或者說自己對於數學有叫全面的認識了嗎?


不能。能不能成為數學家看的是能不能在某個領域取得重要進展,做出重要貢獻。GTM系列涉及的領域太廣,內容重複的也很多。讀完這些書花費大量時間卻還沒進入前沿研究,吃力不討好。精讀幾本還好,讀太多只是在浪費時間。Yau能得菲爾茲獎是因為他解決了Calabi猜想,Perelman能得菲爾茲獎是因為他解決了幾何化猜想和Poincare猜想,不是因為他們懂的多,更不是因為他們讀完了所有領域的數學書。

很多人的錯覺是懂的更多做的成果更好。而實際上懂的更深才能做出更好的數學。Hamilton在1982年就已經造出了Ricci flow,並且開始嘗試用Ricci flow來研究幾何化猜想。Yau的好幾個學生,比如曹懷東,Bennett Chow,施皖雄八幾年就開始跟著Hamilton做Ricci flow。到98年左右,Hamilton在CAG上發過一篇文章在Ricci flow不產生奇點的假設下研究了其收斂性。這篇文章就已經指出了Ricci flow有希望解決幾何化猜想,但他卡在如何處理奇點上。雖然他意識到要對flow做手術,但有一類奇點他無法分類,也就不知道該如何做手術。Perelman開始研究Ricci flow顯然比Hamilton和曹,Chow等都要晚的多。對於Ricci flow,Perelman了解的知識絕對不超過Hamilton。但他能找到Ricci flow的entropy,證明nonlocal collapsing定理。嚴格來說,Perelnan也沒有完全分類奇點,但他能說清楚Hamilton所不能解決的那類奇點的漸近幾何。但這已經足夠保證對Ricci flow做手術並且完成幾何化猜想的證明。年輕數學家能解決前輩不能解決的問題不在於他懂的更多,而在於他有更好的觀點和方法,對問題有更深的理解。

能精通一個領域遠勝於什麼都學。用武俠做類比的話,就像是精通降龍十八掌的喬峰遠勝於會多門武功的慕容復。只有當自己研究的問題本質地涉及到其他領域時,才有必要系統的學習一個新的領域。我讀博的時候也覺得懂的更多的人以後會更厲害。後來身邊好幾個熟人發了四大,duke這個級別的論文,他們在發這些文章以前並沒有表現的特別聰明,也能明顯感覺到他們在某些領域懂的不多,但他們能專註於自己的問題。當時我們覺得最聰明的,懂的最多的那個人雖然也發了不少好文章,但他目前所取得的成果則不如前面說的那幾個。他懂的很多,讀博同時參加兩個不同方向的討論班並且還都講。當時大家都特別佩服,現在事後想起來,可能正是因為精力分散才導致他目前的發展沒有達到我們預想的程度吧。


GTM 280多本,而且很多都是內容有大量重複的。真有能力全部讀完看懂的,制約他的會是時間、精力,而不是學習能力。。而且GTM又不是多深的數學書,大部分領域只是入門教材而已。讀過GTM離真正進入研究前沿還有相當距離呢。所謂GTM,其實在北清科復浙等等學校完全可以作為本科生高年級選修課或者討論班的素材;很多針對數學本科生以及低年級研究生的數學暑期學校的內容也與GTM層次的教材重疊。

而且GTM不一定就是對應領域的好的入門教材,有些太老了,有些太淺了,也不夠全面。你看GTM里還有1970年代的著作,真了解當代數學史的人就知道70年代的數學和現在的前沿數學有多大差別。丘成桐證明Calabi猜想是在1976年,在那之後Calabi-Yau流形這個名詞才正式進入數學文獻。對比一下現在微分幾何、代數幾何里隨處可見的CY流形字樣,是不是有一種歷史感撲面而來?


孩子 你是剛讀大學嗎?

老實說 你想讀完GTM是不可能的。

一般的數學研究生一個學期也就只能讀完一兩本 能讀完兩本的通常是因為這兩本可能比較薄 比較簡單

比較難的GTM 像著名的52在伯克利是那裡的學生五個學期的教材

Serre的局部域你零基礎能在一年讀完就不錯了

GTM系列目前已經出到大約280了

就打你一學期兩本 一年四本你也要七十年才能學完 而且這已經是按照最理想的情況來算了

但是要成為數學家 一般的都是在三十歲以前就開始獨立做研究了 頂多只有十年時間給你學知識

再加上一般從研究生就要開始讀論文了

所以 綜上 題主 你對於數學的認識還停留在不切實際的幻想階段

想要真正從事數學研究 並且像自己說的想對數學有一個全面的認識首先就是要放棄那些幼稚的 不切實際的幻想

然後腳踏實地 從基礎的開始一步步學起

你如果天賦異稟 完全靠自學也差不多兩年就能從零基礎到能讀GTM程度的書了

關鍵是入門以後的選擇 根據自己的喜好先選個分支入手

對數學的全面認識並不是像初學者想像的一開始什麼都學 而是在一個領域紮下根後再向其它分支延拓 這樣十年二十年你差不多確實能對現今數學的大致面貌有一個比較深刻的了解

當然前提是你好學 有的人做研究就喜歡在他那狹小的領域 這個另當別論

如果你說的全面認識是指像希爾伯特 龐加萊那樣成為精通所有主流分支的大家

那麼沒人能告訴你怎樣成為 因為即使是希爾伯特自己也沒能把他的學生都培養得和他一樣

更何況在我們這個時代 數學的廣度 深度和一百年前都不能同日而語了

所以 還是那句話 題主你首先得學會放棄不切實際的幻想

當然了 初學者往往都不服氣 認為別人做不到我就做不到嗎?

