数学
计算流体力学基础及其应用 豆瓣
作者: 约翰D.安德森 出版社: 机械工业出版社 2007 - 6
《计算流体力学基础及其应用》是计算流体力学(CFD)方面的入门书。本书首先介绍了计算流体力学的基础知识,然后通过四个精心挑选的例子介绍了计算流体力学中的重要方法和处理技巧。这些例子都有理论上的解析解,读者可以将cFD计算的结果与解析解进行对比,从而更深入地了解cFD的基本概念、思路、方法、用途和优缺点。在此基础上,本书的最后一部分介绍了计算流体力学中的几个前沿问题。
矩阵计算 豆瓣
Matrix Computations,3E
作者: Gene H.Golub / Charles F.Van Loan 译者: 袁亚湘 出版社: 人民邮电出版社 2011 - 3
本书是国际上数值计算方面的权威著作,有“圣经”之称。被美国加州大学、斯坦福大学、华盛顿大学、芝加哥大学、中国科学院研究生院等很多世界知名学府用作相关课程的教材或主要参考书。
本书系统地介绍了矩阵计算的基本理论和方法。书中的许多算法都有现成的软件包实现,每节后还附有习题,并有注释和大量参考文献,非常有助于自学。
自动机理论、语言和计算导论(英文版.第3版) 豆瓣
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
作者: John E. Hopcroft / Rajeev Motwani 出版社: 机械工业 2008 - 1
本书是关于形式语言、自动机理论和计算复杂性方面的经典教材,是三位理论计算大师的巅峰之作,现已更新到第3版。书中涵盖了有穷自动机、正则表达式与语言、正则语言的性质、上下文无关文法及上下文无关语言、下推自动机、上下文无关语言的,陸质、图灵机、不可判定性以及难解问题等内容。
本书已被世界许多著名大学采用为计算机理论课程的教材或教学参考书,适合用作国内高校计算机专业高年级本科生或研究生的教材,还可供从事理论计算工作的研究人员参考。
圆锥曲线的几何性质 豆瓣
A Treatise on Geometrical Conics
作者: [英] A. 科克肖特, F. B. 沃尔特斯 出版社: 上海教育出版社 2002 - 1
《圆锥曲线的几何性质》采用综合法,从图形到图形,以平面几何知识为主,立体几何知识为辅,介绍了圆锥曲线的大批几何性质。主要内容包括:抛物线、正射影、椭圆、双曲线、直角双曲线、圆柱面和圆锥面的截线等等。
希尔伯特 豆瓣
Hilbert
8.8 (5 个评分) 作者: [美] 康斯坦丝·瑞德 译者: 袁向东 / 李文林 出版社: 上海科技出版社 2006 - 7
《希尔伯特数学世界的亚历山大》是被科学界公认的经典读本。大卫·希尔伯特是20世纪上半叶国际数学界的一位领袖人物,他于1900年在巴黎第二届国际数学家大会上提出的23个数学问题,激发了整个数学界的想象力,造就了20世纪一大批著名的数学家。此后,这些问题几乎成为检阅数学重大成就的一张航图。这位创造20世纪数学史奇迹的数学家和数学思想家,就像数学世界的亚历山大,在整个数学版图上留下了巨大显赫的名声。全书以平静的笔触叙述了这位极富想象力的人在一个极抽象的世界里如鱼得水、平淡而又神奇的一生。
Hilbert 豆瓣
作者: Constance Reid 出版社: Springer 1996 - 4
"It presents a sensitive portrait of a great human being. It describes accurately and intelligibly on a nontechnical level the world of mathematical ideas in which Hilbert created his masterpieces. And it illuminates the background of German social history against which the drama of Hilberts life was played. Beyond this, it is a poem in praise of mathematics." -SCIENCE
我和爷爷熊庆来 豆瓣
作者: 熊有德 2009 - 4
《我和爷爷熊庆来》讲述了:作者熊有德女士曾在爷爷熊庆来身边度过了她的青少年时代。正是因为这段难忘的岁月,使熊有德女士能够有机会近距离地接触和了解一代数学大师的思想和生平。不少的媒体都刊登过有关熊庆来先生的回忆文章,坊间也有多种关于他的传记作品,但熊有德女士都不太满意,她觉得很多作品仅仅是从学术的角度来解读,有的甚至把爷爷熊庆来神化了,尤其是对他的生活和思想,很少有客观真实的描写。所以,她一直有个夙愿,在有生之年用文字给世人留下一个真实的熊庆来。在熊庆来先生去世四十周年之际,熊有德女士终于写完了这部厚重的回忆录,而此时她已是花甲之年。
熊有德女士坦言除了了却夙愿,这部作品她也是专门写给年轻人看的。她在序言里写道:“我的这一本书写在爷爷去世四十周年纪念的前夕,是对爷爷的纪念,也是对后来人的一个鼓励,希望后人接过接力棒,把知识分子的美德,清贫刻苦、努力钻研、为国为民的好风格代代传下去。”虽然逝者已去,但他用毕生精力所铸就的不朽丰碑仍将永远耸立在那里,他的精神也将永留世间。
超弦理论 豆瓣
作者: (日)大栗博司 译者: 逸 宁 出版社: 人民邮电出版社 2014
“空间”和“时间”究竟是什么?
