"数学小子"丛书（全5册），ISBN：9787530741580，作者：（美）玛瑞琳·伯恩斯 等文，（美）戴比·泰勒 等图，班春虹 等译 康福特先生和太太正在准备一次家庭聚会。康福特先生开始做他最拿手的意大利面条和肉丸子，康福特太太则认真地摆放着8张桌子和32把椅子，以确保每位客人都有座位……

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

《数学建模案例选集》由一些长期从事数学应用研究并有丰富教学经验的教师集体完成，这些案例有的来自他们完成的实际课题，有的根据他们了解的实际背景和掌握资料做了重新编纂，也有的是基于他们实际经验对现成的数学建模实例做了精心改编，内容涉及工程、管理、信息、医疗、地震、社会等领域实际问题的数学建模。

Leonhard Euler's polyhedron formula describes the structure of many objects - from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. "Euler's Gem" tells the illuminating story of this indispensable mathematical idea. From ancient Greek geometry to today's cutting-edge research, "Euler's Gem" celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2.David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and, how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, "Euler's Gem" will fascinate every mathematics enthusiast.

《Markov过程导论》是一本很好的随机过程的入门书籍，主要介绍可数状态空间上的；Markov过程的基本理论，内容包括Doeblin理论。一般的遍历理论、连续时间Markov过程和可逆Markov过程。书中每一章后面都提供了不同难易程度的练习题，并对一些富有挑战性的问题给出了有益的提示。为了便于阅读，最后一章概要地；介绍了有关测度论的基础知识。

本书共分三编：第一编试题，共包括1～68届美国大学生数学竞赛试题及解答；第二编培训，包括100道培训试题；第三编研究，包括六大问题——(一)Mendeleev问题；(二)Thue—Siegel—Roth定理；(三)函数唯一性理论；(四)不动点问题；(五)Beatty定理与Lambek—Moser定理；(六)Catalan猜想。 本书适合于数学奥林匹克竞赛选手和教练员、高等院校相关专业研究人员及数学爱好者使用。