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最全美国研究生教材系列丛书(GTM)书目,收藏了!

Appmath MathematicsClub 2022-10-14

书单名如下

1 Introduction to Axiomatic Set Theory, Gaisi Takeuti, W. M. Zaring 

2 Measure and Category, John C. Oxtoby  

3 Topological Vector Spaces, H.H. Schaefer, M.P. Wolff 

4 A Course in Homological Algebra, Peter Hilton, Urs Stammbach

5 Categories for the Working Mathematician, Saunders Mac Lane 

6 Projective Planes, Hughes, Piper 

7 A Course in Arithmetic, Jean-Pierre Serre 

8 Axiomatic Set Theory, Gaisi Takeuti, Zaring 

9 Introduction to Lie Algebras and Representation Theory, James E. Humphreys 

10 A Course in Simple-Homotopy Theory, M. M. Cohen 

11 Functions of One Complex Variable I, John B. Conway

12 Advanced Mathematical Analysis, R. Beals

13 Rings and Categories of Modules, Frank W. Anderson, Kent R. Fuller

14 Stable Mappings and Their Singularities, Golubitsky, Guillemin 

15 Lectures in Functional Analysis and Operator Theory, S. K. Berberian 

16 The Structure of Fields, D. Winter 

17 Random Processes, M. Rosenblatt 

18 Measure Theory, Paul R. Halmos

19 A Hilbert Space Problem Book, Paul R. Halmos 

20 Fibre Bundles, Dale Husemoller

21 Linear Algebraic Groups, James E. Humphreys

22 An Algebraic Introduction to Mathematical Logic, Barnes, Mack 

23 Linear Algebra, Werner H. Greub

24 Geometric Functional Analysis and Its Applications, Holmes 

25 Real and Abstract Analysis, Edwin Hewitt, Karl Stromberg 

26 Algebraic Theories, Manes 

27 General Topology, John L. Kelley

28 Commutative Algebra I, Oscar Zariski, Pierre Samuel, Cohen

29 Commutative Algebra II, Oscar Zariski, Pierre Samuel 

30 Lectures in Abstract Algebra I, Nathan Jacobson 

31 Lectures in Abstract Algebra II, Nathan Jacobson 

32 Lectures in Abstract Algebra III, Nathan Jacobson 

33 Differential Topology, Morris W. Hirsch 

34 Principles of Random Walk, Frank Spitzer 

35 Several Complex Variables and Banach Algebras, Herbert Alexander, John Wermer 

36 Linear Topological Spaces, John L. Kelley, Isaac Namioka 

37 Mathematical Logic, J. Donald Monk 

38 Several Complex Variables, Grauert, Fritzsche 

39 An Invitation to C * -Algebras, William Arveson 

40 Denumerable Markov Chains, John George Kemeny, Snell, Knapp et al. 

41 Modular Functions and Dirichlet Series in Number Theory, Tom M. Apostol 

42 Linear Representations of Finite Groups, Jean-Pierre Serre, Scott 

43 Rings of Continuous Functions, Gillman, Jerison 

44 Elementary Algebraic Geometry, K. Kendig 

45 Probability Theory I, M. Loève 

46 Probability Theory II, M. Loève 

47 Geometric Topology in Dimensions 2 and 3, Edwin E. Moise 

48 General Relativity for Mathematicians, R.K. Sachs, H. Wu 

49 Linear Geometry, K.W. Gruenberg, A.J. Weir 

50 Fermat's Last Theorem, Harold M. Edwards 

51 A Course in Differential Geometry, Klingenberg 

52 Algebraic Geometry, Robin Hartshorne 

53 A Course in Mathematical Logic, Yu. I. Manin 

54 Combinatorics with Emphasis on the Theory of Graphs, Graver, Watkins 

55 Introduction to Operator Theory I, Brown, Pearcy 

56 Algebraic Topology: An Introduction, William S. Massey 

57 Introduction to Knot Theory, Richard H. Crowell, Ralph H. Fox 

58 P-adic Numbers, p-adic Analysis, and Zeta-Functions, Neal Koblitz 

59 Cyclotomic Fields, Serge Lang 

60 Mathematical Methods of Classical Mechanics, V. I. Arnold 

61 Elements of Homotopy Theory, George W. Whitehead 

62 Fundamentals of the Theory of Groups, Kargapolov, Merzljakov, Burns 

63 Graph Theory, Béla Bollobás 

