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發表於 09-6-19 06:22 PM |只看該作者 |倒序瀏覽 |打印

入門書藉/進階書籍:

以下的書籍適合剛讀完AL Pure Maths, Applied Maths的朋友讀. 如果你有志大學讀maths, 精算, physics, quant finance, economics, engine, computer science….依幾本書係可以幫你明白大學數學同中學數學既唔同, post d links出黎純為幫大家由AL Pure轉讀大學數學時睇睇大學數學既levels, 本人極力推介一些problem solving既書例如How to prove it或how to solve跟其它數學書一齊睇, 咁對你將來學analysis或者其它branches of maths都有幫助.書籍如下:

problem solving/proofs:

G. Polya, ?How to Solve It: A New Aspect of Mathematical Method?http://rapidshare.com/files/32713392/0691023565.rar
若你是數學本科生, 一定要睇. 若你是physics, economics, engine, computer science生, 睇左都會對你有幫助.

Daniel J. Velleman, How to Prove It: A Structured Approach
http://rapidshare.com/files/4498 ... oach-0521675995.zip
覺得analysis難嗎? 或許因為你沒有看這本書. 看看吧, 你會得益良多的.

Calculus:

Michael Spivak, Calculus (3rd Edition)
http://www.filestube.com/46a3b9f261123ec203ea/go.html
(solution) http://rapidshare.com/files/118577498/dfaff.rar
極好的微積分書. 如果你覺得little rudin太難, apostal又未睇得明, 計熟這本經典先吧. 計好那些exercises同埋對埋answers睇下自己差幾遠, 幾個月後你會覺得自己勁左.

Tom M. Apostol, Calculus: One-Variable Calculus with an Introduction to Linear Algebra
(volume 1) http://depositfiles.com/en/files/qyq5hita7
(volume 2) http://depositfiles.com/en/files/26bz7ypj6
覺得spivak calculus唔夠喉, 無cover到multi-variables calculus, Apostol 幫你到! 詳盡, 多examples….一一係兩本書既強項. Exercises或者不夠spivak的富有挑戰性, 但已經好過thomas calculus好多了.

Richard Courant; Fritz John, "Introduction to Calculus and Analysis, Volume 1"
http://rapidshare.com/files/6558 ... us_and_Analysis.rar
本人十分鐘意既經典之作. Courant係一個很好的數學家. 寫書文筆一流, 解釋很清楚, 卷二cover好多advanced calculus內容可惜網上不能下載. 這裏只有volume 1. 如果有興趣, 可以到你們的大學圖書館借.

Linear Algebra:

Stephen H. Friedberg, Arnold J. Insel , Lawrence E. Spence “Linear Algebra"
(Volume 1) http://depositfiles.com/en/files/3421866
(Volume 2) http://depositfiles.com/en/files/3421862
樓上介紹過的linear algebra書, 一開始已經由vector space入手, 非常formal. 入門那些問題都係based-on problems and proofs, 對數學系人仕來說係必需之書.
Sheldon Axler "Linear Algebra Done Right"
http://uploading.com/files/4HOKBY1S/0387982582.rar.html
程度比上一本進階少少, 係作者對 vector space既解釋更formal. 如果睇完上一本可以睇埋依本.

Advanced Calculus/Analysis

Michael Spivak, "Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus"
http://rapidshare.com/files/189399134/spivak.rar
想正統咁學multi-variables calculus? 依本就岩你. 記住讀好baby spivak先好讀依本, 唔係好易失方向.

Tom M. Apostol "Mathematical Analysis, 2 Ed."
http://depositfiles.com/en/files/bavkahn9j
(solutions) http://www.csie.ntu.edu.tw/~b89089/solution.html
認為little rudin太難嗎? 聽完apostol既calculus覺得好好? 依本就岩你.
無需多講, 好多人都知正野.

Robert S. Strichartz, "The Way of Analysis” http://depositfiles.com/en/files/56wgxuyy3
覺得Rudin同apostol解釋唔好? 依本書就一步一步教你點思考analysis. 入面有有幾個chapters教differential equations, fourier series依d實用野. 係一本好書.

A Kolmogorov and S Fomin, Introductory Real Analysis
http://rs297.rapidshare.com/file ... gorov__S._Fomin.pdf
依本由set theory同埋metric space教analysis. 經典之作. 到而家我都會成日睇返佢教metric 同topological spaces個d chapters. 如果想讀topology, 依本係你要睇.

Robert G. Bartle, "The elements of real analysis"
http://mihd.net/0tac2w
樓上提到的analysis書, 小弟無睇過, 不評價.

p.s. 有些巴打pm小弟話download唔到或者開唔到. 其實某d files係djvu files黎.

[ 本帖最後由 kwoklap 於 2009-6-19 06:24 PM 編輯 ]