The study of graph theory started over two hundreds years ago. The earliest known paper is due to Euler（1736） about the seven bridges of Korugsberg. Since 1960s， graph theory has developed very fast and numerous results on graph theory sprung forth. There are many nice and celebrated problems in graph theory， such as Hamiltonian problem， four-color problem， Chinese postman problem， etc. Moreover， graph theory is widely applied in chemistry， computer science， biology and other disciplines. As a subfield in discrete mathematics， graph theory has attracted much attention from all perspectives.All graphs are considered only finite， simple， undirected graphs with no loops and no multiple edges. Let G be a graph. The Hamiltonian cycle problem is one of the most well-known problems in graph theory. A cycle which contains every vertex of G is called a Hamiltonian cycle. A cycle is called a chorded cycle if this cycle contains at least one chord. A k-factor in a graph G is a spanning k-regular subgraph of G， where k is a positive integer. There exists many interesting results about the existence of k-factor， by applying Tuttes Theorem， however， we mainly focus on the existence of 2-factor throughout this thesis. Clearly， a Hamiltonian cycle is a 2-factor with exactly one component. From this point of view， it is a more complex procedure to find the condition to ensure the existence of 2-factor in a given graph. The most usual technique to resolve 2-factor problems is to find a minimal packing and then extend it to a required 2-factor.The book is concerned with structural invariants for packing cycles in a graph and partitions of a graph into cycles， i.e.， finding a prescribed number of vertex-disjoint cycles and vertex-partitions into a prescribed number of cycles in graphs. It is well-known that the problem of determining whether a given graph has such partitions or not， is NP-complete. Therefore， many researchers have investigated degree conditions for packing and partitioning. This book mainly focuses on the following invariants for such problems： minimum degree， average degree （also extremal function）， degree sum of independent vertices and the order condition with minimum degree.

This book is intended to have three roles and to serve three associated audiences： anintroductory text on Bayesian inference starting from first principles， a graduate text oneffective current approaches to Bayesian modeling and computation in statistics and relatedfields， and a handbook of Bayesian methods in applied statistics for general users of andresearchers in applied statistics. Although introductory in its early sections， the book isdefinitely not elementary in the sense of a first text in statistics. The mathematics usedin our book is basic probability and statistics， elementary calculus， and linear algebra. Areview of probability notation is given in Chapter 1 along with a more detailed list of topicsassumed to have been studied. The practical orientation of the book means that the reader'sprevious experience in probability， statistics， and linear algebra should ideally have includedstrong computational components.To write an introductory text alone would leave many readers with only a taste of theconceptual elements but no guidance for venturing into genuine practical applications， be-yond those where Bayesian methods agree essentially with standard non-Bayesian analyses.On the other hand， we feel it would be a mistake to present the advanced methods with-out first introducing the basic concepts from our data-analytic perspective. Furthermore，due to the nature of applied statistics， a text on current Bayesian methodology would beincomplete without a variety of worked examples drawn from real applications. To avoidcluttering the main narrative， there are bibliographic notes at the end of each chapter andreferences at the end of the book.

本书是自世界著名大学剑桥大学出版社引进的英文版数学教程，中文书名可译为《实分析演讲集》作者是芬纳.拉尔森教授，他任教于澳大利亚阿德莱德大学。剑桥大学出版社对本书的介绍是这样写的： 本书是为本科学生准备的对实分析的严谨的介绍，从全序域的定理和一些集合论知识开始。本书避免了任何关于实数的先入之见，只把它们当作全序域的元素来研究。包括所有的标准主题，以及对三角函数的适当处理，许多人认为这些内容都是理所应当的。书的最后几章提供了一个详细的、基于实例的对应用在实线上的微分方程的度量空间的介绍。 作者的阐述简明扼要，帮助学生抓住要点。本书包括200多个不同难度的练习题，其中许多题都涉及正文中的理论内容。该书非常适合本科二年级学生和需要掌握实分析基础知识的更高年级的学生阅读。