64 Fourier Series I, Edwards 

65 Differential Analysis on Complex Manifolds, R.O. Wells Jr. 

66 Introduction to Affine Group Schemes, W.C. Waterhouse 

67 Local Fields, Jean-Pierre Serre, Greenberg 

68 Linear Operators on Hilbert Spaces, Weidmann, Szuecs 

69 Cyclotomic Fields II, Serge Lang 

70 Singular Homology Theory, William S. Massey 

71 Riemann Surfaces, Herschel Farkas, Irwin Kra 

72 Classical Topology and Combinatorial Group Theory, John Stillwell 

73 Algebra, Thomas W. Hungerford 

74 Multiplicative Number Theory, Harold Davenport, Hugh Montgomery 

75 Basic Theory of Algebraic Groups and Lie Algebras, G. P. Hochschild 

76 Algebraic Geometry, Iitaka 

77 Lectures on the Theory of Algebraic Numbers, Hecke, Brauer, Goldman et al. 

78 A Course in Universal Algebra, Burris, Sankappanavar (Online [1]) 

79 An Introduction to Ergodic Theory, Peter Walters 

80 A Course in the Theory of Groups, Derek J.S. Robinson 

81 Lectures on Riemann Surfaces, Forster, Gilligan 

82 Differential Forms in Algebraic Topology, Raoul Bott, Loring Tu 

83 Introduction to Cyclotomic Fields, Lawrence C. Washington 

84 A Classical Introduction to Modern Number Theory, Ireland, Rosen 

85 Fourier Series A Modern Introduction, R. E. Edwards 

86 Introduction to Coding Theory, J.H. van Lint

87 Cohomology of Groups, Kenneth S. Brown 

88 Associative Algebras, R.S. Pierce 

89 Introduction to Algebraic and Abelian Functions, Serge Lang 

90 An Introduction to Convex Polytopes, Arne Brondsted 

91 The Geometry of Discrete Groups, Alan F. Beardon 

92 Sequences and Series in Banach Spaces, J. Diestel 

93 Modern Geometry - Methods and Applications I, Dubrovin, Fomenko, Novikov et al. 

94 Foundations of Differentiable Manifolds and Lie Groups, Frank W. Warner 

95 Probability, Shiryaev, Boas 

96 A Course in Functional Analysis, John B. Conway 

97 Introduction to Elliptic Curves and Modular Forms, Neal Koblitz 

98 Representations of Compact Lie Groups, Broecker, Dieck 

99 Finite Reflection Groups, Grove, Benson 

100 Harmonic Analysis on Semigroups, Berg, Christensen, Ressel 

101 Galois Theory, Harold M. Edwards 

102 Lie Groups, Lie Algebras, and Their Representations, V. S. Varadarajan 

103 Complex Analysis, Serge Lang 

104 Modern Geometry - Methods and Applications II, Dubrovin, Fomenko, Novikov et al. 

105 SL2(R), Serge Lang 

106 The Arithmetic of Elliptic Curves, Joseph H. Silverman 

107 Applications of Lie Groups to Differential Equations, Peter J. Olver 

108 Holomorphic Functions and Integral Representations in Several Complex Variables, R. Michael Range 

109 Univalent Functions and Teichmüller Spaces, O. Lehto 

110 Algebraic Number Theory, Serge Lang 

111 Elliptic Curves, Dale Husemöller 

112 Elliptic Functions, Serge Lang 

113 Brownian Motion and Stochastic Calculus, Ioannis Karatzas, Steven Shreve 

114 A Course in Number Theory and Cryptography, Neal Koblitz 

115 Differential Geometry, Berger, Gostiaux, Levy 

116 Measure and Integral, John L. Kelley, Srinivasan 

117 Algebraic Groups and Class Fields, Jean-Pierre Serre 

118 Analysis Now, Gert K. Pedersen 

119 An Introduction to Algebraic Topology, Joseph J. Rotman 

120 Weakly Differentiable Functions, William P. Ziemer 

121 Cyclotomic Fields I-II, Serge Lang, Karl Rubin 

122 Theory of Complex Functions, Remmert, Burckel 

123 Numbers, Lamotke, Ewing, Ebbinghaus et al. 

124 Modern Geometry - Methods and Applications III, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Petrovich Novikov et al. 

