《微分流形与黎曼几何引论(英文版 第2版修订版)》是一本非常好的微分流形入门书。全书从一些基本的微积分知识入手，然后一点点深入介绍，主要内容有：流形介绍、多变量函数和映射、微分流形和子流形、流形上的向量场、张量和流形上的张量场、流形上的积分法、黎曼流形上的微分法以及曲率。书后有难度适中的习题，全书配有很多精美的插图。
《微分流形与黎曼几何引论(英文版 第2版修订版)》非常适合初学者阅读，可作为数学系、物理系、机械系等理工科高年级本科生和研究生的教材。

个人觉得是非常好的微分方程教材

An introductory text in nonlinear dynamics and chaos, emphasizing applications in several areas of science, which include vibrations, biological rhythms, insect outbreaks, and genetic control systems. Contains a rich selection of illustrations, with many exercises and examples. Softcover.

"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature

本书是根据美国科学院院士，著名数学家P·格列菲斯在北京大学讲课的讲稿整理写成的。本书篇幅虽不大，但内容丰富，阐述精炼，引人入胜。书中深入浅出地介绍了正则化定理，Riemann-Roch定理，Abel定理等代数曲线论的重要结果，以及这些定理的应用和重要的几何事实。读者只要具有大学复变函数论和抽象代数的基础知识即可阅读此书。 本书可作为大学数学系高年级学生和研究生教材，也可供数学工作者参考。

Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between.

Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work.
The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation.
By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling.

Walter Rudin's memoirs should prove to be a delightful read specifically to mathematicians, but also to historians who are interested in learning about his colorful history and ancestry. Characterized by his personal style of elegance, clarity, and brevity, Rudin presents in the first part of the book his early memories about his family history, his boyhood in Vienna throughout the 1920s and 1930s, and his experiences during World War II.
Part II offers samples of his work, in which he relates where problems came from, what their solutions led to, and who else was involved. As those who are familiar with Rudin's writing will recognize, he brings to this book the same care, depth, and originality that is the hallmark of his work.

《概率(第2卷)(修订和补充第3版)》是俄国著名数学家A.H.施利亚耶夫的力作。施利亚耶夫是现代概率论奠基人、前苏联科学院院士、著名数学家A.H.柯尔莫戈洛夫的学生，在概率统计界和金融数学界影响极大。《概率(第2卷)(修订和补充第3版)》作为莫斯科大学最为出色的概率教材之一。分为一、二两卷，并配有习题集。第二卷《概率(第2卷)(修订和补充第3版)》是离散时间随机过程（随机序列）的内容。重点讲述（强和弱）平稳序列、鞅和马尔可夫链，并给出了随机序列中的估计和过滤问题、随机金融数学、保险理论和最优停时问题等领域的应用。书后附有概率的数学理论形成的简史。在图书文献资料中，指出了所引用结果的出处，并且给出了注释。此外，还列出了相应的补充文献资料。第一卷《概率(第2卷)(修订和补充第3版)》是初等概率论的内容，可以作为初步了解概率论学科的教材。大部分内容涉及以柯尔莫戈洛夫公理化体系为基础的初等概率论、概率论的数学基础、概率测度的收敛性和极限定理等基本问题。

The first two ch

本书是Л.C庞特里亚金院士根据他多年在莫斯科大学数学力学系所用的讲义编成的一本教材。它的第一次出版是在1961年，现在的第6版有不少的修改。本书从编写的指导思想到内容的具体安排上，与传统教材有很大的不同。作者从常微分方程在现代科学技术方面的应用出发，对材料作了新的选择和安排，不仅讲述了纯数学的常微分方程理论，同时还讲述了有关的技术应用本身。全书包括引论，常系数线性方程，变系数线性方程，存在性定理，稳定性共五章，另外还有两个与本书内容密切联系的附录，即一些分析问题和线性代数知识。每节后面都有例子或者实际应用问题。.
本书可供高等学校数学、物理、工程及相关专业的本科生、硕士生、教师，以及相关领域的研究人员参考使用。...

