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标签：数学
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A Concise Course in Algebraic Topology
Algebraic topology is a basic part of modern mathematics and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry and Lie groups. This book provides a treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology and the book concludes with a list of suggested readings for those interested in delving further into the field. -
Advanced Linear Algebra (Third Edition)
This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems. -
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Lectures on Linear Algebra
Prominent Russian mathematician's concise, well-written exposition considers: n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, introduction to tensors, more. Not designed as an introductory text. 1961 edition. -
Algebraic Topology
This set of notes, for graduate students who are specializing in algebraic topology, adopts a novel approach to the teaching of the subject. It begins with a survey of the most beneficial areas for study, with recommendations regarding the best written accounts of each topic. Because a number of the sources are rather inaccessible to students, the second part of the book comprises a collection of some of these classic expositions, from journals, lecture notes, theses and conference proceedings. They are connected by short explanatory passages written by Professor Adams, whose own contributions to this branch of mathematics are represented in the reprinted articles. -
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Hodge Theory and Complex Algebraic Geometry II
The 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard-Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant cycles follow. The main results of the second part are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly Nori's connectivity theorem, which generalizes the above. The last part of the book is devoted to the relationships between Hodge theory and algebraic cycles. The book concludes with the example of cycles on abelian varieties, where some results of Bloch and Beauville, for example, are expounded. The text is complemented by exercises giving useful results in complex algebraic geometry. It will be welcomed by researchers in both algebraic and differential geometry. -
微分几何基础
《微分几何基础(英文版)》介绍了微分拓扑、微分几何以及微分方程的基本概念。《微分几何基础(英文版)》的基本思想源于作者早期的《微分和黎曼流形》，但重点却从流形的一般理论转移到微分几何，增加了不少新的章节。这些新的知识为Banach和Hilbert空间上的无限维流形做准备，但一点都不觉得多余，而优美的证明也让读者受益不浅。在有限维的例子中，讨论了高维微分形式，继而介绍了Stokes定理和一些在微分和黎曼情形下的应用。给出了Laplacian基本公式，展示了其在浸入和浸没中的特征。书中讲述了该领域的一些主要基本理论，如：微分方程的存在定理、唯一性、光滑定理和向量域流，包括子流形管状邻域的存在性的向量丛基本理论，微积分形式，包括经典2-形式的辛流形基本观点，黎曼和伪黎曼流形协变导数以及其在指数映射中的应用，Cartan-Hadamard定理和变分微积分第一基本定理。目次：（第一部分）一般微分方程；微积分；流形；向量丛；向量域和微分方程；向量域和微分形式运算；Frobenius定理；（第二部分）矩阵、协变导数和黎曼几何：矩阵；协变导数和测地线；曲率；二重切线丛的张量分裂；曲率和变分公式；半负曲率例子；自同构和对称；浸入和浸没；（第三部分）体积形式和积分：体积形式；微分形式的积分；Stokes定理；Stokes定理的应用；谱理论。 -
Principles of Harmonic Analysis
The book is written for graduate students who have read the first book and like to see the proofs which were not given there and/or want to see the full extent of the theory. On the other hand it can be read independently from the first one, only a modest knowledge on Fourier series/tranform is required to understand the examples. This book fills a major gap in the textbook literature, as a full proof of Pontryagin Duality and Plancherel Theorem is hard to come by. It is usually given in books that focus on C*-algebras and thus carry too much technical overload for the reader who only wants these basic results of Harmonic Analysis. Other proofs use the structure theory which carries the reader away in a different direction. Here the authors consider the Banach-algebra approach more elegant and enlighting. They provide a streamlined approach that reaches the main results directly, and they also give the generalizations to the non-Abelian case. Another main pillar of Harmonic analysis is the Poisson Summation Formula. We give its generalization to LCA-groups. The Selberg Trace Formula is considered the generalization of the Poisson Formula to non-abelian groups. The authors give the first textbook approach to this deep and useful formula in full generality. The last two chapters are devoted to examples of applications of the Selberg Trace Formula. -