那麼回答這個問題的最好答案就是親身去嘗試 如果你在認真學了幾年數學以後還能堅持這個想法 那麼祝你好運!


不能,這只是剛剛達到清北數學大神的起步水平而已。但這些大神在未名湖讀博四天王面前不過是螻蟻,而四天王中最強的在保福寺橋師資三聖者面前也只是一根手指就會被碾壓的神魂俱滅,灰燼沉入未名湖。而三聖者中的最強者要經歷七七四十九重考核天劫才能有機會步入水木講壇,在這裡,已經不僅僅是武力的對決,甚至金口一開便是萬鈞壓頂,僅僅用言語便能虐遍三界,稱為「講師」……

至於副教授,那已經不是吾輩凡人所能知的境界了,傳說中再往上還有七層天,十八泰透,每一層的差距都有如須彌芥子……我只能告訴你,數宗強者,恐怖如斯!


GTM目前已經出了284本,大概每年還在新增2-4本的速度。我覺得GTM這麼變態的書,一個月讀完一本是極限了。假設每年GTM系列新增3本,全部讀完整個GTM系列需要284除以(12-3)約等於32年,18歲開始讀,讀完50歲了,基本上已經到了數學教授不在一線做研究的年齡了。

其實我覺得一個人選擇一個數學分支領域能夠cover to cover地讀完10本GTM,還沒有被勸退,還沒有懷疑自己是不是合適學數學。這個人只要沉下心來做數學研究,一定大有可為,離數學家並不遙遠。

附284本書的名字,本本都是難啃的骨頭:

1. Introduction to Axiomatic Set Theory, Gaisi Takeuti, Wilson M. Zaring (1982, 2nd ed., ISBN 978-1-4613-8170-9)

2. Measure and Category - A Survey of the Analogies between Topological and Measure Spaces, John C. Oxtoby (1980, 2nd ed., ISBN 978-0-387-90508-2)

3. Topological Vector Spaces, H. H. Schaefer, M. P. Wolff (1999, 2nd ed., ISBN 978-0-387-98726-2)

4. A Course in Homological Algebra, Peter Hilton, Urs Stammbach (1997, 2nd ed., ISBN 978-0-387-94823-2)

5. Categories for the Working Mathematician, Saunders Mac Lane (1998, 2nd ed., ISBN 978-0-387-98403-2)

6. Projective Planes, Daniel R. Hughes, Fred C. Piper, (1982, ISBN 978-3-540-90043-6)

7. A Course in Arithmetic, Jean-Pierre Serre (1996, ISBN 978-0-387-90040-7)

8. Axiomatic Set Theory, Gaisi Takeuti, Wilson M. Zaring, (1973, ISBN 978-3-540-90050-4)

9. Introduction to Lie Algebras and Representation Theory, James E. Humphreys (1997, ISBN 978-0-387-90053-7)

10. A Course in Simple-Homotopy Theory, Marshall. M. Cohen, (1973, ISBN 0-387-90056-X)

11. Functions of One Complex Variable I, John B. Conway (1978, 2nd ed., ISBN 978-0-387-90328-6)

12. Advanced Mathematical Analysis, Richard Beals (1973, ISBN 978-0-387-90065-0)

13. Rings and Categories of Modules, Frank W. Anderson, Kent R. Fuller (1992, 2nd ed., ISBN 978-0-387-97845-1)

14. Stable Mappings and Their Singularities, Martin Golubitsky, Victor Guillemin, (1974, ISBN 978-0-387-90072-8)

15. Lectures in Functional Analysis and Operator Theory, Sterling K. Berberian, (1974, ISBN 978-0-387-90080-3)

16. The Structure of Fields, David J. Winter, (1974, ISBN 978-3-540-90074-0)

17. Random Processes, Murray Rosenblatt, (1974, ISBN 978-0-387-90085-8)

18. Measure Theory, Paul R. Halmos (1974, ISBN 978-0-387-90088-9)

19. A Hilbert Space Problem Book, Paul R. Halmos (1982, 2nd ed., ISBN 978-0-387-90685-0)

20. Fibre Bundles, Dale Husemoller (1994, 3rd ed., ISBN 978-0-387-94087-8)

21. Linear Algebraic Groups, James E. Humphreys (1998, ISBN 978-0-387-90108-4)

22. An Algebraic Introduction to Mathematical Logic, Donald W. Barnes, John M. Mack (1975, ISBN 978-0-387-90109-1)

23. Linear Algebra, Werner H. Greub (1981, ISBN 978-0-387-90110-7)

24. Geometric Functional Analysis and Its Applications, Richard B. Holmes, (1975, ISBN 978-0-387-90136-7)

25. Real and Abstract Analysis, Edwin Hewitt, Karl Stromberg (1975, ISBN 978-0-387-90138-1)

26. Algebraic Theories, Ernest G. Manes, (1976, ISBN 978-3-540-90140-2)

27. General Topology, John L. Kelley (1975, ISBN 978-0-387-90125-1)

28. Commutative Algebra I, Oscar Zariski, Pierre Samuel (1975, ISBN 978-0-387-90089-6)

29. Commutative Algebra II, Oscar Zariski, Pierre Samuel (1975, ISBN 978-0-387-90171-8)

30. Lectures in Abstract Algebra I: Basic Concepts, Nathan Jacobson (1976, ISBN 978-0-387-90181-7)

31. Lectures in Abstract Algebra II: Linear Algebra, Nathan Jacobson (1984, ISBN 978-0-387-90123-7)

32. Lectures in Abstract Algebra III: Theory of Fields and Galois Theory, Nathan Jacobson (1976, ISBN 978-0-387-90168-8)

33. Differential Topology, Morris W. Hirsch (1976, ISBN 978-0-387-90148-0)

34. Principles of Random Walk, Frank Spitzer (2001, ISBN 978-0-387-95154-6)

35. Several Complex Variables and Banach Algebras, Herbert Alexander, John Wermer (1998, 3rd ed., ISBN 978-0-387-98253-3)