物质的本原不是点,而是弦?
黑洞、高维度空间应该如何解释?
“超弦理论”是继牛顿力学、爱因斯坦相对论之后,时空概念的“第三次革命”。“超弦理论”统一了引力理论与量子力学的矛盾,超越了“弦理论”的局限,解释“标准模型”中“费米子”与包括“上帝粒子”的“玻色子”的振动形态。本书中,大栗教授以通俗、风趣的语言讲解了量子物理基础、“弦理论”到“超弦理论”的最新发展、“超弦理论”的理论原理及证明,并在“超弦理论”下重新思考与探究了时空概念。
数学巨匠 豆瓣
作者: [英]约安·詹姆斯 译者: 潘澍原 / 林开亮 出版社: 上海科技教育出版社 2016 - 9
本书介绍了60位数学家的生平,从1707年出生的欧拉到1903年出生的冯·诺伊曼。他们通过各自的思想、教学或是其他方式,对数学作出了重要贡献。
这60位数学家经历多样、命运各异。他们中仅有3位女性,分别是热尔曼、柯瓦列夫斯卡娅和诺特。他们在文化上非常多元化,特别是犹太人占了很大比例。虽然有一些人来自非常富有的家庭,但大多数人出身贫寒。总的来说,比起他们的父母来,他们的社会地位得到了显著提升。这些人中的大部分都有着寻常的天分。阅读本书,你就能了解数学如何改变了他们的命运,以及他们如何改变了数学。
An Introduction to Systems Biology 豆瓣
作者: Uri Alon 出版社: Chapman and Hall/CRC 2006 - 7
Thorough and accessible, this book presents the design principles of biological systems, and highlights the recurring circuit elements that make up biological networks. It provides a simple mathematical framework which can be used to understand and even design biological circuits. The text avoids specialist terms, focusing instead on several well-studied biological systems that concisely demonstrate key principles. "An Introduction to Systems Biology: Design Principles of Biological Circuits" builds a solid foundation for the intuitive understanding of general principles. It encourages the reader to ask why a system is designed in a particular way and then proceeds to answer with simplified models.
Symmetry 豆瓣
作者: Hermann Weyl 出版社: Princeton University Press 1983 - 1
Defines symmetry through a discussion of its many uses in a wide variety of fields both academic and natural.
对称 豆瓣
作者: [德] 赫尔曼·外尔 出版社: 上海科教出版社 2005 - 4
本书是20世纪大数学家外尔阐释对称思想的力作。对称是人类千百年来试图理解和建立秩序、优美、完美所依据的概念之一。本书从对称意味着比例之和谐这一概念出发,从双侧对称性、平移对称性、旋转对称性、装饰对称性、晶体对称性等对称性的几何概念,逐步深入、最后上升到作为所有这些特殊形式基础的普遍的抽象数学思想。
Numerical Optimization 豆瓣
作者: Jorge Nocedal / Stephen Wright 出版社: Springer 2006 - 7
Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.
