微积分:  rant,f.john,introd ction to calc l s and analysis vol i&ii t.m.apostol calc l s vol i&ii t.m.apostol mathematical analysis r din "principles of mathematical analysis" spivak "calc l s on manifolds" v.a.zorich,mathematical analysis vol i&ii springer-verlag 代数: friedberg "linear algebra" 4th ed. prentice hall axler "linear algebra done right" 2nd ed. springer-verlag hoffman & k nz , linear algebra basic algebra i&ii, 2nd edition by n. jacobson algebra by serge lang d mmit & foote "abstract algebra" wiley h ngerford "abstract algebra: an introd ction" brookscole 分析: real & complex analysis, 3rd edition by w. r din royden "real analysis" 3rd ed. prentice hall ahlfors "complex analysis" 3rd ed. mcgraw-hill hormander "an intro to complex analysis in several variables" conway "f nctions of one complex variable i&ii springer-verlag conway a co rse in f nctional analysis f nctional analysis, 3rd edition by w. r din 几何与拓扑: basic topology by armstrong differential geometry of c rves and s rfaces by manfredo do carmo hatcher "algebraic topology" cambridge up m nkries "topology" 2nd ed. prentice hall m. postnikov,analytic geometry, mir p blishers m. postnikov,linear algebra and differential geometry,mir p blishers a.t.fomenko differential geometry and topology,cons ltants b rea d brovin, fomenko, novikov "modern geometry-methods and applications"vol 1-3 a comprehensive introd ction to differential geometry vol 1-5 ,by michael spivak 方程: earl.a. coddington,theory of ordinary differential eq ations,mcgraw-hill aleksei.a.dezin,partial differential eq ations,springer-verlag evans "partial differential eq ations" 98 ams ordinary differential eq ations by v. i. arnold geometrical methods in the theory of ordinary differential eq ations by v. i. arnold 教材与参考书目 1,微积分原理i&ii  rant,f.john,introd ction to calc l s and analysis vol i&ii t.m.apostol calc l s vol i&ii 张筑生,"数学分析新讲"(1~3册),北大版 常庚哲,"数学分析教程"(上,下册),高教版 陈纪修,"数学分析"(上,下册),高教版 2,解析几何 丘维生,"解析几何",北大版 南开数学系,"空间解析几何",高教版 m. postnikov,analytic geometry, mir p blishers 3,线性代数i&ii 蓝以中,"高等代数简明教程"(上,下册),北大版 丘维生,"高等代数"(上,下册),高教版 李炯生,"线性代数",科大版 friedberg "linear algebra" 4th ed. prentice hall axler "linear algebra done right" 2nd ed. springer-verlag hoffman & k nz , linear algebra 4,集合论原理 耿素云,集合论与图论,北京大学出版社 elements of set theory by herbert enderton set theory by thomas j. jech 5,离散数学原理 耿素云,离散数学,高教版 discrete mathematics and its applications kenneth h. rosen 6,普通物理学i&ii 力学,赵凯华和罗蔚茵编写的"新概念物理教程"力学部分 高等教育出版社 热学,赵凯华和罗蔚茵编写的"新概念物理教程"热学部分. 高等教育出版社 电磁学,赵凯华和陈熙谋编写的"电磁学",高等教育出版社. 光学,赵凯华和钟锡华编写的"光学",北京大学出版社 7,数学分析原理i&ii r din "principles of mathematical analysis" spivak "calc l s on manifolds" v.a.zorich,mathematical analysis vol i&ii springer-verlag 8,抽象代数i&ii 莫宗坚,"代数学"(上,下册),北大版 basic algebra i&ii, 2nd edition by n. jacobson algebra by serge lang d mmit & foote "abstract algebra" wiley h ngerford "abstract algebra: an introd ction" brookscole 9,拓扑学原理 尤承业,"基础拓扑学讲义",北大版 basic topology by armstrong 10,微分几何原理 陈维桓,"微分几何初步" differential geometry of c rves and s rfaces by manfredo do carmo m. postnikov,linear algebra and differential geometry,mir p blishers a.t.fomenko differential geometry and topology,cons ltants b rea 11,常微分方程i&ii 丁同仁,"常微分方程教程",高教版 ordinary differential eq ations by v. i. arnold geometrical methods in the theory of ordinary differential eq ations by v. i. arnold earl.a. coddington,theory of ordinary differential eq ations,mcgraw-hill 12,概率论原理 汪仁官,"概率论引论",北大版 a first co rse in probability by sheldon ross 13,统计学原理 陈家鼎,"数理统计学讲义",高教版 r. larsen and m. marx: an introd ction to mathematical statistics, prentice-hall, 1986. 