125 Complex Variables, Berenstein, Gay 

126 Linear Algebraic Groups, Armand Borel 

127 A Basic Course in Algebraic Topology, William S. Massey 

128 Partial Differential Equations, Jeffrey Rauch 

129 Representation Theory, William Fulton, Joe Harris 

130 Tensor Geometry, C.T.J. Dodson, T. Poston 

131 A First Course in Noncommutative Rings, T.Y. Lam 

132 Iteration of Rational Functions, Alan F. Beardon 

133 Algebraic Geometry, Joe Harris 

134 Coding and Information Theory, Steven Roman 

135 Advanced Linear Algebra, Steven Roman 

136 Algebra, Adkins, Weintraub 

137 Harmonic Function Theory, Axler, Bourdon, Ramey 

138 A Course in Computational Algebraic Number Theory, Henri Cohen

139 Topology and Geometry, Glen E. Bredon 

140 Optima and Equilibria, Jean-Pierre Aubin 

141 Gröbner Bases, Becker, Weispfenning, Kredel 

142 Real and Functional Analysis, Serge Lang

143 Measure Theory, J.L. Doob 

144 Noncommutative Algebra, Farb, Dennis 

145 Homology Theory, James W. Vick 

146 Computability, Douglas S. Bridges 

147 Algebraic K-Theory and Its Applications, Jonathan Rosenberg 

148 An Introduction to the Theory of Groups, Joseph J. Rotman 

149 Foundations of Hyperbolic Manifolds, John G. Ratcliffe 

150 Commutative Algebra with a View Toward Algebraic Geometry, David Eisenbud 

151 Advanced Topics in the Arithmetic of Elliptic Curves, Joseph H. Silverman 

152 Lectures on Polytopes, Günter M. Ziegler 

153 Algebraic Topology, William Fulton 

154 An Introduction to Analysis, Brown, Pearcy 

155 Quantum Groups, Christian Kassel 

156 Classical Descriptive Set Theory, Alexander S. Kechris 

157 Integration and Probability, Malliavin, Airault, Kay et al. 

158 Field Theory, Steven Roman 

159 Functions of One Complex Variable II, John B. Conway 

160 Differential and Riemannian Manifolds, Serge Lang 

161 Polynomials and Polynomial Inequalities, Borwein, Erdelyi 

162 Groups and Representations, Alperin, Bell 

163 Permutation Groups, Dixon, Mortimer 

164 Additive Number Theory I, Melvyn B. Nathanson 

165 Additive Number Theory II, Melvyn B. Nathanson 

166 Differential Geometry, R.W. Sharpe, Shiing-Shen Chern 

167 Field and Galois Theory, Patrick Morandi 

168 Combinatorial Convexity and Algebraic Geometry, Guenter Ewald 

169 Matrix Analysis, Rajendra Bhatia 

170 Sheaf Theory, Glen E. Bredon 

171 Riemannian Geometry, Peter Petersen 

172 Classical Topics in Complex Function Theory, Remmert, Kay 

173 Graph Theory, Reinhard Diestel 

174 Foundations of Real and Abstract Analysis, Douglas S. Bridges 

175 An Introduction to Knot Theory, W. B. Raymond Lickorish 

176 Riemannian Manifolds, John M. Lee 

177 Analytic Number Theory , Donald J. Newman 

178 Nonsmooth Analysis and Control Theory, Clarke, Ledyaev, Stern et. al 

179 Banach Algebra Techniques in Operator Theory, Ronald G. Douglas 

180 A Course on Borel Sets, S.M. Srivastava 

181 Numerical Analysis, Rainer Kress 

182 Ordinary Differential Equations, Walter, Thompson 

183 An Introduction to Banach Space Theory, Robert E. Megginson 

184 Modern Graph Theory, Béla Bollobás 

185 Using Algebraic Geometry, Cox, Little, O Shea 

186 Fourier Analysis on Number Fields, Ramakrishnan, Valenza 

187 Moduli of Curves, Harris, Morrison 

188 Lectures on the Hyperreals, Robert Goldblatt 

189 Lectures on Modules and Rings, Tsit-Yuen Lam 

190 Problems in Algebraic Number Theory, Esmonde, Murty 

191 Fundamentals of Differential Geometry, Serge Lang 

192 Elements of Functional Analysis Hirsch, Lacombe, Levy 

193 Advanced Topics in Computational Number Theory, Henri Cohen

194 One-Parameter Semigroups for Linear Evolution Equations, Engel, Nagel 

195 Elementary Methods in Number Theory, Melvyn B. Nathanson 

196 Basic Homological Algebra, M. Scott Osborne 

197 The Geometry of Schemes, Eisenbud, Harris 

198 A Course in p-adic Analysis, Alain Robert 

199 Theory of Bergman Spaces, Hedenmalm, Korenblum, Zhu 

200 An Introduction to Riemann-Finsler Geometry, David Bao, Shiing-Shen Chern, Zhongmin Shen 201 Diophantine Geometry, Hindry, Joseph H. Silverman