本书为民国时期中学生用的英文原版教材的影印版，书中介绍了代数的相关理论及应用，同时配以相应的习题，以供读者更好的理解。本书适合中学生师生及数学爱好者阅读参考。

《应用随机过程》是应用随机过程教材，其内容包括概率论的基础知识、随机过程的基本概念和基本类型、离散（连续）时间的马尔可夫链、泊松过程、鞅过程、布朗运动和平稳过程等。《应用随机过程》尽量采用通俗易懂的方法介绍随机过程中的基本概念和基本理论，更加强调理论的直观解释和应用，选取了大量与社会、经济、金融、生物等领域相关的例题和习题，可供读者自学、参考。《应用随机过程》可以作为工程硕士和非数学类专业本科生的应用教材或教学参考书，也可为从事与随机过程相关的教学和工程技术人员提供参考。

《解析几何》一方面内容充实，通俗易懂，是学习几何学的入门教材。书中既讲解了空间解析几何的基本内容和方法（向量代数，仿射坐标系，空间的直线和平面，常见曲面等），又讲解了仿射几何学中的基本内容和思想（仿射坐标变换，二次曲线的仿射理论，仿射变换和等距变换等），还介绍了射影几何学中的基本知识，较好地反映了几何学课程的全貌。该书突出几何思想的教育，强调形与数的结合；方法上强调解析法和综合法并重；内容编排上采用“实例一理论一应用”的方式，具体易懂；内容选取上兼顾各类高校的教学情况，具有广泛的适用性。《解析几何》表达通顺，说理严谨，阐述深入浅出。另一方面注意培养读者的空间想象能力，这尤其体现在第三章中关于旋转面、柱面和锥面方程的建立。《解析几何》论证严谨，同时又力求简明；叙述上深入浅出，条理清楚，注意讲清所讨论问题的来龙去脉。

本书主要研究非线性随机结构在非平稳随机地震作用下的随机反应，即非线性复合随机振动系统的随机反应。利用Monte Carlo法、摄动虚拟激励法、频域传递函数摄动法研究结构随机阻尼对结构位移响应的影响。本书可供高校相关专业师生和专业研究人员阅读参考。本书主要研究非线性随机结构在非平稳随机地震作用下的随机反应，即非线性复合随机振动系统的随机反应。利用Monte Carlo法、摄动虚拟激励法、频域传递函数摄动法研究结构随机阻尼对结构位移响应的影响。本书可供高校相关专业师生和专业研究人员阅读参考。

《研究生数学建模精品案例（第二卷）》精选了2013～2017年中国研究生数学建模竞赛的七个赛题.《研究生数学建模精品案例（第二卷）》共分8章，内容包括对中国研究生数学建模竞赛的思考、水面舰艇编队防空和信息化战争评估模型、微蜂窝环境中无线接收信号的特性分析、乘用车物流运输计划问题、机动目标的跟踪与反跟踪、面向节能的单/多列车优化决策问题、多无人机协同任务规划、多波次导弹发射中的规划问题.每个案例自成体系，可以独立阅读.

“离散数学”是研究离散结构及其相互关系的学科，是计算机科学与技术专业的核心基础课程。《离散数学（第二版）》共五篇九章，系统介绍数理逻辑、集合论、图论、代数系统、组合与计数的基本概念和基本原理。《离散数学（第二版）》内容符合新工科教育的要求，满足计算机科学与技术等专业的教学需求，内容体系严谨，叙述深入浅出，证明推演详尽。同时，《离散数学（第二版）》详细介绍相关知识在计算机科学中的应用实例及算法分析，紧密结合实际应用，对每章知识进行归纳总结，对典型例题进行详细分析解答，并配有大量习题及上机实验。

全书包括函数极限与连续、导数与微分及其应用、积分及其应用、常微分方程、向量代数及空间解析几何、多元函数微积分、无穷级数、数学实验与数学建模简介。在实际教学中，可根据实际教学需要，参照不同专业的学时数，选择与专业需要匹配的教学内容进行教学。