具有基本解决方案的具有挑战性的数学问题，卷一（修订版） Challenging Mathematical Problems with Elementary Solutions, Vol. I: Volume 1 (Revised)

基本信息

Series:Dover Books on Mathema 1.4tics

Format:Paperback / softback 239 pages

Publisher:Dover Publications Inc.

Imprint:Dover Publications Inc.

ISBN:9780486655369

Published:28 Mar 2003

Weight:298g

Dimensions:216 x 137 x 13 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

这套两卷书专为高年级高中生、本科生、研究生、数学教师以及任何热爱数学挑战的人士设计，提供了广泛的具有挑战性的问题 - 从相对简单到极其困难。事实上，有些问题堪称杰出数学家的杰出成就。

本书译自知名的俄罗斯著作《初等阐述中的非初等问题》，主要目的是让读者了解各种新的数学事实、思想和方法。虽然大多数问题代表了高等（“非初等”）数学的问题，但大多数问题都可以用初等数学来解决。事实上，在大多数情况下，不需要高中课程以外的数学知识。

卷一包含 100 个问题，并附有详细的解决方案，所有问题都涉及概率论和组合分析。主题包括整数作为和与积的表示、棋盘上的组合问题、组合分析的几何问题、二项式系数问题、计算概率问题、具有无限多种可能结果的实验​​以及具有连续可能结果的实验​​。

第二卷包含来自数学各个分支的 74 个问题，涉及点和线、平面上的点格、拓扑、凸多边形、对象分布、非十进制计数、素数理论等主题。在这两卷中，给出问题的陈述，然后是给出完整解决方案的部分。答案和提示在书的后面给出。

这本内容广泛的汇编非常适合作为教材、自学或数学俱乐部的工作资源，它提供了 174 个精心挑选的问题，将测试几乎所有学生、教师或数学家的数学敏锐度和解决问题的能力。

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.

作者简介

伊萨克·莫伊谢耶维奇·亚格洛姆 (1921 年 3 月 6 日 - 1988 年 4 月 17 日) 是苏联数学家，著有通俗数学书籍，部分书籍由他的双胞胎兄弟阿基瓦·亚格洛姆合著。

亚格洛姆于 1945 年在莫斯科大学获得博士学位，师从维尼阿明·卡根。作为多部译成英文的书籍的作者，他享有国际声誉，这些书籍已成为学术参考标准。他对学习（教学法）重要性的关注使他的书籍成为学生愉快的体验。他的俄罗斯讣告的七位作者叙述道“......他的兴趣广泛得令人难以置信：他对历史和哲学有着浓厚的兴趣，对文学和艺术有着强烈的热爱和渊博的学识，经常就各种各样的话题发表报告和演讲（例如，关于亚历山大·勃洛克、安娜·阿赫玛托娃和荷兰画家 M.C. 埃舍尔），积极参加雅罗斯拉夫尔电影俱乐部和莫斯科作曲家之家音乐俱乐部的工作，并经常参加数学语言学和符号学会议。”

Isaak Moiseevich Yaglom (6 March 1921 – 17 April 1988) was a Soviet mathematician and author of popular mathematics books, some with his twin Akiva Yaglom.

Yaglom received a Ph.D. from Moscow State University in 1945 as student of Veniamin Kagan. As the author of several books, translated into English, that have become academic standards of reference, he has an international stature. His attention to the necessities of learning (pedagogy) make his books pleasing experiences for students. The seven authors of his Russian obituary recount "…the breadth of his interests was truly extraordinary: he was seriously interested in history and philosophy, passionately loved and had a good knowledge of literature and art, often came forward with reports and lectures on the most diverse topics (for example, on Alexander Blok, Anna Akhmatova, and the Dutch painter M. C. Escher), actively took part in the work of the cinema club in Yaroslavl and the music club at the House of Composers in Moscow, and was a continual participant of conferences on mathematical linguistics and on semiotics."