagogically successful problem-solving approach to linear algebra, this work fills a gap in the literature that is sharply divided between, on the one end, elementary texts with only limited exercises and examples, and, at the other extreme, books too advanced in prerequisites and too specialized in focus to appeal to a wide audience.

Instead, "Essential Linear Algebra" clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications and connections to fields such as biology, economics, computer graphics, electrical engineering, cryptography, and political science. It is thus to be expected that every chapter should contain subject matter that is far from elementary.

The end result of reading the book is that the material treated has become for the reader "three-dimensional" as it were, as in a hologram, capable of being viewed from all sides. Similar ebooks.

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## Putnam and Beyond - Titu

Mathematical Olympiad Challenges. Titu Andreescu. Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals.

An important feature of the work is the comprehensive background material provided with each grouping of problems. Problems and Theorems in Classical Set Theory. Peter Komjath. Although the? The invention of forcing produced a powerful, technically sophisticated tool for solving unsolvable problems. Still, most results of the pre-Cohen era can be digested with just the knowledge of a commonsense introduction to the topic. And it is a worthy e?

In this volume we o? Most of classical set theory is covered, classical in the sense that independence methods are not used, but classical also in the sense that most results come fromtheperiod,say,— Challenging Problems in Geometry. Alfred S. Designed for high school students and teachers with an interest in mathematical problem-solving, this volume offers a wealth of nonroutine problems in geometry that stimulate students to explore unfamiliar or little-known aspects of mathematics.

Included are nearly problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency, and many other subjects.

Within each topic, the problems are arranged in approximate order of difficulty. Detailed solutions as well as hints are provided for all problems, and specific answers for most. Invaluable as a supplement to a basic geometry textbook, this volume offers both further explorations on specific topics and practice in developing problem-solving techniques.

### Samenvatting

Rooted in a pedagogically successful problem-solving approach to linear algebra, this work fills a gap in the literature that is sharply divided between, on the one end, elementary texts with only limited exercises and examples, and, at the other extreme, books too advanced in prerequisites and too specialized in focus to appeal to a wide audience. Instead, "Essential Linear Algebra" clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications and connections to fields such as biology, economics, computer graphics, electrical engineering, cryptography, and political science.

Mathematics as Problem Solving: Edition 2. Alexander Soifer. This book joins several other books available for the preparation of young scholars for a future that involves solving mathematical pr- lems. This training not only increases their? The book is a diversi?

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The introductory explanations and worked problems help guide the reader without turning the additional problems into rote repe- tions of the solved ones. Putnam and Beyond fills the need for problem-based texts that specifically target the Putnam exams.

### Table of contents

He is also involved in mathematics competitions such as the mathematical Olympiads and the W. Putnam Mathematical Competition. Titu Andreescu , University of Texas-Dallas, is highly involved with mathematics contests and olym. See All Customer Reviews. Shop Textbooks.

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