36. Linear Topological Spaces, John L. Kelley, Isaac Namioka (1982, ISBN 978-0-387-90169-5)

37. Mathematical Logic, J. Donald Monk (1976, ISBN 978-0-387-90170-1)

38. Several Complex Variables, H. Grauert, K. Fritzsche (1976, ISBN 978-0-387-90172-5)

39. An Invitation to {displaystyle C^{*}}-Algebras, William Arveson (1976, ISBN 978-0-387-90176-3)

40. Denumerable Markov Chains, John G. Kemeny, J. Laurie Snell, Anthony W. Knapp, D.S. Griffeath (1976, ISBN 978-0-387-90177-0)

41. Modular Functions and Dirichlet Series in Number Theory, Tom M. Apostol (1989, 2nd ed., ISBN 978-0-387-97127-8)

42. Linear Representations of Finite Groups, Jean-Pierre Serre, Leonhard L. Scott (1977, ISBN 978-0-387-90190-9)

43. Rings of Continuous Functions, Leonard Gillman, Meyer Jerison (1976, ISBN 978-0-387-90198-5)

44. Elementary Algebraic Geometry, Keith Kendig (1977, ISBN 978-0-387-90199-2)

45. Probability Theory I, M. Loève (1977, 4th ed, ISBN 978-0-387-90210-4)

46. Probability Theory II, M. Loève (1978, 4th ed, ISBN 978-0-387-90262-3)

47. Geometric Topology in Dimensions 2 and 3, Edwin E. Moise (1977, ISBN 978-0-387-90220-3)

48. General Relativity for Mathematicians, R. K. Sachs, H. Wu (1983, ISBN 978-0-387-90218-0)

49. Linear Geometry, K. W. Gruenberg, A. J. Weir (2010, ISBN 978-0-387-90227-2)

50. Fermats Last Theorem: A Genetic Introduction to Algebraic Number Theory, Harold M. Edwards (2000, ISBN 978-0-387-90230-2)

51. A Course in Differential Geometry, William Klingenberg, D. Hoffman (1983, ISBN 978-0-387-90255-5)

52. Algebraic Geometry, Robin Hartshorne (2010, ISBN 978-1-4419-2807-8)

53. A Course in Mathematical Logic for Mathematicians, Yu. I. Manin, Boris Zilber (2009, 2nd ed., ISBN 978-1-4419-0614-4)

54. Combinatorics with Emphasis on the Theory of Graphs, Mark E. Watkins, Jack E. Graver (1977, ISBN 978-0-387-90245-6)

55. Introduction to Operator Theory I: Elements of Functional Analysis, Arlen Brown, Carl Pearcy (1977, ISBN 978-0-387-90257-9)

56. Algebraic Topology: An Introduction, William S. Massey (1977, ISBN 978-0-387-90271-5)

57. Introduction to Knot Theory, Richard H. Crowell, Ralph H. Fox (1977, ISBN 978-0-387-90272-2)

58. p-adic Numbers, p-adic Analysis, and Zeta-Functions, Neal Koblitz (1984, 2nd ed., ISBN 978-0-387-96017-3)

59. Cyclotomic Fields, Serge Lang (1978, ISBN 978-0-387-90307-1)

60. Mathematical Methods of Classical Mechanics, V. I. Arnold, A. Weinstein, K. Vogtmann (1989, 2nd ed., ISBN 978-0-387-96890-2)

61. Elements of Homotopy Theory, George W. Whitehead (1978, ISBN 978-0-387-90336-1)

62. Fundamentals of the Theory of Groups, M. I. Kargapolov, J. I. Merzljakov (1979, ISBN 978-1-4612-9966-0)

63. Graph Theory - An Introductory Course, Béla Bollobás (1979, ISBN 978-1-4612-9969-1)

64. Fourier Series - A Modern Introduction Volume 1, R. E. Edwards (1979, 2nd ed., ISBN 978-1-4612-6210-7)

65. Differential Analysis on Complex Manifolds, Raymond O. Wells, Jr. (2008, 3rd ed., ISBN 978-0-387-73891-8)

66. Introduction to Affine Group Schemes, W. C. Waterhouse (1979, ISBN 978-1-4612-6219-0)

67. Local Fields, Jean-Pierre Serre (1979, ISBN 978-0-387-90424-5)

68. Linear Operators in Hilbert Spaces, Joachim Weidmann [de] (1980, ISBN 978-1-4612-6029-5)

69. Cyclotomic Fields II, Serge Lang (1980, ISBN 978-1-4684-0088-5)

70. Singular Homology Theory, William S. Massey (1980, ISBN 978-1-4684-9233-0)

71. Riemann Surfaces, Herschel Farkas [de], Irwin Kra (1992, 2nd ed., ISBN 978-0-387-97703-4)

72. Classical Topology and Combinatorial Group Theory, John Stillwell (1980, 2ed 1993, ISBN 978-0-3879-7970-0)

73. Algebra, Thomas W. Hungerford (1974, ISBN 978-0-387-90518-1)

74. Multiplicative Number Theory, Harold Davenport, Hugh Montgomery (2000, 3rd ed., ISBN 978-0-387-95097-6)

75. Basic Theory of Algebraic Groups and Lie Algebras, G. P. Hochschild (1981, ISBN 978-1-4613-8116-7)

76. Algebraic Geometry - An Introduction to Birational Geometry of Algebraic Varieties, Shigeru Iitaka (1982, ISBN 978-1-4613-8121-1)