The 1-2-3 of Modular Forms
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications, and together they form a comprehensive survey for the novice and a useful reference for a broad group of mathematicians. -
金榜图书·李永乐·王式安唯一考研数学系列
2011版数学基础过关660题：数学三，ISBN：9787560534411，作者：李永乐 主编 -
你好!数学.第二辑 最亲切的数学概念启蒙图画书
你好！数学.最亲切的数学概念启蒙图画书（第2阶段10册套装），ISBN：9787535361158，作者：仇艳 译 （韩国）古艺江，等编 （韩国）车正仁 等绘 -
Elementary Differential Equations with Boundary Value Problems
The Sixth Edition of this acclaimed differential equations book remains the same classic volume it's always been, but has been polished and sharpened to serve readers even more effectively. Offers precise and clear-cut statements of fundamental existence and uniqueness theorems to allow understanding of their role in this subject. Features a strong numerical approach that emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques. Inserts new graphics and text where needed for improved accessibility. A useful reference for readers who need to brush up on differential equations. -
Introduction to Topology
For juniors and seniors of various majors, taking a first course in topology. This book introduces topology as an important and fascinating mathematics discipline. Students learn first the basics of point-set topology, which is enhanced by the real-world application of these concepts to science, economics, and engineering as well as other areas of mathematics. The second half of the book focuses on topics like knots, robotics, and graphs. The text is written in an accessible way for a range of undergraduates to understand the usefulness and importance of the application of topology to other fields. -
群与对称
《群与对称(英文版)》内容简介：numbers measure size, groups measure symmetry. the first statement comes as no surprise; after all, that is what numbers are for. the second will be exploited here in an attempt to introduce the vocabulary and some of the highlights of elementary group theory. a word about content and style seems appropriate. in this volume, the emphasis is on examples throughout, with a weighting towards the symmetry groups of solids and patterns. almost all the topics have been chosen so as to show groups in their most natural role, acting on （or permuting） the members ora set, whether it be the diagonals of a cube, the edges of a tree, or even some collection of subgroups of the given group. the material is divided into twenty-eight short chapters, each of which introduces a new result or idea.a glance at the contents will show that most of the mainstays of a first course arc here. the theorems of lagrange, cauchy, and sylow all have a chapter to themselves, as do the classifcation of finitely generated abelian groups, the enumeration of the finite rotation groups and the plane crystallographic groups, and the nielsen-schreier theorem. -
代数复杂性理论
《国外数学名著系列(影印版)25:代数复杂性理论》全面系统地讲述了代数复杂性理论的知识，书中包含了近400个习题和超过500个参考文献，对初学者和科研人员都有很高的参考价值。 -
模型论引论
《模型论引论》以现代观点介绍模型论，着重强调其在代数学中的应用。前半部分包括模型构造技巧的经典论述，如类型空间，素模型，饱和模型，可数模型，不可辨元等理论及其应用。在书中后半部分，作者首先介绍莫利的范畴性定理，随之讨论定性理论，着重论述Ω-稳定性理论。最后，作者举例阐明了赫鲁索夫斯基如何将这些理论运用于丢番图几何。《模型论引论》显著特色之一是包含一些其他入门型教材所未涉及的重要论题，如Ω-稳定群和强级小集的几何学。 -
多元统计分析及R语言建模
《暨南大学研究生教材•多元统计分析及R语言建模》共分15章，主要内容有：多元数据的收集和整理、多元数据的直观显示、线性与非线性模型及广义线性模型、判别分析、聚类分析、主成分分析、因子分析、对应分析、典型相关分析等常见的主流方法。《暨南大学研究生教材•多元统计分析及R语言建模》还参考国内外大量文献，系统地介绍了这些年在经济管理等领域应用颇广的一些较新方法，可作为统计学专业本科生和研究生的多元分析课程教材。《暨南大学研究生教材•多元统计分析及R语言建模》还可作为非统计学专业研究生的量化分析教材。 -
初等不等式的证明方法
韩京俊所著《初等不等式的证明方法》共分15章，选取300余个国内外 初等不等式的典型问题，以解析解题方法，并对部分问题加以拓展，不少例 题都配有较大篇幅的注解。《初等不等式的证明方法》的一大特色是从“一 名高中生的视角出发”，侧重解题与命题的思想和探索。本书可作为数学奥 林匹克训练的参考教材，供高中及以上文化程度的学生、教师使用，也可作 为不等式爱好者及从事初等不等式研究的相关专业人员阅读参考。
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