数学
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线性代数刘金旺,夏学文主编21世纪高等学校数学系列教材。本书共六章,即n阶行列式、矩阵、向量组与矩阵的秩、线性方程组、特征值及其二次型、线性空间与线性变换,每章均配有习题和参考答案。
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初等数论刘效丽主编;课程教材研究所,数学课程教材研究开发中心编高等师范院校小学教育专业数学教材。本书系统地介绍了初等数论的基础知识。内容包括:整数的整除性、同余与同余方程、不定方程。
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数学猴在武李毓佩著暂缺简介...
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实分析和抽象分析基础Douglas S.Bridges著The core chapters of this volume provide a complete course on metric, normed, and Hilbert spaces, and include many results and exercises seldom found in texts on analysis at this level. The author covers an unusually wide range of material in a clear and concise format including elementary real analysis, Lebesgue integration on R, and an introduction to functional analysis. This makes a versatile text also suited for courses on real analysis, metric spaces, abstract analysis, and modern analysis. The book begins with a comprehensive chapter providing a fast-paced course on real analysis, and is followed by an introduction to the Lebesgue integral. This provides a reference for later chapters as well as an introduction for students with only the typical sequence of undergraduate calculus courses as prerequisites. Other features include a chapter introducing functional analysis, the Hahn-Banach theorem and duality, separation theorems, the Baire Category Theorem, the Open Mapping Theorem and their consequences, and unusual applications such as weak solutions of the Dirichlet Problem and Pareto optimality in Mathematical Economics. Of special interest is the unique collection of nearly 750 exercises, many with guidelines for their solutions. The exercises include applications and extensions of the main propositions and theorems, results that fill in gaps in proofs or that prepare for proofs later in the book, pointers to new branches of the subject, and difficult challenges for the very best students.本书为英文版。
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泛函微分方程理论( )Jack Hale著Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more comprehensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research.
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保险和金融用的例外事件模型( )Paul Embrechts等著In a recent issue, The New Scientist ran a cover story under the title: "Mission improbable. How to predict the unpredictable"; see Matthews [448]. In it, the author describes a group of mathematicians who claim that extreme value theory (EVT) is capable of doing just that: predicting the occurrence of rare events, outside the range of available data. All members of this group, the three of us included, would immediately react with: "Yes, but, ...", or, "Be aware...". Rather than at this point trying to explain what EVT can and cannot do, we would like to quote two members of the group referred to in [448]. Richard Smith said, "There is always going to be an element of doubt, as one is extrapolating into areas one doesn't know about. But what EVT is doing is making the best use of whatever data you have about extreme phenomena." Quoting from Jonathan Tawn, "The key message .is that EVT cannot do magic - but it can do a whole lot better than empirical curvefitting and guesswork. My answer to the sceptics is that if people aren't given well-founded methods like EVT, they'll just use dubious ones instead."此书为英文版。
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组合图论谢政,戴丽编著研究生教材 国防科技大学研究生教材专项经费资助。本书共10章,包括图的基本概念、树、通能性、遍历性、匹配、Ramsey数、着色、平面图、有向图、图的空间与矩阵以及图的计算等图论基本内容和理论。还介绍了相异代表系、鸽巢原理、容斥原理、递推关系、生成函数和Polya计数定理等经典的组合数学原理。
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线性代数教程包研科等编著《线性代数教程》是根据教育部对工科线性代数教学的基本要求,结合辽宁工程技术大学近几年在线性代数教学改革实践中的经验与体会,并参考了工科硕士研究生入学考试大纲编写而成。在内容的处理上,以线性代数核心内容的统一性和规律性为依据,突出了向量、矩阵和行列式的工具性和内在联系,将有关内容相对集中编排在一起讲授。介绍了向量、矩阵、行列式的基本概念及其各种运算;以线性方程组的可解性为纽带,将向量、矩阵、行列式与线性方程组解的存在性及其解的表达问题紧密地联系在一起;进而,初步地讨论了线性空间的代数结构和度量结构;以方阵的对角化问题为主线,把线性变换、特征值与特征向量、二次型问题联系起来。淡化了计算技巧,突出了向量运算、矩阵运算与行列式运算的联系。重点放在便于计算机实现、基于矩阵初等变换的基本计算能力的培养,并在随后的线性方程组理论、线性空间理论和二次型理论中得到进一步确认。这样处理的优点是显然的,有利于学生逻辑思维能力和抽象思维能力的培养,有利于领会线性代数基本概念和方法的威力。但是,这种处理使得学生在入门阶段需要掌握的概念相对较多,对此在教学中应予以足够的重视,有针对性地进行强化训练。在这本32课时线性代数教程的编写中,对一些冗繁或较难的定理证明。或示例说明,或用楷体字排版,供读者阅读参考。对一些拓展性的内容,以及在概念和理论的链条上非必须的内容也做了楷体字排版的处理。教学中配套使用的习题另册编印。我们在编写过程中注意到实例和范例的教学价值,选用了一些有实际背景的问题作为例题,试图克服数学概念从定义到定义的“抽象配种”所带来的问题。由于知识和水平所限,疏漏之处在所难免,诚望读者不吝赐教,批评指正。《线性代数教程》由包研科主编。其中第1章由包研科编写,第2章由于清江编写,第3章由柴岩编写,第4章由曾繁会编写。全书的统稿和整理由包研科完成,书稿的誊清由胡行华、齐俊玲共同完成。
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钱伟长教授九十华诞祝寿文集周哲玮主编上海大学为钱伟长教授的九十华诞举行了一系列的学术活动和庆贺活动。《钱伟长教授九十华诞祝寿文集》收入钱校长创办的《应用数学和力学》杂志的编委和上海市应用数学和力学研究所的研究人员最近几年的最新成果和学术成就,以作祝贺。
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院士成才启示录孙殿义,卢盛魁主编中国科学院院士和中国工程院院士作为我国科技界的佼佼者,创造出了许多令世人瞩目的科技成果,人们在敬佩的同时,对他们的成长、成才、成功的经历也有浓厚的兴趣。新近出版的《院士成才启示录》将满足人们一“睹”院士成才之路的愿望。这本书是由中国科学院和中国工程院168位院士亲笔所写或者亲自讲述的短文组成的,编辑者匠心独运地把这些文章分成了9个部分,本书则包括理想与立志;做人与做事,打好基础与全面发展;好学与勤奋,意志与毅力。这些精短篇章,尤其是院士们本人写的文章,不仅仅在平实的语句中给我们以深刻的思想和智慧,更在轻松的语调中给我们以优美的文字享受。你清晰地感觉到这是一次轻松的文字旅行,我们是在与和蔼可亲的长辈愉悦的交谈。他们丝毫也没有院士大科学家的脾气和威严,他们似乎就是我们的长辈,在我们自己家的书房里在对我们谆谆教诲。为使读者更充分地领略院士们的风采,书中还穿插了210多张珍贵的院士们的工作照和生活照。中科院院长路甬祥在此书的序中指出,《院士成才启示录》所展现的中国科学院、中国工程院两院院士成才的经验和体会,对如何培养、造就知识创新人才将有诸多的启示。