出版社: 世界图书出版公司 Springer 北京世图 世界图书出版公司北京公司
册数: 96
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系列丛书是 Springer-Verlag 出版社出版的数学方向的一系列研究生教科书。作者都是该领域的专家，每本书都从基础讲起，易于入门。
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抽象代数讲义（第1卷）
作者: Nathan Jacobson
出版社: 北京世图
出版年: 2000-12
The present volume is the first of three that will be published under the general title Lectures in lbstract fllgebra. These vol-umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and a...
The present volume is the first of three that will be published under the general title Lectures in lbstract fllgebra. These vol-umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale University. The general plan of the work is as follows.The present first volume gives an introduction to abstract algebra and gives an account of most of the important algebraic concepts. In a treatment of this type it is impossible to give a comprehensive account of the topics which are introduced. Nevertheless we have tried to go beyond ?the foundations and elementary properties of the algebraic sys-tems. This has necessitated a certain amount of selection and omission. We feel that even at the present stage a deeper under-standing of a few topics is to be preferred to a superficial under-standing of many.
此书为英文版！
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测度论
作者: Paul R.Halmos
出版社: 世界图书出版公司
出版年: 1998-8
My main purpose in this book is to present a unified treatment of that part of measure theory which in recent years has shown itself to be most useful for its applications in modern analysis. If I have accomplished my purpose, then the book should be found usable both as a text f...
My main purpose in this book is to present a unified treatment of that part of measure theory which in recent years has shown itself to be most useful for its applications in modern analysis. If I have accomplished my purpose, then the book should be found usable both as a text for students and as a source of reference for the more advanced mathematician. I have tried to keep to a minimum the amount of new and unusual terminology and notation. In the few places where my nomenclature differs from that in the existing literature of measure theory, I was motivated by an attempt to harmonize with the usage of other parts of mathematics. There are, for instance, sound algebraic reasons for using the terms "lattice" and "ring" for certain classes of sets--reasons which are more cogent than the similarities that caused Hausdorff to use "ring" and "field."
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抽象代数讲义 第2卷
作者: Nathan Jacobson
出版社: 北京世界图书出版公司
出版年: 2000-12
The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I￡ogroups, rings, fields, homomorphisms, is presup-posed. However, we have tried...
The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I￡ogroups, rings, fields, homomorphisms, is presup-posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume.References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any 'student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra.
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代数几何
作者: R.Hartshorne
出版社: 世界图书出版公司
出版年: 1999-11
This book provides an introduction to abstract algebraic geometry using the methods of schemes and cohomology. The main objects of study are algebraic varieties in an affine or projective space over an algebraically closed field; these are introduced in Chapter I, to establish a ...
This book provides an introduction to abstract algebraic geometry using the methods of schemes and cohomology. The main objects of study are algebraic varieties in an affine or projective space over an algebraically closed field; these are introduced in Chapter I, to establish a number of basic concepts and examples. Then the methods of schemes and cohomology are developed in Chapters II and III, with emphasis on applications rather than excessive generality. The last two chapters of the book (IV and V) use these methods to study topics in the classical theory of algebraic curves and surfaces.
本书为英文版。
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代数
作者: Thomas W.Hungerford
出版社: 世界图书出版公司
出版年: 1900-1
This book is int
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代数拓扑的微分形式
作者: R.Bott
出版社: 世界图书出版公司
出版年: 1999-11
The guiding principle in this book is to use differential forms as an aid in exploring some of the less digestible aspects of algebraic topology. Accordingly, we move primarily in the realm of smooth manifolds and use the de Rham theory as a prototype of all of cohomology. For ap...
The guiding principle in this book is to use differential forms as an aid in exploring some of the less digestible aspects of algebraic topology. Accordingly, we move primarily in the realm of smooth manifolds and use the de Rham theory as a prototype of all of cohomology. For applications to homotopy theory we also discuss by way of analogy cohomology with arbitrary coefficients. Although we have in mind an audience with prior exposure to algebraic or differential topology, for the most part a good knowledge of linear algebra, advanced calculus, and point-set topology should suffice. Some acquaintance with manifolds, simplicial complexes, singular homology and cohomology, and homotopy groups is helpful, but not really necessary. Within the text itself we have stated with care the more advanced results that are needed, so that a mathematically mature reader who accepts these background materials on faith should be able to read the entire book with the minimal prerequisites.
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经典力学的数学方法
作者: V.I.Arnold
出版社: 世界图书出版公司
出版年: 1999-11
Part of Preface to the second edition
The main part of this book was written twenty years ago. The ideas and methods of symplectic geometry, developed in this book, have now found many applications in mathematical physics and in other domains of applied mathematics, as ...
Part of Preface to the second edition
The main part of this book was written twenty years ago. The ideas and methods of symplectic geometry, developed in this book, have now found many applications in mathematical physics and in other domains of applied mathematics, as well as in pure mathematics itself. Especially, the theory of short wave asymptotic expansions has reached a very sophiscated level, with many important applications to optics, wave theory, acoustics, spectroscopy, and even chemistry; this development was parallel to the development of the theories of Lagrange and Legendre singularities, that is, of singularities of caustics and of wave fronts, of their topology and their perestroikas (in Russian metamorphoses were always called "perestroikas," as in "Morse perestroika" for the English "Morse surgery"; now that the word perestroika has become international, we may preserve the Russian term in translation and are not obliged to substitute "metamorphoses" for "perestroikas" when speaking of wave fronts, caustics, and so on.
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单复变函数
作者: John B.Conway
出版社: 世界图书出版公司(此信息作废)
出版年: 2004-11
This book is intended as a textbook for a first course in the theory offunctions of one complex variable for students who are mathematicallymature enough to understand and execute arguments. The actual pre-requisites for reading this book are quite minimal; not much more tha...
This book is intended as a textbook for a first course in the theory offunctions of one complex variable for students who are mathematicallymature enough to understand and execute arguments. The actual pre-requisites for reading this book are quite minimal; not much more than astiff course in basic calculus and a few facts about partial derivatives. Thetopics from advanced calculus that are used (e.g., Leibniz's rule for differ-entiating under the integral sign) are proved in detail.
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布朗运动和随机计算
作者: 爱卡拉察斯
出版社: 世界图书出版公司(此信息作废)
出版年: 2006-5
《布朗运动和随机计算(第2版)》是Springer《数学研究生丛书》之113卷，是国内外公认的金融数学经典教材，各章有习题详解。
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为数学家写的广义相对论
作者: R.K.Sachs
出版社: 世界图书出版公司
出版年: 2000-12
While using this book in classes, we found that our canonical reader can learn nonquantum physics rather quickly. Indeed, equipped with geometric intuition and a facility with abstract arguments, he is in a position to deal directly with the general, currently accepted models used...
While using this book in classes, we found that our canonical reader can learn nonquantum physics rather quickly. Indeed, equipped with geometric intuition and a facility with abstract arguments, he is in a position to deal directly with the general, currently accepted models used in relativity without being handicapped by the prejudices that inevitably come with years of Newtonian training in the standard physics curriculum. However, this shortcut does involve a price: one cannot really see the diversity of special cases behind the deceptively simple foundation without spending more time than a mathematics student normally can or should. We have felt for a long time that a serious effort should be made by physicists to communicate with mathematicians somewhat along the line of this book. We started with the aim of keeping the physics honest, keeping th9 mathematics honest, and keeping the logical distinction between the two straight. But we were ill-prepared for the attendant trauma of such an undertaking.
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