概率论与随机过程中的泛函分析(影印版) 豆瓣
作者: 博布罗斯基 出版社: 高等教育出版社 2008 - 3
本书主要包含国外反映近代数学发展的纯数学与应用数学方面的优秀书籍,天元基金邀请国内各个方向的知名数学家参与选题的工作,经专家遴选、推荐而出版。
目录
Preface
1 Preliminaries, notations and conventions
1.1 Elements of topology
1.2 Measure theory
1.3 Functions of bounded variation. Riemann-Stieltjes integral
1.4 Sequences of independent random variables
1.5 Convex functions. Holder and Minkowski inequalities
1.6 The Cauchy equation
2 Basic notions in functional analysis
2.1 Linear spaces
2.2 Banach spaces
2.3 The space of bounded linear operators
3 Conditional expectation
3.1 Projections in Hilbert spaces
3.2 Definition and existence of conditional expectation
3.3 Properties and examples
3.4 The Radon-Nikodym Theorem
3.5 Examples of discrete martingales
3.6 Convergence of self-adjoint operators
3.7 ... and of martingales
4 Brownian motion and l-Iilbert spaces
4.1 Gaussian families & the definition of Brownian motion
4.2 Complete orthonormal sequences in a Hilbert space
4.3 Construction and basic properties of Brownian motion
4.4 Stochastic integrals
5 Dual spaces and convergence of probability measures
5.1 The Hahn-Banach Theorem
5.2 Form of linear functionals in specific Banach spaces
5.3 Thedual of an operator
5.4 Weak and weak* topologies
5.5 The Central Limit Theorem
5.6 Weak convergence in metric spaces
5.7 Compactness everywhere
5.8 Notes on other modes of convergence
6 The Gelfand transform and its applications
6.1 Banach algebras
6.2 The Gelfand transform
6.3 Examples of Gelfand transform
6.4 Examples of explicit calculations of Gelfand transform
6.5 Dense subalgebras of C(S)
6.6 Inverting the abstract Fourier transform
6.7 The Factorization Theorem
7 Semigroups of operators and Levy processes
7.1 The Banach-Steinhaus Theorem
7.2 Calculus of Banach space valued functions
7.3 Closed operators
7.4 Semigroups of operators
7.5 Brownian motion and Poisson process semigroups
7.6 More convolution semigroups
7.7 The telegraph process semigroup
7.8 Convolution semigroups of measures on semigroups
8 Markov processes and semigroups of operators
8.1 Semigroups of operators related to Markov processes
8.2 The Hille-Yosida Theorem
8.3 Generators of stochastic processes
8.4 Approximation theorems
9 Appendixes
9.1 Bibliographical notes
9.2 Solutions and hints to exercises
9.3 Some commonly used notations
References
Index
Functional Analysis For Probability And Stochastic Processes 豆瓣
作者: Bobrowski, Adam 出版社: Cambridge Univ Pr 2005 - 9
This text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.
力学和对称性导论 豆瓣
作者: [美]马斯登 出版社: 清华大学 2006 - 8
本书阐述了力学与对称性的理论及其进展, 将力学中的几何观点与固体分析结合起来, 深入研究了力学中诸如连续介质力学的变分和哈密顿结构、流体力学、等离子体物理等基本问题; 提供了具体模型中有用的工具, 如应用能量- 开西米尔和能量-动量方法的新的稳定性和分岔准则, 基于具有几何精确性的更新程序和变分积分子的新的数值码,以及在控制理论和机器人学中的新的再定向技术等;介绍了对称性在力学中的广泛应用, 如在约化, 稳定性, 分岔, 关于一个给定的系统对称群的解的对称性的破坏, 可积系统求显式解, 以及对于特殊系统(如Kowalewski顶)的深入理解等问题中的应用。
本书(英文版)附有解题指南和互联网补充, 为读者提供了重要的相关知识。
作者美国加州理工学院Marsden 教授和加州大学圣克鲁斯分校及瑞士联邦工学院Ratiu教授都是相关领域的国际著名专家, 他们从丰富的视角, 深刻阐述了力学和对称性基本理论的大部分内容, 为读者提供了广博而详实的理论和应用分析。
Introduction to Computing Systems 豆瓣
作者: Yale N. Patt / Sanjay J. Patel 出版社: McGraw-Hill Education 2003 - 8
"Introduction to Computing Systems: From bits & gates to C & beyond", now in its second edition, is designed to give students a better understanding of computing early in their college careers in order to give them a stronger foundation for later courses. The book is in two parts: the underlying structure of a computer, and programming in a high level language and programming methodology. To understand the computer, the authors introduce the LC-3 and provide the LC-3 Simulator to give students hands-on access for testing what they learn. To develop their understanding of programming and programming methodology, they use the C programming language.The book takes a "motivated" bottom-up approach, where the students first get exposed to the big picture and then start at the bottom and build their knowledge bottom-up. Within each smaller unit, the same motivated bottom-up approach is followed. Every step of the way, students learn new things, building on what they already know. The authors feel that this approach encourages deeper understanding and downplays the need for memorizing. Students develop a greater breadth of understanding, since they see how the various parts of the computer fit together.
The Elements of Statistical Learning 豆瓣 Goodreads
9.8 (10 个评分) 作者: Trevor Hastie / Robert Tibshirani 出版社: Springer 2009 - 10
During the past decade there has been an explosion in computation and information technology. With it have come vast amounts of data in a variety of fields such as medicine, biology, finance, and marketing. The challenge of understanding these data has led to the development of new tools in the field of statistics, and spawned new areas such as data mining, machine learning, and bioinformatics. Many of these tools have common underpinnings but are often expressed with different terminology. This book describes the important ideas in these areas in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with a liberal use of color graphics. It is a valuable resource for statisticians and anyone interested in data mining in science or industry. The book's coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting---the first comprehensive treatment of this topic in any book. This major new edition features many topics not covered in the original, including graphical models, random forests, ensemble methods, least angle regression & path algorithms for the lasso, non-negative matrix factorization, and spectral clustering. There is also a chapter on methods for "wide" data (p bigger than n), including multiple testing and false discovery rates.