77. Lectures on the Theory of Algebraic Numbers, E. T. Hecke (1981, ISBN 978-0-387-90595-2)

78. A Course in Universal Algebra, Burris, Stanley and Sankappanavar, H. P. (Online) (1981 ISBN 978-0-3879-0578-5)

79. An Introduction to Ergodic Theory, Peter Walters (1982, ISBN 978-0-387-95152-2)

80. A Course in the Theory of Groups, Derek J.S. Robinson [de] (1996, 2nd ed., ISBN 978-0-387-94461-6)

81. Lectures on Riemann Surfaces, Otto Forster [de] (1981, ISBN 978-0-387-90617-1)

82. Differential Forms in Algebraic Topology, Raoul Bott, Loring W. Tu (1982, ISBN 978-0-387-90613-3)

83. Introduction to Cyclotomic Fields, Lawrence C. Washington (1997, 2nd ed., ISBN 978-0-387-94762-4)

84. A Classical Introduction to Modern Number Theory, Kenneth Ireland, Michael Rosen (1990, 2nd ed., ISBN 978-0-387-97329-6)

85. Fourier Series - A Modern Introduction Volume 2, R. E. Edwards (1982, 2nd ed., ISBN 978-1-4613-8158-7)

86. Introduction to Coding Theory, J. H. van Lint (3rd ed 1998, ISBN 3-540-64133-5)

87. Cohomology of Groups, Kenneth S. Brown (1982, ISBN 978-1-4684-9329-0)

88. Associative Algebras, R. S. Pierce (1982, ISBN 978-1-4757-0165-4)

89. Introduction to Algebraic and Abelian Functions, Serge Lang (1982, 2nd ed., ISBN 978-0-387-90710-9)

90. An Introduction to Convex Polytopes, Arne Brondsted (1983, ISBN 978-1-4612-1148-8)

91. The Geometry of Discrete Groups, Alan F. Beardon [de] (1983, 2nd print 1995, ISBN 978-1-4612-7022-5)

92. Sequences and Series in Banach Spaces, J. Diestel (1984, ISBN 978-1-4612-9734-5)

93. Modern Geometry — Methods and Applications Part I: The Geometry of Surfaces, Transformation Groups, and Fields, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Novikov (1992, 2nd ed., ISBN 978-0-387-97663-1)

94. Foundations of Differentiable Manifolds and Lie Groups, Frank W. Warner [de] (1983, ISBN 978-0-387-90894-6)

95. Probability-1, Probability-2, Albert N. Shiryaev (2016, 2019, 3rd ed., ISBN 978-0-387-72205-4, ISBN 978-0-387-72207-8)

96. A Course in Functional Analysis, John B. Conway (2007, 2nd ed., ISBN 978-0-387-97245-9)

97. Introduction to Elliptic Curves and Modular Forms, Neal I. Koblitz (1993, 2nd ed., ISBN 978-0-387-97966-3)

98. Representations of Compact Lie Groups, Theodor Br?cker [de], Tammo tom Dieck (1985, ISBN 978-3-540-13678-1)

99. Finite Reflection Groups, L.C. Grove, C.T. Benson (1985, 2nd ed., ISBN 978-0-387-96082-1)

100. Harmonic Analysis on Semigroups - Theory of Positive Definite and Related Functions, Christian Berg, Jens Peter Reus Christensen, Paul Ressel (1984, ISBN 978-0-387-90925-7)

101. Galois Theory, Harold M. Edwards (1984, ISBN 978-0-387-90980-6)

102. Lie Groups, Lie Algebras, and Their Representations, V. S. Varadarajan (1984, ISBN 978-0-387-90969-1)

103. Complex Analysis, Serge Lang (1999, 4th ed., ISBN 978-0-387-98592-3)

104. Modern Geometry — Methods and Applications Part II: The Geometry and Topology of Manifolds, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Novikov (1985, ISBN 978-0-387-96162-0)

105. SL2(R), Serge Lang (1985, ISBN 978-0-387-96198-9)

106. The Arithmetic of Elliptic Curves, Joseph H. Silverman (2009, 2nd ed., ISBN 978-0-387-09493-9)

107. Applications of Lie Groups to Differential Equations, Peter J. Olver (2ed 1993, ISBN 978-1-4684-0276-6)

108. Holomorphic Functions and Integral Representations in Several Complex Variables, R. Michael Range (1986, ISBN 978-0-387-96259-7)

109. Univalent Functions and Teichmüller Spaces, O. Lehto (1987, ISBN 978-1-4613-8654-4)

110. Algebraic Number Theory, Serge Lang (1994, 2nd ed., ISBN 978-0-387-94225-4)

111. Elliptic Curves, Dale Husem?ller [de] (2004, 2nd ed., ISBN 978-0-387-95490-5)

112. Elliptic Functions, Serge Lang (1987, 2nd ed., ISBN 978-0-387-96508-6)

113. Brownian Motion and Stochastic Calculus, Ioannis Karatzas, Steven Shreve (2ed 2000, ISBN 978-0-387-97655-6)

114. A Course in Number Theory and Cryptography, Neal Koblitz (2ed 1994, ISBN 978-1-4684-0312-1)

115. Differential Geometry: Manifolds, Curves and Surfaces, Marcel Berger, Bernard Gostiaux (1988, ISBN 978-0-387-96626-7)

