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題 名 | 數學的嚴格化--微積分學基礎的建構=The Instillation of Rigor in Mathematics--The Building for Rationale of Calculus |
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作 者 | 劉豐榮; | 書刊名 | 正修通識教育學報 |
卷 期 | 6 2009.06[民98.06] |
頁 次 | 頁175-200 |
分類號 | 314.1 |
關鍵詞 | 微積分基本定理; 極限; 一致收斂; The fundamental theorem of calculus; Limit; Uniform convergent; |
語 文 | 中文(Chinese) |
中文摘要 | 自十七世紀末,牛頓和萊布尼茲發明微積分以來,它夾著廣大的威力,成為數學界的新寵兒。然而其理論基礎卻建立在鬆散的直覺幾何上,常遭人詬病,最後終於引起「數學史上的第二次危機」,而微積分基礎的重建工程也吸引許多數學家投入其中,幸運的是在眾人努力下,終於完成這項偉大工作。 本文是作者繼之前「飛逝瞬間的計算~微積分的誕生」之「關於微積分發展簡史」之系列作品之一,旨在與讀者共同分享數學發展過程的艱辛,祈能豐富學子們的數學文化素養。文共分五段,第一段簡介微積分的基礎問題。第二段則探討柯西的生平及其工作。第三段介紹黎曼的生平及其積分工作。第四段則介紹實數系的建構工程:戴德金切割。最後我們介紹魏爾斯史特拉斯的偉大成就。 |
英文摘要 | From the ends of 17th century, Newton and Leibniz invented calculus, it has clamped the general solve might, becomes the new mathematics cosset. However its rationale actually establishes in the loose intuition geometry, cause to be denounced, and causes ”The second crisis in the mathematics history”. But the calculus foundation reconstruction project also attracts many mathematicians to invest. Fortunately, under the numerous people endeavor, finally completes this great work. This article is one of series works continues of ”The development of history for calculus”, lasting ”The instantaneous computation~The birth of calculus”, for the purpose of sharing the difficulty of mathematics developing process together with the reader, prays enrich the scholars mathematics culture accomplishment. The article divides five sections. The first section discusses the rationale question of calculus. The second section discusses the biography of Cauchy and his work. The third section introduces the biography and he integral work of Riemann. The fourth section introduced the department for the construction project of real number: Dedkind cut. Finally we introduce the history and the great achievement of Weirestrass. |
本系統中英文摘要資訊取自各篇刊載內容。