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1ãJames R. Munkres, Topologyï¼è¾æ°çææå¦çææéç¨äºæ¬ç§é«å¹´çº§æç 究çä¸å¹´çº§ï¼
2ãBasic Topology by Armstrongï¼æ¬ç§çææå¦ææï¼
3ãKelley, General Topologyï¼ä¸è¬ææå¦çç»å
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4ãWillard, General Topologyï¼ä¸è¬ææå¦æ°çç»å
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5ãGlen Bredon, Topology and geometryï¼ç 究çä¸å¹´çº§çææãå ä½ææï¼
6ãIntroduction to Topological Manifolds by John M. Leeï¼ç 究çä¸å¹´çº§çææãå ä½ææï¼æ¯ä¸æ¬æ°ä¹¦ï¼
7ãFrom calculus to cohomology by Madsenï¼å¾å¥½çæ¬ç§ç代æ°ææãå¾®åæµå½¢ææã
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1ãAbstract Algebra Dummitï¼æ好çæ¬ç§ä»£æ°å¦åè书ï¼æ åçç 究çä¸å¹´çº§ä»£æ°ææï¼
2ãAlgebra Langï¼æ åçç 究çä¸ãäºå¹´çº§ä»£æ°ææï¼é¾åº¦å¾é«ï¼éåä½åè书ï¼
3ãAlgebra Hungerfordï¼æ åçç 究çä¸å¹´çº§ä»£æ°ææï¼éåä½åè书ï¼
4ãAlgebra M,Artinï¼æ åçæ¬ç§ç代æ°ææï¼
5ãAdvanced Modern Algebra by Rotmanï¼è¾æ°çç 究ç代æ°ææï¼å¾å
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6ãAlgebraï¼a graduate course by Isaacsï¼è¾æ°çç 究ç代æ°ææï¼
7ãBasic algebra Vol I&II by Jacobsonï¼ç»å
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1ãWalter Rudin, Principles of mathematical analysisï¼æ¬ç§æ°å¦åæçæ ååè书ï¼
2ãWalter Rudin, Real and complex analysisï¼æ åçç 究çä¸å¹´çº§åæææï¼
3ãLars V. Ahlfors, Complex analysisï¼æ¬ç§é«å¹´çº§åç 究çä¸å¹´çº§ç»å
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4ãFunctions of One Complex Variable Iï¼J.B.Conwayï¼ç 究ç级å«çååéå¤åæç»å
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5ãLang, Complex analysisï¼ç 究ç级å«çååéå¤åæåè书ï¼
6ãComplex Analysis by Elias M. Steinï¼è¾æ°çç 究ç级å«çååéå¤åæææï¼
7ãLang, Real and Functional analysisï¼ç 究ç级å«çåæåè书ï¼
8ãRoyden, Real analysisï¼æ åçç 究çä¸å¹´çº§å®åæææï¼
9ãFolland, Real analysisï¼æ åçç 究çä¸å¹´çº§å®åæææã
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1ãCommutative ring theory, by H. Matsumuraï¼è¾æ°çç 究ç交æ¢ä»£æ°æ åææï¼
2ãCommutative Algebra I&II by Oscar Zariski , Pierre Samuelï¼ç»å
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3ãAn introduction to Commutative Algebra by Atiyahï¼æ åç交æ¢ä»£æ°å
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4ãAn introduction to homological algebra ,by weibelï¼è¾æ°çç 究çäºå¹´çº§åè°ä»£æ°ææï¼
5ãA Course in Homological Algebra by P.J.Hilton,U.Stammbachï¼ç»å
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6ãHomological Algebra by Cartanï¼ç»å
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7ãMethods of Homological Algebra by Sergei I. Gelfand, Yuri I. Maninï¼é«çº§ãç»å
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8ãHomology by Saunders Mac Laneï¼ç»å
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9ãCommutative Algebra with a view toward Algebraic Geometry by Eisenbudï¼é«çº§ç代æ°å ä½ã交æ¢ä»£æ°çåè书ï¼ææ°ç交æ¢ä»£æ°å
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1ãAlgebraic Topology, A. Hatcherï¼ææ°çç 究ç代æ°æææ åææï¼
2ãSpaniers âAlgebraic Topologyâï¼ç»å
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3ãDifferential forms in algebraic topology, by Raoul Bott and Loring W. Tuï¼ç 究ç代æ°æææ åææï¼
4ãMassey, A basic course in Algebraic topologyï¼ç»å
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5ãFulton , Algebraic topologyï¼a first courseï¼å¾å¥½æ¬ç§çé«å¹´çº§åç 究çä¸å¹´çº§ç代æ°ææåè书ï¼
6ãGlen Bredon, Topology and geometryï¼æ åçç 究ç代æ°ææææï¼æç¸å½ç¯å¹
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7ãAlgebraic Topology Homology and Homotopyï¼é«çº§ãç»å