116. Measure and Integral — Volume 1, John L. Kelley, T.P. Srinivasan (1988, ISBN 978-0-387-96633-5)

117. Algebraic Groups and Class Fields, Jean-Pierre Serre (1988, ISBN 978-1-4612-6993-9)

118. Analysis Now, Gert K. Pedersen (1989, ISBN 978-0-387-96788-2)

119. An Introduction to Algebraic Topology, Joseph J. Rotman, (1988, ISBN 978-0-3879-6678-6)

120. Weakly Differentiable Functions — Sobolev Spaces and Functions of Bounded Variation, William P. Ziemer (1989, ISBN 978-0-387-97017-2)

121. Cyclotomic Fields I and II, Serge Lang (1990, Combined 2nd ed. ISBN 978-1-4612-6972-4)

122. Theory of Complex Functions, Reinhold Remmert (1991, ISBN 978-0-387-97195-7)

123. Numbers, Heinz-Dieter Ebbinghaus et al. (1990, ISBN 978-0-387-97497-2)

124. Modern Geometry — Methods and Applications Part III: Introduction to Homology Theory, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Novikov (1990, ISBN 978-0-387-97271-8)

125. Complex Variables — An Introduction, Carlos A. Berenstein, Roger Gay (1991, ISBN 978-0-387-97349-4)

126. Linear Algebraic Groups, Armand Borel (1991, ISBN 978-1-4612-6954-0)

127. A Basic Course in Algebraic Topology, William S. Massey (1991, ISBN 978-0-3879-7430-9)

128. Partial Differential Equations, Jeffrey Rauch (1991, ISBN 978-1-4612-6959-5)

129. Representation Theory, William Fulton, Joe Harris (1991, ISBN 978-3-5400-0539-1)

130. Tensor Geometry — The Geometric Viewpoint and its Uses, Christopher T. J. Dodson, Timothy Poston (1991, 2nd ed., ISBN 978-3-540-52018-4)

131. A First Course in Noncommutative Rings, T. Y. Lam (2001, 2nd ed., ISBN 978-0-387-95183-6)

132. Iteration of Rational Functions — Complex Analytic Dynamical Systems, Alan F. Beardon (1991, ISBN 978-0-387-95151-5)

133. Algebraic Geometry, Joe Harris (1992, ISBN 978-0-387-97716-4)

134. Coding and Information Theory, Steven Roman (1992, ISBN 978-0-387-97812-3)

135. Advanced Linear Algebra, Steven Roman (2008, 3rd ed., ISBN 978-0-387-72828-5)

136. Algebra — An Approach via Module Theory, William Adkins, Steven Weintraub (1992, ISBN 978-0-387-97839-0)

137. Harmonic Function Theory, Sheldon Axler, Paul Bourdon, Wade Ramey (2001, 2nd ed., ISBN 978-0-387-95218-5)

138. A Course in Computational Algebraic Number Theory, Henri Cohen (1996, ISBN 0-387-55640-0)

139. Topology and Geometry, Glen E. Bredon (1993, ISBN 978-0-387-97926-7)

140. Optima and Equilibria, Jean-Pierre Aubin (1998, ISBN 978-3-642-08446-1)

141. Gr?bner Bases — A Computational Approach to Commutative Algebra, Thomas Becker, Volker Weispfenning (1993, ISBN 978-0-387-97971-7)

