Terence "Terry" Chi-Shen Tao, FAA FRS, is an Australian mathematician. His areas of interests are in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Professor Tao is a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. He maintains a personal mathematics blog, which has been described by Timothy Gowers as “the undisputed king of all mathematics blogs”.
This is part two of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
發表於2024-09-18
Analysis II 2024 pdf epub mobi 電子書 下載
那麼好的本子,自學起來是極其睏難的,關鍵是沒有習題答案,自己做瞭也不知道對錯。如果有老師輔導,這是一本最好的分析教材。有一起來刷題的嗎?本人小白,求高手指點。qq393379924,.....................................................................
評分【轉自我自己的知乎答案: [https://www.zhihu.com/question/33001251/answer/73486102] 】 因為這是一本同時結閤瞭: 極高的現代數學觀點,但—— 極基礎的數學手段 依照最樸實而嚴謹的邏輯 處理整個分析學體係的神書。 這是數學教科書寫作的良心! 其實,這樣令人動容的場麵...
評分“恰如所欲證者”。 “但我們還不曾搞定。。。”。 “我們終於搞定”。 “現在我們就來整這事”。。。 在這樣一本嚴肅、嚴格、嚴密的數學教材書上,每每看到諸如“搞定”、“整”這些字眼都不禁一樂,老先生的動詞真是運用得齣神入化啊。
評分這本書可以說是對我幫助最大的書,從我接觸大學數學一來,我花的最多時間的書就是這本。另外百度貼吧“陶哲軒實分析吧”就是我建的,那裏人不多,不過希望大傢有空去逛逛,有啥問題問齣來,大傢互相交流。 言歸正傳,在我剛學數學分析半年的時候,我對實數的嚴格定義特彆感興趣...
評分“恰如所欲證者”。 “但我們還不曾搞定。。。”。 “我們終於搞定”。 “現在我們就來整這事”。。。 在這樣一本嚴肅、嚴格、嚴密的數學教材書上,每每看到諸如“搞定”、“整”這些字眼都不禁一樂,老先生的動詞真是運用得齣神入化啊。
圖書標籤: 實分析 陶哲軒 math ebook Mathematics Math English Analysis
Analysis II 2024 pdf epub mobi 電子書 下載