USA Mathematical Olympiads 1972-1986 Problems and Solutions (Anneli Lax New Mathematical Library)

出版者:Mathematical Assn of America

作者:Murray Klamkin (ed.)

页数:0

出版时间:1989-01

价格:USD 22.00

装帧:Paperback

isbn号码:9780883856345

丛书系列:New Mathematical Library

具体描述

People delight in working on problems "because they are there," for the sheer pleasure of meeting a challenge. This is a book full of such delights. In it, Murray S. Klamkin brings together 75 original USA Mathematical Olympiad (USAMO) problems for yearss 1972-1986, with many improvements, extensions, related exercises, open problems, referneces and solutions, often showing alternative approaches. The problems are coded by subject, and solutions are arranged by subject, e.g., algebra, number theory, solid geometry, etc., as an aid to those interested in a particular field. Included is a Glossary of frequently used terms and theorems and a comprehensive bibliography with items numbered and referred to in brackets in the text. This a collection of problemsand solutions of arresting ingenuit, all accessible to secondary school students.

The USAMO has been taken annually by about 150 of the nation's best high school mathematics students. This exam helps to find and encourage high school students with superior mathematical talent and creativity and is the culmination of a three-tiered competition that begins with the American High School Mathematics Examination (AHSME) taken by over 400, 000 students. The eight winners of the USAMO are canidates for the US team in the International Mathematical Olympiad. Schools are encouraged to join this large and important enterprise. See page x of the preface for further information. this book includes a list of all of the top contestants in the USAMO and their schools.

The problems are intriguing and the solutions elegant and informative. Students and teachers will enjoy working these challenging problems. Indeed, all hose who are mathematically inclined will find many delights and pleasant challenges in this book.

用户评价

总而言之，这份汇编不仅仅是工具书，更像是一份收藏品。它捕捉到了一个特定时期美国奥数竞赛的精髓，是数学爱好者和有志于深入研究分析的学者不可多得的资源。它的分量和深度，足以让一个有经验的解题者沉浸其中数周甚至数月，从中汲取营养。我个人认为，如果你想真正理解奥赛数学的深度和广度，并希望将自己的解题能力提升到一个更高的层次，那么这本书提供了一个无与伦比的训练场，它所带来的思维上的锤炼，是任何速成班都无法企及的宝贵财富。

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这套书的装帧设计实在是令人眼前一亮，纸张的质感摸上去非常舒服，封面采用的字体和排版都透露出一种经典的美感，虽然是老版本的题目汇编，但出版社的用心程度让人感觉像是拿到了一本全新的、精心制作的艺术品。内页的印刷清晰度也无可挑剔，即便是复杂的数学符号和图表都能准确无误地呈现出来，长时间阅读下来眼睛也不会感到疲劳。我可以想象，对于那些热爱纯数学，尤其是热衷于奥林匹克竞赛数学的读者来说，仅仅是拥有这套书本身就是一种享受。每一次翻阅，都能感受到纸张与油墨散发出的那种沉静而厚重的知识气息，这与现在很多匆忙出版的电子书或廉价印刷品形成了鲜明的对比。

我必须得说，光是通读目录和前言部分，就足以让人对接下来的内容充满期待。这份资料的编纂显然是经过了深思熟虑和长期积累的，它不仅仅是一个简单的题目罗列，更像是一份历史的见证。从1972年到1986年，这中间横跨了十多年的时间，这些题目无疑代表了当时美国数学教育和选拔体系中的最高水准和最核心的思维方向。对于一个渴望提升自身数学直觉和解题技巧的进阶学习者而言，这种跨越时间维度的系统性回顾，比零散地做几道现代的、可能受特定教学流派影响的题目要有效得多。它提供了一个广阔的视角，让人得以一窥那个时代顶尖数学思维的脉络。

从教学法的角度来看，这份资料的组织结构也颇具匠心。它并非简单地按年份堆砌，而是将不同年份的题目巧妙地穿插在一起，使得读者在解决一个阶段性难题后，能够立刻面对一个性质迥异的新挑战，有效避免了思维的固化。每道题目的详细解答部分，无论是代数、几何、数论还是组合，都展示了严谨的逻辑推导和丰富的技巧运用。即便是对于那些看起来非常基础的题目，其解析过程也往往包含着对更深层数学原理的探讨，这无疑极大地拓宽了读者的知识边界，使人明白，数学的美感往往隐藏在最简洁的表述之下。