142. Real and Functional Analysis, Serge Lang (1993, 3rd ed., ISBN 978-0-387-94001-4)

143. Measure Theory, J. L. Doob (1994, ISBN 978-0-387-94055-7)

144. Noncommutative Algebra, Benson Farb, R. Keith Dennis (1993, ISBN 978-0-387-94057-1)

145. Homology Theory — An Introduction to Algebraic Topology, James W. Vick (1994, 2nd ed., ISBN 978-0-387-94126-4)

146. Computability — A Mathematical Sketchbook, Douglas S. Bridges (1994, ISBN 978-0-387-94174-5)

147. Algebraic K-Theory and Its Applications, Jonathan Rosenberg (1994, ISBN 978-0-387-94248-3)

148. An Introduction to the Theory of Groups, Joseph J. Rotman (1995, 4th ed., ISBN 978-0-387-94285-8)

149. Foundations of Hyperbolic Manifolds, John G. Ratcliffe (2019, 3rd ed., ISBN 978-3-030-31597-9)

150. Commutative Algebra — with a View Toward Algebraic Geometry, David Eisenbud (1995, ISBN 978-0-387-94269-8)

151. Advanced Topics in the Arithmetic of Elliptic Curves, Joseph H. Silverman (1994, ISBN 978-0-387-94328-2)

152. Lectures on Polytopes, Günter M. Ziegler (1995, ISBN 978-0-387-94365-7)

153. Algebraic Topology — A First Course, William Fulton (1995, ISBN 978-0-387-94327-5)

154. An Introduction to Analysis, Arlen Brown, Carl Pearcy (1995, ISBN 978-0-387-94369-5)

155. Quantum Groups, Christian Kassel (1995, ISBN 978-0-387-94370-1)

156. Classical Descriptive Set Theory, Alexander S. Kechris (1995, ISBN 978-0-387-94374-9)

157. Integration and Probability, Paul Malliavin (1995, ISBN 978-0-387-94409-8)

158. Field Theory, Steven Roman (2006, 2nd ed., ISBN 978-0-387-27677-9)

159. Functions of One Complex Variable II, John B. Conway (1995, ISBN 978-0-387-94460-9)

160. Differential and Riemannian Manifolds, Serge Lang (1995, ISBN 978-0-387-94338-1)

161. Polynomials and Polynomial Inequalities, Peter Borwein, Tamas Erdelyi (1995, ISBN 978-0-387-94509-5)

162. Groups and Representations, J. L. Alperin, Rowen B. Bell (1995, ISBN 978-0-387-94526-2)

163. Permutation Groups, John D. Dixon, Brian Mortimer (1996, ISBN 978-0-387-94599-6)

164. Additive Number Theory The Classical Bases, Melvyn B. Nathanson (1996, ISBN 978-0-387-94656-6)

165. Additive Number Theory: Inverse Problems and the Geometry of Sumsets, Melvyn B. Nathanson (1996, ISBN 978-0-387-94655-9)

166. Differential Geometry — Cartans Generalization of Kleins Erlangen Program, R. W. Sharpe (1997, ISBN 978-0-387-94732-7)

167. Field and Galois Theory, Patrick Morandi (1996, ISBN 978-0-387-94753-2)

168. Combinatorial Convexity and Algebraic Geometry, Guenter Ewald (1996, ISBN 978-1-4612-8476-5)

169. Matrix Analysis, Rajendra Bhatia (1997, ISBN 978-0-387-94846-1)

170. Sheaf Theory, Glen E. Bredon (1997, 2nd ed., ISBN 978-0-387-94905-5)

171. Riemannian Geometry, Peter Petersen (2016, 3rd ed., ISBN 978-3-319-26652-7)

172. Classical Topics in Complex Function Theory, Reinhold Remmert (1998, ISBN 978-0-387-98221-2)

173. Graph Theory, Reinhard Diestel [de] (2017, 5th ed., ISBN 978-3-662-53621-6)

174. Foundations of Real and Abstract Analysis, Douglas S. Bridges (1998, ISBN 978-0-387-98239-7)

175. An Introduction to Knot Theory, W. B. Raymond Lickorish (1997, ISBN 978-1-4612-6869-7)

176. Introduction to Riemannian Manifolds, John M. Lee (2018, 2nd ed., ISBN 978-3-319-91754-2)

177. Analytic Number Theory , Donald J. Newman (1998, ISBN 978-0-387-98308-0)

178. Nonsmooth Analysis and Control Theory, Francis H. Clarke, Yuri S. Ledyaev, Ronald J. Stern, Peter R. Wolenski (1998, ISBN 978-0-387-98336-3)

179. Banach Algebra Techniques in Operator Theory, Ronald G. Douglas (1998, 2nd ed., ISBN 978-0-387-98377-6)

180. A Course on Borel Sets, S. M. Srivastava (1998, ISBN 978-0-387-98412-4)

181. Numerical Analysis, Rainer Kress (1998, ISBN 978-0-387-98408-7)

182. Ordinary Differential Equations, Wolfgang Walter (1998, ISBN 978-0-387-98459-9)

183. An Introduction to Banach Space Theory, Robert E. Megginson (1998, ISBN 978-0-387-98431-5)

184. Modern Graph Theory, Béla Bollobás (1998, ISBN 978-0-387-98488-9)

185. Using Algebraic Geometry, David A. Cox, John Little, Donal OShea (2005, 2nd ed., ISBN 978-0-387-20706-3)

186. Fourier Analysis on Number Fields, Dinakar Ramakrishnan, Robert J. Valenza (1999, ISBN 978-0-387-98436-0)

187. Moduli of Curves, Joe Harris, Ian Morrison (1998, ISBN 978-0-387-98438-4)

188. Lectures on the Hyperreals, Robert Goldblatt (1998, ISBN 978-1-4612-6841-3)

189. Lectures on Modules and Rings, Tsit-Yuen Lam (1999, ISBN 978-0-387-98428-5)

190. Problems in Algebraic Number Theory, M. Ram Murty, Jody Indigo Esmonde (2005, 2nd ed., ISBN 978-0-387-22182-3)

191. Fundamentals of Differential Geometry, Serge Lang (1999, ISBN 978-0-387-98593-0)

192. Elements of Functional Analysis, Francis Hirsch, Gilles Lacombe (1999, ISBN 978-0-387-98524-4)

193. Advanced Topics in Computational Number Theory, Henri Cohen (2000, ISBN 0-387-98727-4)

194. One-Parameter Semigroups for Linear Evolution Equations, Engel, Nagel (2000, ISBN 978-0-387-98463-6)

195. Elementary Methods in Number Theory, Melvyn B. Nathanson (2000, ISBN 978-0-387-98912-9)

196. Basic Homological Algebra, M. Scott Osborne (2000, ISBN 978-0-387-98934-1)

197. The Geometry of Schemes, Eisenbud, Joe Harris (2000, ISBN 978-0-387-98638-8)

198. A Course in p-adic Analysis, Alain M. Robert (2000, ISBN 978-0-387-98669-2)

199. Theory of Bergman Spaces, Hakan Hedenmalm, Boris Korenblum, Kehe Zhu (2000, ISBN 978-0-387-98791-0)

200. An Introduction to Riemann-Finsler Geometry, David Bao, Shiing-Shen Chern, Zhongmin Shen (2000, ISBN 978-1-4612-7070-6)