In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find. Among these are: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and a full exposition of Steenrod squares and powers. Researchers will also welcome this aspect of the book.

《代数拓扑导论(英文版)》介绍了：There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to .I.H.C. Whitehead. Of course, this is false, as a giance at the books of Hilton and Wylie, Maunder, Munkres, and Schubert reveals. Still, the canard does reflect some truth. Too often one finds too much generality and too little attention to details.

What makes populations stabilize? What makes them fluctuate? Are populations in complex ecosystems more stable than populations in simple ecosystems? In 1973. Robert May addressed these questions in this classic book. May investigated the mathematical roots of population dynamics and argued - counter to most current biological thinking - that complex ecosystems in themselves do not lead to population stability. Stability and Complexity in Model Ecosystems played a key role in introducing nonlinear mathematical models and the study of deterministic chaos into ecology, a role chronicled in James Gleick's book Chaos. In the quarter century since its first publication, the book's message has grown in power. Nonlinear models are now at the center of ecological thinking, and current threats to biodiversity have made questions about the role of ecosystem complexity more crucial than ever. In a new introduction, the author addresses some of the changes that have swept biology and the biological world since the book's first publication.

This famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms.
The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and homomorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the corresponding Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontrjagin's duality theorem for Abelian groups.
The continued importance of Lie groups in mathematics and theoretical physics make this an indispensable volume for researchers in both fields.
Table of Contents:
INTRODUCTION vii
I. THE CLASSICAL LINEAR GROUPS 1
II. TOPOLOGICAL GROUPS 25
III. MANIFOLDS 68
IV. ANALYTIC GROUPS. LIE GROUPS 99
V. THE DIFFERENTIAL CALCULUS 0F CARTAN 139
VI. COMPACT LIE GROUPS AND THEIR REPRESENTATIONS 171
INDEX 215

Since his death in 1996, many scientific meetings have been dedicated to the memory of Paul ErdAs. From July 4 to 11, 1999, the conference "Paul ErdAs and his Mathematics" was held in Budapest, with the ambitious goal of showing the whole range of ErdAs' work - a difficult task in view of ErdAs' versatility and his broad scope of interest in mathematics. According to this goal, the topics of lectures, given by the leading specialists of the subjects, included number theory, combinatorics, analysis, set theory, probability, geometry and areas connecting them, like ergodic theory. The conference has contributed to changing the common view that ErdAs worked only in combinatorics and combinatorial number theory. In the present two volumes, the editors have collected, besides some personal reminiscences by Paul's old friends, mainly survey articles on his work, and on areas he initiated or worked in.

本书通过大量丰富的实例，帮助读者从基本的常微分方程向更多高级概念(偏微分方程、傅里叶级数和边界值问题等)顺利过渡。作者轻松的语言风格使得书中的材料通俗易懂，尤其适合那些渴望了解更多和更深微积分知识的读者。
本书强调理论与实践相结合，介绍了大量偏微分方程在工程和物理学方面的应用，并且提供了相关数学证明和偏微分方程的原理。此外，本书的每一节后都配备了大量的习题，并提供了注释、图标或重要的公式等，突出了书中的重点与难点，方便读者自学。
本书提倡读者利用计算机辅助学习，旨在使读者更直观，更清晰地理解和掌握书中所讲述的题材。读者可以利用从作者网站上下载的Mathematica文件进行上机实践。
本书系统讲解偏微分方程及其定解问题的求解方法，通过大量实例讨论微分方程解的性质，特别强调傅里叶级数在求解边值问题中的作用。书中配有丰富的例题与习题，还采用“专题问题”较为系统地研究某个具体问题，补充和扩展了正文内容。
本书内容丰富、推导严密，包含大量物理背景，为理解和掌握偏微分方程提供了有效途径。本书可作为高等院校数学及相关专业学生的偏微分方程课程教材，同时也可作为工程技术人员、科技工作者的参考书。