14,复分析原理 方企勤,"复变函数教程",北大版 龚升,"简明复分析",北大版 ahlfors "complex analysis" 3rd ed. mcgraw-hill conway "f nctions of one complex variable i&ii springer-verlag 15,理论物理学i&ii 量子力学:曾谨言,"量子力学教程",高等教育出版社出版 电动力学:郭硕鸿,"电动力学",高等教育出版社出版. 理论力学:周伯衍, "理论力学教程"高等教育出版社. 热力学与统计物理:汪志诚,"热力学与统计物理",高等教育出版社出版. 16,实分析i&ii 周民强,"实变函数",北大版 夏道行,"实变函数论与泛函分析"(上册),高教版 real & complex analysis, 3rd edition by w. r din royden "real analysis" 3rd ed. prentice hall 严加安,"测度论讲义",科学版 程士宏,"测度论与概率论",北大版 halmos,"meas re theory"(gtm 18) 17,交换代数i&ii 冯克勤,"交换代数基础",高教版 comm tative algebra i&ii by oscar zariski , pierre sam el 18,拓扑学i&ii m nkries "topology" 2nd ed. prentice hall 熊金成,"点集拓扑讲义",高教版 hatcher "algebraic topology" cambridge up spaniers "algebraic topology" 张筑生,"微分拓扑新讲",北大版 19,微分几何i&ii 陈省身,"微分几何讲义",北大版 陈维桓,"微分流形初步",高教版 苏步青, "微分几何",高教版 a.t.fomenko differential geometry and topology,cons ltants b rea d brovin, fomenko, novikov "modern geometry-methods and applications"vol 1-3 a comprehensive introd ction to differential geometry vol 1-5 ,by michael spivak 20,数理逻辑原理 王捍贫, 数理逻辑, 北京大学出版社,1997 h.b.enderton, a mathematical introd ction to logic. academic press, new york, 1972. 21,复分析i&ii real & complex analysis, 3rd edition by w. r din conway "f nctions of one complex variable i&ii springer-verlag 史济怀,"多复变函数论基础",高教版 张南岳,"复变函数论选讲",北大版 hormander "an intro to complex analysis in several variables" 22,泛函分析i&ii 张恭庆,"泛函分析讲义"(上,下册),北大版 夏道行,"实变函数论与泛函分析"(下册),高教版 conway a co rse in f nctional analysis f nctional analysis, 3rd edition by w. r din 23,黎曼几何原理i&ii 陈维桓,"黎曼几何引论"(上,下册),北大版 伍宏熙,"黎曼几何初步",北大版 d brovin, fomenko, novikov "modern geometry-methods and applications"vol 1-3 24,偏微分方程i&ii 姜礼尚,"数学物理方程讲义",高教版 谷超豪,"数学物理方程",高教版 aleksei.a.dezin,partial differential eq ations,springer-verlag evans "partial differential eq ations" 98 ams l. hormander "linear partial differential operators, " i&ii 25,概率理论 程士宏,"高等概率论",北大版 严士健,"概率论基础",北大版 probability: theory and examples by richard a. d rrett fo ndations of modern probability by olav kallenberg 适合对已经熟悉概率论的人做案边参考,观点较高,也很简洁精要,但不适合做教材. ch ng kailai, a co rse in probability theory feller, an introd ction to probability theory and its applications,i&ii 26,数值分析 李庆扬,"数值分析" r.l. b rden and d. faires, n merical analysis, 7th edition, thomson learning. j. stoer and r. b lirsch, an introd ction to n merical analysis, springer-verlag, 27,统计学理论 陈希孺,数理统计引论,科学出版社 陈希孺,高等数理统计,科大版 statistical inference by george casella, roger l. berger, cassell 28,随机过程 钱敏平,龚光鲁,随机过程,北京大学出版社 钱敏平,龚光鲁,随机微分方程,北京大学出版社 s.m. ross, stochastic processes, john wiley & sons, 1983 a first co rse in stochastic processes by sam el karlin, howard taylor a second co rse in stochastic processes by sam el karlin, howard taylor the theory of stochastic processes i &ii gikhman, i.i., skorokhod, a.v.