201. Diophantine Geometry, Marc Hindry, Joseph H. Silverman (2000, ISBN 978-0-387-98975-4)

202. Introduction to Topological Manifolds, John M. Lee (2011, 2nd ed., ISBN 978-1-4419-7939-1)

203. The Symmetric Group — Representations, Combinatorial Algorithms, and Symmetric Functions, Bruce E. Sagan (2001, 2nd ed., ISBN 978-0-387-95067-9)

204. Galois Theory, Jean-Pierre Escofier (2001, ISBN 978-0-387-98765-1)

205. Rational Homotopy Theory, Yves Félix, Stephen Halperin, Jean-Claude Thomas (2000, ISBN 978-0-387-95068-6)

206. Problems in Analytic Number Theory, M. Ram Murty (2007, 2nd ed., ISBN 978-0-387-95143-0)

207. Algebraic Graph Theory, Chris Godsil, Gordon Royle (2001, ISBN 978-0-387-95241-3)

208. Analysis for Applied Mathematics, Ward Cheney (2001, ISBN 978-0-387-95279-6)

209. A Short Course on Spectral Theory, William Arveson (2002, ISBN 978-0-387-95300-7)

210. Number Theory in Function Fields, Michael Rosen (2002, ISBN 978-0-387-95335-9)

211. Algebra, Serge Lang (2002, Revised 3rd ed, ISBN 978-0-387-95385-4)

212. Lectures on Discrete Geometry, Ji?í Matou?ek (2002, ISBN 978-0-387-95374-8)

213. From Holomorphic Functions to Complex Manifolds, Klaus Fritzsche [de], Hans Grauert (2002, ISBN 978-0-387-95395-3)

214. Partial Differential Equations, Jürgen Jost, (2013, 3rd ed., ISBN 978-1-4614-4808-2)

215. Algebraic Functions and Projective Curves, David M. Goldschmidt, (2003, ISBN 978-0-387-95432-5)

216. Matrices — Theory and Applications, Denis Serre, (2010, 2nd ed., ISBN 978-1-4419-7682-6)

217. Model Theory: An Introduction, David Marker, (2002, ISBN 978-0-387-98760-6)

218. Introduction to Smooth Manifolds, John M. Lee (2012, 2nd ed., ISBN 978-1-4419-9981-8)

219. The Arithmetic of Hyperbolic 3-Manifolds, Colin Maclachlan, Alan W. Reid, (2003, ISBN 978-0-387-98386-8)

220. Smooth Manifolds and Observables, Jet Nestruev, (2003, ISBN 978-0-387-95543-8 )

221. Convex Polytopes, Branko Grünbaum (2003, ISBN 0-387-00424-6)

222. Lie Groups, Lie Algebras, and Representations - An Elementary Introduction, Brian C. Hall, (2015, 2nd ed., ISBN 978-3-319-13466-6)

223. Fourier Analysis and its Applications, Anders Vretblad, (2003, ISBN 978-0-387-00836-3)

224. Metric Structures in Differential Geometry, Walschap, G., (2004, ISBN 978-0-387-20430-7)

225. Lie Groups, Daniel Bump, (2013, 2nd ed., ISBN 978-1-4614-8023-5)

226. Spaces of Holomorphic Functions in the Unit Ball, Kehe Zhu, (2005, ISBN 978-0-387-22036-9)

227. Combinatorial Commutative Algebra, Ezra Miller, Bernd Sturmfels, (2005, ISBN 978-0-387-22356-8)

228. A First Course in Modular Forms, Fred Diamond, J. Shurman, (2006, ISBN 978-0-387-23229-4)

229. The Geometry of Syzygies, David Eisenbud (2005, ISBN 978-0-387-22215-8)

230. An Introduction to Markov Processes, Daniel W. Stroock, (2014, 2nd ed., ISBN 978-3-540-23499-9)

231. Combinatorics of Coxeter Groups, Anders Bj?rner, Francisco Brenti, (2005, ISBN 978-3-540-44238-7)

232. An Introduction to Number Theory, Everest, Graham., Ward, T., (2005, ISBN 978-1-85233-917-3)

233. Topics in Banach Space Theory, Albiac, F., Kalton, N. J., (2016, 2nd ed., ISBN 978-3-319-31555-3)

234. Analysis and Probability — Wavelets, Signals, Fractals, Jorgensen, P. E. T., (2006, ISBN 978-0-387-29519-0)

235. Compact Lie Groups, M. R. Sepanski, (2007, ISBN 978-0-387-30263-8)

236. Bounded Analytic Functions, Garnett, J., (2007, ISBN 978-0-387-33621-3)

237. An Introduction to Operators on the Hardy-Hilbert Space, Ruben A. Martinez-Avendano, Peter Rosenthal, (2007, ISBN 978-0-387-35418-7)

238. A Course in Enumeration, Aigner, M., (2007, ISBN 978-3-540-39032-9)

239. Number Theory — Volume I: Tools and Diophantine Equations, Cohen, H., (2007, ISBN 978-0-387-49922-2)

240. Number Theory — Volume II: Analytic and Modern Tools, Cohen, H., (2007, ISBN 978-0-387-49893-5)

241. The Arithmetic of Dynamical Systems, Joseph H. Silverman, (2007, ISBN 978-0-387-69903-5)

242. Abstract Algebra, Grillet, Pierre Antoine, (2007, ISBN 978-0-387-71567-4)

243. Topological Methods in Group Theory, Geoghegan, Ross, (2007, ISBN 978-0-387-74611-1)

244. Graph Theory, Adrian Bondy, U.S.R. Murty, (2008, ISBN 978-1-84628-969-9)

245. Complex Analysis: Introduced in the Spirit of Lipman Bers, Gilman, Jane P., Kra, Irwin, Rodríguez, Rubí E. (2007, ISBN 978-0-387-74714-9)

