What Is Mathematics? An Elementary Approach to Ideas and Methods
暫譯: 什麼是數學?基本概念與方法的入門探討

Richard Courant, Herbert Robbins

  • 出版商: Oxford University
  • 出版日期: 1996-07-18
  • 售價: $1,210
  • 貴賓價: 9.5$1,150
  • 語言: 英文
  • 頁數: 592
  • 裝訂: Paperback
  • ISBN: 0195105192
  • ISBN-13: 9780195105193
  • 無法訂購

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商品描述

For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.

Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.

Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.

Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.

商品描述(中文翻譯)

超過兩千年來,對數學的熟悉被視為每位有文化的人的智力裝備中不可或缺的一部分。然而,今天,數學在教育中的傳統地位正面臨嚴重的危機。數學的教學與學習已淪為死記硬背的領域,其結果雖然能夠達到令人滿意的形式能力,但卻無法帶來真正的理解或更大的智力獨立性。理查德·庫朗(Richard Courant)和赫伯特·羅賓斯(Herbert Robbins)的這本經典著作的新版本旨在解決這個問題。其目標是將意義重新帶回數學中。

《數學是什麼?第二版》是為初學者和學者、學生和教師、哲學家和工程師所寫,是一部閃耀著數學瑰寶的作品,提供了一幅有趣且易於理解的數學世界畫像。涵蓋從自然數和數字系統到幾何構造和射影幾何,從拓撲學和微積分到原則問題和連續體假設,這部引人入勝的調查讓讀者能夠深入探討數學作為一個有機整體,而不是空洞的解題訓練。各章節大多相互獨立,並且從基本到更高級的討論逐步深入,讀者可以輕鬆選擇特別感興趣的領域,而不會影響對後續部分的理解。

《數學是什麼?第二版》由伊恩·斯圖爾特(Ian Stewart)更新了一章,提供了對近期數學發展的新見解,並描述了四色定理和費馬最後定理的證明,這些問題在庫朗和羅賓斯撰寫這部傑作時仍然未解,但此後已經得到了解決。

形式數學就像拼寫和語法——是正確應用當地規則的問題。意義深遠的數學則像新聞報導——它講述了一個有趣的故事。但與某些新聞報導不同的是,這個故事必須是真實的。最好的數學就像文學——它在你眼前賦予故事生命,並在智力和情感上讓你參與其中。《數學是什麼》就像一部優秀的文學作品——它為任何有興趣的人打開了一扇通往數學世界的窗。