All the mathematics you missed : but need to know for graduate school = 数学拾遗 : 研究生必备数学...

作者：  Thomas A. Garrity著.

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简介：　　Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge ,but few have such a backgroud .This book will help stedents see the broad outline of mathematics and to fill in the gaps in their knowlegde. 　　The author explains the basic points and a few key results of the most important undergradute topics in mathematics ,emphasizing the intutions behind the subject.The topics include linear algebra,vector calculus,differential geometry,real analysis ,point-set topology,differential equations,probability theory,complex analysis,abstract algebra,and more.An annotated biliography offers a guide to further reading and more rigorous foundations. 　　This book will be an essential resource for advanced undergraduate and beginning graduate students in mathematics,the physical sciences,engineering,computer science,statistics,and economics,and for anyone else who needs to quickly learn some serious mathemaics.　　

Fixed point theory and applications = 不动点理论和应用 /

作者：  Ravi P. Agarwal, Maria Meehan & Donal O'Regan.

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简介：　　This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of current interest in analysis. Topological considerations play a crucial role, including a final chapter on the relationship with degree theory. Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type. ... 　　

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简介：review: `an excellent text....the postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succint manner.' - american scientist, from a review of the first edition book description　　 reviews from the first edition:　　 "an excellent text … the postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (american scientist)　　 "no matter how gently one introduces students to the concept of dirac’s bras and kets, many are turned off. shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (physics bulletin)　　 "this massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. the style is conversational, more like a corridor talk or lecture notes, though arranged as a text. … it would be particularly useful to beginning students and those in allied areas like quantum chemistry." (mathematical reviews)　　 r. shankar has introduced major additions and updated key presentations in this second edition of principles of quantum mechanics. new features of this innovative text include an entirely rewritten mathematical introduction, a discussion of time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. additional highlights include:　　 - clear, accessible treatment of underlying mathematics　　 - a review of newtonian, lagrangian, and hamiltonian mechanics　　 - student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates　　 - unsurpassed coverage of path integrals and their relevance in contemporary physics　　 the requisite text for advanced undergraduate- and graduate-level students, principles of quantum mechanics, second edition is fully referenced and is supported by many exercises and solutions. the book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

Group theory in physics

作者：  Wu-Ki Tung[著]

出版社：世界图书出版公司北京公司,2011

简介：《物理学中的群论》内容简介：group theory provides the natural mathematical language to formulate symmetry principles and to derive their consequences in mathematics and in physics. the "special functions" of mathematical physics, which pervade mathematical analysis,classical physics, and quantum mechanics, invariably originate from underlying symmetries of the problem although the traditional presentation of such topics may not expressly emphasize this universal feature. modern developments in all branches of physics are putting more and more emphasis on the role of symmetries of the underlying physical systems. thus the use of group theory has become increasingly important in recent years. however, the incorporation of group theory into the undergraduate or graduate physics curriculum of most universities has not kept up with this development. at best, this subject is offered as a special topic course, catering to a restricted class of students. symptomatic of this unfortunate gap is the lack of suitable textbooks on general group-theoretical methods in physics for all serious students of experimental and theoretical physics at the beginning graduate and advanced undergraduate level. this book is written to meet precisely this need. there already exist, of course, many books on group theory and its applications in physics. foremost among these are the old classics by weyl, wigner, and van der waerden. for applications to atomic and molecular physics, and to crystal lattices in solid state and chemical physics, there are many elementary textbooks emphasizing point groups, space groups, and the rotation group. reflecting the important role played by group theory in modern elementary particle theory, many current books expound on the theory of lie groups and lie algebras with emphasis suitable for high energy theoretical physics. finally, there are several useful general texts on group theory featuring comprehensiveness and mathematical rigor written for the more mathematically oriented audience. experience indicates, however, that for most students, it is difficult to find a suitable modern introductory text which is both general and readily understandable.

Mathematical concepts of quantum mechanics = 量子力学中的数学概念 / Enl. 2nd print.

作者：  Stephen J. Gustafson, Israel Michael Sigal.

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简介：《量子力学中的数学概念(英文版)》介绍了：The first fifteen chapters of these lectures （omitting four to six chapters each year） cover a one term course taken by a mixed group of senior undergraduate and junior graduate students specializing either in mathematics or physics. Typically, the mathematics students have some background in advanced analysis, while the physics students have had introductory quantum mechanics. To satisfy such a disparate audience, we decided to select material which is interesting from the viewpoint of modern theoretical physics, and which illustrates an interplay of ideas from various fields of mathematics such as operator theory, probability, differential equations, and differential geometry. Given our time constraint, we have often pursued mathematical content at the expense of rigor. However, wherever we have sacrificed the latter, we have tried to explain whether the result is an established fact, or, mathematically speaking, a conjecture, and in the former case, how a given argument can be made rigorous. The present book retains these features.

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简介：　　This book is intended to provide a reasonable selr-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the familiarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuting theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. 　　 　　　　本书为英文版。　　

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简介：Summary: Publisher Summary 1 A Course in Game Theorypresents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.   Publisher Summary 2 Presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts.