Mathematics: Its Content, Methods and Meaning
暫譯: 數學：其內容、方法與意義

Aleksandrov, A. D., Kolmogorov, A. N., Lavrent'ev, M. a.

Mathematics: Its Content, Methods and Meaning
  • 出版商: Dover Publications
  • 出版日期: 1999-07-07
  • 售價: $2,180
  • 貴賓價: 9.5 折 $2,071
  • 語言: 英文
  • 頁數: 1120
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 0486409163
  • ISBN-13: 9780486409160
  • 相關分類: 工程數學 Engineering-mathematics

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

". . . Nothing less than a major contribution to the scientific culture of this world." -- The New York Times Book Review
This major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated development. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."
Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It further examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, groups, and other algebraic systems.
Thorough, coherent explanations of each topic are further augmented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference.
"This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." -- Social Science

商品描述(中文翻譯)

「……對於這個世界的科學文化來說，無疑是一項重大的貢獻。」-- 紐約時報書評

這本關於數學的重大調查，展示了18位傑出的俄羅斯數學家的作品，涵蓋了初級和高級層面的材料，涉及數學的20個主要主題領域，從其簡單的起源到隨後的複雜發展。正如紐約大學的莫里斯·克萊因教授所指出的，「這部獨特的作品呈現了數學的驚人全景。它是對數學在初級和高級層面上所包含內容的最佳印刷回答。」

本書的第一部分是對數學的概述和分析，接下來的三個主要部分進一步探討解析幾何、代數和常微分方程。第二部分介紹偏微分方程，以及曲線和曲面的理論、變分法和複變函數。它還進一步研究質數、概率論、近似以及計算機在數學中的角色。實變函數理論開啟了最後一部分，隨後討論線性代數、非歐幾里得幾何、拓撲學、函數分析、群論及其他代數系統。

每個主題的徹底且連貫的解釋都得到了大量插圖的補充，每章結尾都有建議的閱讀清單。這部數學傑作曾以三卷本的形式發行，現在以方便且價格適中的單卷本版本提供，非常適合學習或參考。

「這是一部對於一部驚人且艱深的數學傑作的精湛英語翻譯……」-- 社會科學

作者簡介

The Russian Equation
Representative of the tremendous impact which Russian mathematicians have had on the Dover list since the Sputnik era is this outstanding book edited by A. D. Aleksandrov and others.

Critical Acclaim for Mathematics: Its Content, Methods and Meaning:
"In effect, these volumes present a do-it-yourself course for the person who would like to know what the chief fields of modern mathematics are all about but who does not aspire to be a professional mathematician or a professional user of mathematics. The coverage is extremely wide, including such important areas as linear algebra, group theory, functional analysis, ordinary and partial differential equations, the theory of functions of real and complex variables, and related subjects. . . . What makes these volumes so readable as compared with usual mathematics textbooks is the emphasis here upon basic concepts and results rather than upon the intricate and wearying proofs that make such demands in conventional textbooks and courses. There are proofs in these volumes, but usually they are presented only for the most important results, and even then to emphasize key areas and to illustrate the kind of methodology employed. . . . It is hard to imagine that any intelligent American with a curious mind and some good recollection of his high school and college mathematics would not find many entrancing discoveries in the intellectual gold mine that is this work." -- The New York Times Book Review

"An excellent reference set for bright high school students and beginning college students . . . also of value to their teachers for lucid discussions and many good elementary examples in both familiar and unfamiliar branches. The intelligentsia of laymen who care to tackle more than today's popular magazine articles on mathematics will find many rewarding introductions to subjects of current interest." -- The Mathematics Teacher

"Whether a physicist wishes to know what a Lie algebra is or how it is related to a Lie group, or an undergraduate would like to begin the study of homology, or a crystallographer is interested in Fedorov groups, or an engineer in probability, or any scientist in computing machines, he will find here a connected, lucid account." -- Science

作者簡介(中文翻譯)

《俄羅斯方程式》

俄羅斯數學家自史普特尼克時代以來對多佛書單所產生的巨大影響的代表作，就是這本由 A. D. Aleksandrov 等人編輯的傑出書籍。

《數學：內容、方法與意義》的評論：

「實際上，這些卷冊為那些希望了解現代數學主要領域但不想成為專業數學家或數學專業使用者的人提供了一個自學課程。內容涵蓋極為廣泛，包括線性代數、群論、泛函分析、常微分方程和偏微分方程、實變數和複變數函數理論及相關主題……這些卷冊之所以比一般數學教科書更易讀，是因為它們強調基本概念和結果，而不是傳統教科書和課程中繁瑣且令人疲憊的證明。這些卷冊中有證明，但通常僅針對最重要的結果呈現，甚至在那時也只是為了強調關鍵領域並說明所採用的方法論……很難想像，任何一位具有好奇心的聰明美國人，對他高中和大學數學有良好記憶的人，會在這部作品這個智力金礦中找不到許多迷人的發現。」-- 《紐約時報書評》

「對於聰明的高中生和初學大學生來說，這是一套極好的參考書……對於他們的老師來說，這也具有價值，因為書中有清晰的討論和許多良好的基本例子，涵蓋熟悉和不熟悉的領域。那些願意超越當今流行雜誌文章的外行知識分子，將會在這裡找到許多有價值的當前興趣主題的介紹。」-- 《數學教師》

「無論物理學家想知道什麼是李代數或它與李群的關係，或本科生想開始學習同調，或結晶學家對費多羅夫群感興趣，或工程師對概率感興趣，或任何科學家對計算機感興趣，他們都會在這裡找到一個連貫且清晰的說明。」-- 《科學》

類似商品