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8ãA Concise Course in Algebraic Topology by J.P.Mayï¼ç 究ç代æ°ææçå
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9ãElements of Homotopy Theory by G.W. Whiteheadï¼é«çº§ãç»å
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1ãRoyden, Real analysisï¼æ åç 究çåæææï¼
2ãWalter Rudin, Real and complex analysisï¼æ åç 究çåæææï¼
3ãHalmosï¼âMeasure Theoryâï¼ç»å
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4ãWalter Rudin, Functional analysisï¼æ åçç 究çæ³å½åæææï¼
5ãConway,A course of Functional analysisï¼æ åçç 究çæ³å½åæææï¼ 6ãFolland, Real analysisï¼æ åç 究çå®åæææï¼
7ãFunctional Analysis by Laxï¼é«çº§çç 究çæ³å½åæææï¼
8ãFunctional Analysis by Yoshidaï¼é«çº§çç 究çæ³å½åæåè书ï¼
9ãMeasure Theory, Donald L. Cohnï¼ç»å
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1ãHirsch, Differential topologyï¼æ åçç 究çå¾®åææææï¼æç¸å½é¾åº¦ï¼
2ãLang, Differential and Riemannian manifoldsï¼ç 究çå¾®åæµå½¢çåè书ï¼é¾åº¦è¾é«ï¼
3ãWarner,Foundations of Differentiable manifolds and Lie groupsï¼æ åç 究çå¾®åæµå½¢ææï¼æç¸å½çç¯å¹
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4ãRepresentation theory: a first course, by W. Fulton and J. Harrisï¼æ群åå
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5ãLie groups and algebraic groups, by A. L. Onishchik, E. B. Vinbergï¼æ群çåè书ï¼
6ãLectures on Lie Groups W.Y.Hsiangï¼æ群çåè书ï¼
7ãIntroduction to Smooth Manifolds by John M. Leeï¼è¾æ°çå
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8ãLie Groups, Lie Algebras, and Their Representation by V.S. Varadarajanï¼æéè¦çæ群ãæ代æ°åè书ï¼
9ãHumphreys, Introduction to Lie Algebras and Representation Theory , SpringerVerlag, GTM9ï¼æ åçæ代æ°å
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1ãPeter Petersen, Riemannian Geometryï¼æ åçé»æ¼å ä½ææï¼
2ãRiemannian Manifolds: An Introduction to Curvature by John M. Leeï¼ææ°çé»æ¼å ä½ææï¼
3ãdoCarmo, Riemannian Geometry.ï¼æ åçé»æ¼å ä½ææï¼
4ãM. Spivak, A Comprehensive Introduction to Differential Geometry IâVï¼å
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5ãHelgason , Differential Geometry,Lie groups,and symmetric spacesï¼æ åçå¾®åå ä½ææï¼
6ãLang, Fundamentals of Differential Geometryï¼ææ°çå¾®åå ä½ææï¼å¾éåä½åè书ï¼
7ãkobayashi/nomizu, Foundations of Differential Geometryï¼ç»å
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8ãBoothby,Introduction to Differentiable manifolds and Riemannian Geometryï¼æ åçå¾®åå ä½å
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9ãRiemannian Geometry I.Chavelï¼ç»å
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10ãDubrovin, Fomenko, Novikov âModern geometry-methods and applicationsâVol 1â3ï¼ç»å
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1ãHarris,Algebraic Geometry: a first courseï¼ä»£æ°å ä½çå
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2ãAlgebraic Geometry Robin Hartshorne ï¼ç»å
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3ãBasic Algebraic Geometry 1&2 2nd ed. I.R.Shafarevich.ï¼é常好ç代æ°å ä½å
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4ãPrinciples of Algebraic Geometry by giffiths/harrisï¼å
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5ãCommutative Algebra with a view toward Algebraic Geometry by Eisenbudï¼é«çº§ç代æ°å ä½ã交æ¢ä»£æ°çåè书ï¼ææ°ç交æ¢ä»£æ°å
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6ãThe Geometry of Schemes by Eisenbudï¼å¾å¥½çç 究ç代æ°å ä½å