202 Introduction to Topological Manifolds, John M. Lee 

203 The Symmetric Group, Bruce E. Sagan 

204 Galois Theory, Jean-Pierre Escofier 

205 Rational Homotopy Theory, Yves Félix, Stephen Halperin, Jean-Claude Thomas

206 Problems in Analytic Number Theory, M. Ram Murty

207 Algebraic Graph Theory, Godsil, Royle 

208 Analysis for Applied Mathematics, Ward Cheney

209 A Short Course on Spectral Theory, William Arveson

210 Number Theory in Function Fields, Michael Rosen 

211 Algebra, Serge Lang 

212 Lectures on Discrete Geometry, Jiri Matousek 

213 From Holomorphic Functions to Complex Manifolds, Fritzsche, Grauert 

214 Partial Differential Equations, Juergen Jost 

215 Algebraic Functions and Projective Curves, David Goldschmidt 

216 Matrices, Denis Serre 

217 Model Theory: An Introduction, David Marker 

218 Introduction to Smooth Manifolds, John M. Lee

219 The Arithmetic of Hyperbolic 3-Manifolds, Maclachlan, Reid 

220 Smooth Manifolds and Observables, Jet Nestruev 

221 Convex Polytopes, Branko Grünbaum 

222 Lie Groups, Lie Algebras, and Representations, Brian C. Hall 

223 Fourier Analysis and its Applications, Anders Vretblad 

224 Metric Structures in Differential Geometry, Walschap, G.

225 Lie Groups, Daniel Bump

226 Spaces of Holomorphic Functions in the Unit Ball, Zhu, K.

227 Combinatorial Commutative Algebra, Ezra Miller, Bernd Sturmfels

228 A First Course in Modular Forms, Fred Diamond, J. Shurman

229 The Geometry of Syzygies, David Eisenbud 

230 An Introduction to Markov Processes, Stroock, D.W.

231 Combinatorics of Coxeter Groups, Anders Björner, Francisco Brenti

232 An Introduction to Number Theory, Everest, G., Ward, T.

233 Topics in Banach Space Theory, Albiac, F., Kalton, N.J.

234 Analysis and Probability · Wavelets, Signals, Fractals, Jorgensen, P.E.T.

235 Compact Lie Groups, M. R. Sepanski

236 Bounded Analytic Functions, Garnett, J.

237 An Introduction to Operators on the Hardy-Hilbert Space, Martinez-Avendano, R.A., Rosenthal, P.

238 A Course in Enumeration, Aigner, M.

239 Number Theory - Volume I: Elementary and Algebraic Methods for Diophantine Equations, Cohen, H

240 Number Theory - Volume II: Analytic and Modern Tools, Cohen, H.

241 The Arithmetic of Dynamical Systems, Joseph H. Silverman

242 Abstract Algebra, Grillet, Pierre Antoine

243 Topological Methods in Group Theory, Geoghegan, Ross

244 Graph Theory, Bondy, J.A., Murty, U.S.R.

245 Complex Analysis: Introduced in the Spirit of Lipman Bers,Gilman, Jane P., Kra, Irwin, Rodriguez, Rubi E.

246 A Course in Commutative Banach Algebras, Kaniuth, Eberhard

247 Braid Groups, Kassel, Christian, Turaev, Vladimir

248 Buildings Theory and Applications, Abramenko, Peter, Brown, Ken

249 Classical Fourier Analysis, Grafakos, Loukas

250 Modern Fourier Analysis, Grafakos, Loukas

251 The Finite Simple Groups, Wilson, Robert, Parker, Christopher W.

252 Distributions and Operators, Grubb, Gerd

253 MacCluer. Elementary Functional Analysis.

254 Stichtenoth. Algebraic Function Fields.and Codes.

255 Goodman,Wallach. Symmetry,Representations,and Invariants.

256 Kemper. A Course in Commutative Algebra.

257 Hartshorne. Deformation Theory.

258 Güler. Foundation of Optimization.

259 Einsiedler,Ward. Ergodic Theory:with a view towards Number Theory.

260 Herzog,Hibi. Monomial Ideals.

261 Çınlar. Probability and Stochastics.

262 Stroock. Essentials of Integration Theory for Analysis.

263 Zhu. Analysis on Fock Spaces.

264 Clarke. Functional Analysis, Calculus of Variations and Optimal Control.

265 Schmüdgen. Unbounded Self-adjoint Operators on Hilbert Space.

266 Penot. Calculus Without Derivatives.

267 Hall. Quantum Theory for Mathematians. 

268 Krantz. Geometric Analysis of the Bergman Kernel and Metric.

269 Osborne. Locally Convex Spaces.




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