246. A Course in Commutative Banach Algebras, Kaniuth, Eberhard, (2008, ISBN 978-0-387-72475-1)

247. Braid Groups, Kassel, Christian, Turaev, Vladimir, (2008, ISBN 978-0-387-33841-5)

248. Buildings Theory and Applications, Abramenko, Peter, Brown, Ken (2008, ISBN 978-0-387-78834-0)

249. Classical Fourier Analysis, Loukas Grafakos (2014, 3rd ed., ISBN 978-1-4939-1193-6)

250. Modern Fourier Analysis, Loukas Grafakos (2014, 3rd ed., ISBN 978-1-4939-1229-2)

251. The Finite Simple Groups, Robert A. Wilson (2009, ISBN 978-1-84800-987-5)

252. Distributions and Operators, Gerd Grubb, (2009, ISBN 978-0-387-84894-5)

253. Elementary Functional Analysis, MacCluer, Barbara D., (2009, ISBN 978-0-387-85528-8)

254. Algebraic Function Fields and Codes, Henning Stichtenoth [de], (2009, ISBN 978-3-540-76877-7)

255. Symmetry, Representations, and Invariants, Goodman, Roe, Wallach, Nolan R., (2009, ISBN 978-0-387-79851-6)

256. A Course in Commutative Algebra, Kemper, Gregor, (2010, ISBN 978-3-642-03544-9)

257. Deformation Theory, Robin Hartshorne, (2010, ISBN 978-1-4419-1595-5)

258. Foundations of Optimization in Finite Dimensions, Osman Guler, (2010, ISBN 978-0-387-34431-7)

259. Ergodic Theory - with a view towards Number Theory, Thomas Ward, Manfred Einsiedler, (2011, ISBN 978-0-85729-020-5)

260. Monomial Ideals, Jürgen Herzog, Hibi Takayuki(2010, ISBN 978-0-85729-105-9)

261. Probability and Stochastics, Erhan Cinlar, (2011, ISBN 978-0-387-87858-4)

262. Essentials of Integration Theory for Analysis, Daniel W. Stroock, (2012, ISBN 978-1-4614-1134-5)

263. Analysis on Fock Spaces, Kehe Zhu, (2012, ISBN 978-1-4419-8800-3)

264. Functional Analysis, Calculus of Variations and Optimal Control, Francis H. Clarke, (2013, ISBN 978-1-4471-4819-7)

265. Unbounded Self-adjoint Operators on Hilbert Space, Konrad Schmüdgen, (2012, ISBN 978-94-007-4752-4)

266. Calculus Without Derivatives, Jean-Paul Penot, (2012, ISBN 978-1-4614-4537-1)

267. Quantum Theory for Mathematicians, Brian C. Hall, (2013, ISBN 978-1-4614-7115-8)

268. Geometric Analysis of the Bergman Kernel and Metric, Krantz, Steven G., (2013, ISBN 978-1-4614-7923-9)

269. Locally Convex Spaces, M Scott Osborne, (2014, ISBN 978-3-319-02044-0)

270. Fundamentals of Algebraic Topology, Steven Weintraub, (2014, ISBN 978-1-4939-1843-0)

271. Integer Programming, Michelangelo Conforti, Gérard P. Cornuéjols, Giacomo Zambelli, (2014, ISBN 978-3-319-11007-3)

272. Operator Theoretic Aspects of Ergodic Theory, Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel, (2015, ISBN 978-3-319-16897-5)

273. Homotopical Topology, Anatoly Fomenko, Dmitry Fuchs, (2016, 2nd ed., ISBN 978-3-319-23487-8)

274. Brownian Motion, Martingales, and Stochastic Calculus, Jean-Fran?ois Le Gall, (2016, ISBN 978-3-319-31088-6)

275. Differential Geometry - Connections, Curvature, and Characteristic Classes, Loring W. Tu (2017, ISBN 978-3-319-55082-4)

276. Functional Analysis, Spectral Theory, and Applications, Manfred Einsiedler, Thomas Ward (2017, ISBN 978-3-319-58539-0)

277. The Moment Problem, Konrad Schmüdgen (2017, ISBN 978-3-319-64545-2)

278. Modern Real Analysis, William P. Ziemer (2017, 2nd ed., ISBN 978-3-319-64628-2)

279. Binomial Ideals, Jürgen Herzog, Takayuki Hibi, Hidefumi Ohsugi (2018, ISBN 978-3-319-95347-2)

280. Introduction to Real Analysis, Christopher Heil (2019, ISBN 978-3-030-26901-2)

281. Intersection Homology Perverse Sheaves with Applications to Singularities, Lauren?iu G. Maxim (2019, ISBN 978-3-030-27644-7)

282. Measure, Integration Real Analysis, Sheldon Axler (2020, ISBN 978-3-030-33143-6)

283. Basic Representation Theory of Algebras, Ibrahim Assem, Flávio U Coelho (2020, ISBN 978-3-030-35117-5)

284. Spectral Theory, David Borthwick (2020, ISBN 978-3-030-38001-4)


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