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7ãThe Red Book of Varieties and Schemes by Mumfordï¼æ åçç 究ç代æ°å ä½å
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8ãAlgebraic Geometry I : Complex Projective Varieties by David Mumfordï¼å¤ä»£æ°å ä½çç»å
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1ãAn Introduction to Harmonic Analysis,Third Edition Yitzhak Katznelsonï¼è°ååæçæ åææï¼å¾ç»å
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2ãEvans, Partial differential equationsï¼åå¾®åæ¹ç¨çç»å
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3ãAleksei.A.Dezinï¼Partial differential equationsï¼Springer-Verlagï¼åå¾®åæ¹ç¨çåè书ï¼
4ãL. Hormander âLinear Partial Differential Operators, â I&IIï¼åå¾®åæ¹ç¨çç»å
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5ãA Course in Abstract Harmonic Analysis by Follandï¼é«çº§çç 究çè°ååæææï¼
6ãAbstract Harmonic Analysis by Ross Hewittï¼æ½è±¡è°ååæçç»å
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7ãHarmonic Analysis by Elias M. Steinï¼æ åçç 究çè°ååæææï¼
8ãElliptic Partial Differential Equations of Second Order by David Gilbargï¼åå¾®åæ¹ç¨çç»å
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9ãPartial Differential Equations ï¼by Jeffrey Rauchï¼æ åçç 究çåå¾®åæ¹ç¨ææã
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1ãFunctions of One Complex Variable IIï¼J.B.Conwayï¼åå¤åçç»å
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2ãLectures on Riemann Surfaces O.Forsterï¼é»æ¼æ²é¢çåè书ï¼
3ãCompact riemann surfaces Jostï¼é»æ¼æ²é¢çåè书ï¼
4ãCompact riemann surfaces Narasimhanï¼é»æ¼æ²é¢çåè书ï¼
5ãHormander â An introduction to Complex Analysis in Several Variablesâï¼å¤å¤åçæ åå
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6ãRiemann surfaces , Langï¼é»æ¼æ²é¢çåè书ï¼
7ãRiemann Surfaces by Hershel M. Farkasï¼æ åçç 究çé»æ¼æ²é¢ææï¼
8ãFunction Theory of Several Complex Variables by Steven G. Krantzï¼é«çº§çç 究çå¤å¤ååè书ï¼
9ãComplex Analysis: The Geometric Viewpoint by Steven G. Krantzï¼é«çº§çç 究çå¤åæåè书ã
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1ãå¤å¤åæï¼2ãå¤å ä½ï¼3ãå ä½åæï¼4ãæ½è±¡è°ååæï¼5ã代æ°å ä½ï¼6ã代æ°æ°è®ºï¼7ãå¾®åå ä½ï¼8ã代æ°ç¾¤ãæ代æ°ä¸éå群ï¼9ãæ³å½åæä¸ç®å代æ°ï¼10ãæ°å¦ç©çï¼11ãæ¦çç论ï¼12ãå¨åç³»ç»ä¸éåç论ï¼13ãæ³ä»£æ°ã
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1ãhalmos ,native set theoryï¼
2ãfraenkel ,abstract set theoryï¼
3ãebbinghaus ,mathematical logicï¼
4ãenderton ,a mathematical introduction to logicï¼
5ãlandau, foundations of analysisï¼
6ãmaclane ,categories for working mathematicanãåºè¯¥å¨æ ¸å¿è¯¾ç¨å¦ä¹ çè¿ç¨ä¸ç©¿æéä¿®
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Walter Rudin, Principles of mathematical analysisï¼
Apostol , mathematical analysisï¼
M.spivak , calculus on manifoldsï¼
Munkres ,analysis on manifoldsï¼
Kolmogorov/fomin , introductory real analysisï¼
Arnold ,ordinary differential equationsã
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linear algebra by Stephen H. Friedbergï¼
linear algebra by hoffmanï¼
linear algebra done right by Axlerï¼
advanced linear algebra by Romanï¼
algebra ,artinï¼
a first course in abstract algebra by rotmanã
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do carmo, differential geometry of curves and surfacesï¼
Differential topology by Pollackï¼
Hilbert ,foundations of geometryï¼
James R. Munkres, Topologyã
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