《素数论》共分5章，从数论的某些经典问题入手，而以对一些重要猜想的讨论作为结束，其间还介绍了Riemannzeta数的基本性质、素数的随机分布，以及素数定理的初等证明等。其目的是想让读者对素数理论有一个初步的了解，并以此为依托来解释为什么如此高度有序的素数序列会蕴涵着大量令人震惊的随机性。书后还列出了若干阅读材料，为进一步的学习指明了方向。

Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

概率统计与我们的生活息息相关，是一门能够即学即用的学问。从骰子游戏的胜负到基本的统计处理，我们用图解说话，助你揭开“统计”迷雾，攻破“概率”难关。 　　《蜗牛科学系列》丛书从基础入手，遵循循序渐进的原则，深入浅出地解说基本的科学原理和最新的科学知识，注重学习方法与兴趣的培养。带着身边的问题走进它，不用死记定理，也不用硬背公式，不再乏味，不再费解，轻松步入神奇有趣、绚丽多姿的科学世界。本书是其中之一。 　　本书是写给觉得“我知道概率统计这个词，就是和现实事物对不上，不理解”，或常常想“我要学习概率统计，可是从哪里开始学呢”的读者。我们的目标是把概率的基本知识解释得通俗易懂，并且尽量具体说明。其中所举事例也尽量争取从我们周围的事情和日常的生活中选取。数学看起来复杂，归根究底，审一个“简单事实的积累”。概率统计也是如此。希望本书能够帮助读者理解概率统计，或者使各位读者燃起学习的兴趣。

偏微分方程是构建科学、工程学和其他领域的数学模型的主要手段。一般情况下，这些模型都需要用数值方法去求解。本书提供了标准数值技术的简明介绍。借助抛物线型、双曲线型和椭圆型方程的一些简单例子介绍了常用的有限差分方法、有限元方法、有限体方法、修正方程分析、辛积分格式、对流扩散问题、多重网格、共轭梯度法。利用极大值原理、能量法和离散傅里叶分析清晰严格地处理了稳定性问题。本书全面讨论了这些方法的性质，并附有典型的图像结果，提供了不同难度的例子和练习。 　　本书可作为数学、工程学及计算机科学专业本科教材，也可供工程技术人员和应用工作者参考。这是一本备受推崇的有关偏微分方程数值技术的教科书，被国外多家知名大学指定为教材。 　　本书讲解了求解偏微分方程的标准数值方法和技术，也提供了该领域的最新发展技术。书中透彻地分析了各种方法的性质，严格地讨论了稳定性问题，提供了各种层次的例题和习题。全书结构清晰有序，叙述言简意赅。是数学、工程学及计算机科学专业学生学习偏微分方程数值解法首选入门教材。

本书是优秀的微分几何教材，内容广泛，不但包含该领域的经典理论，同时还引人了计算机代数系统Maple的内容以及微分几何在现代生活中的实际应用。本书主要介绍了变分法，最优控制理论以及微分几何，并通过这些重要的概念帮助读者理解生活中的各种现象，例如肥皂膜的形成以及质点在曲面上的运动等，具体内容涉及常平均曲率，完整性与高斯一博内定理、极小曲面，变分法与几何等。此外，本书包含大量的练习，给出了相应的提示和解答，并提供了一系列的例子，定义以及注释。 　　本书可作为高等院校数学专业以及其他理工科专业的微分几何教材。对于专业人员而言，本书也极具参考价值。

《有限群的线性表示》是著名法国数学家、菲尔兹奖获得者JeanPierreserre的经典著作。全书分三部分。第一部分讲述有限群的线性表示的最基本的内容，主要是群表示和特征标的对应关系；第二部分对群的常表示做了进一步的阐述，如诱导表示、有理性问题等；第三部分简单讨论了群的模表示理论。《有限群的线性表示》深入浅出，对内容的处理极有特色，是学习有限群的线性表示的经典书籍。 《有限群的线性表示》根据原书第二版的英译本翻译，并根据法文修订第三版作了校订。

Algorithmic puzzles are puzzles involving well-defined procedures for solving problems. This book will provide an enjoyable and accessible introduction to algorithmic puzzles that will develop the reader's algorithmic thinking. The first part of this book is a tutorial on algorithm design strategies and analysis techniques. Algorithm design strategies - exhaustive search, backtracking, divide-and-conquer and a few others - are general approaches to designing step-by-step instructions for solving problems. Analysis techniques are methods for investigating such procedures to answer questions about the ultimate result of the procedure or how many steps are executed before the procedure stops. The discussion is an elementary level, with puzzle examples, and requires neither programming nor mathematics beyond a secondary school level. Thus, the tutorial provides a gentle and entertaining introduction to main ideas in high-level algorithmic problem solving. The second and main part of the book contains 150 puzzles, from centuries-old classics to newcomers often asked during job interviews at computing, engineering, and financial companies. The puzzles are divided into three groups by their difficulty levels. The first fifty puzzles in the Easier Puzzles section require only middle school mathematics. The sixty puzzle of average difficulty and forty harder puzzles require just high school mathematics plus a few topics such as binary numbers and simple recurrences, which are reviewed in the tutorial. All the puzzles are provided with hints, detailed solutions, and brief comments. The comments deal with the puzzle origins and design or analysis techniques used in the solution. The book should be of interest to puzzle lovers, students and teachers of algorithm courses, and persons expecting to be given puzzles during job interviews.

线性代数与解析几何，ISBN：9787302028543，作者：俞正光，李永乐，詹汉生编

Wouldn't it be great if there were a statistics book that made histograms, probability distributions, and chi square analysis more enjoyable than going to the dentist? "Head First Statistics" brings this typically dry subject to life, teaching you everything you want and need to know about statistics through engaging, interactive, and thought-provoking material, full of puzzles, stories, quizzes, visual aids, and real-world examples. Whether you're a student, a professional, or just curious about statistical analysis, "Head First's" brain-friendly formula helps you get a firm grasp of statistics so you can understand key points and actually use them. Learn to present data visually with charts and plots; discover the difference between taking the average with mean, median, and mode, and why it's important; learn how to calculate probability and expectation; and much more."Head First Statistics" is ideal for high school and college students taking statistics and satisfies the requirements for passing the College Board's Advanced Placement (AP) Statistics Exam. With this book, you'll: study the full range of topics covered in first-year statistics; tackle tough statistical concepts using Head First's dynamic, visually rich format proven to stimulate learning and help you retain knowledge; explore real-world scenarios, ranging from casino gambling to prescription drug testing, to bring statistical principles to life; discover how to measure spread, calculate odds through probability, and understand the normal, binomial, geometric, and Poisson distributions; and conduct sampling, use correlation and regression, do hypothesis testing, perform chi square analysis, and more.Before you know it, you'll not only have mastered statistics, you'll also see how they work in the real world. "Head First Statistics" will help you pass your statistics course, and give you a firm understanding of the subject so you can apply the knowledge throughout your life.

《应用随机过程》是现代应用随机过程教材，内容从初等入门到现代前沿，包括预备知识、泊松过程、离散时间马尔可夫链、离散鞅、连续时间马尔可夫链、随机微分方程与宽平稳过程等8章。《应用随机过程》可供高等院校高年级学生与研究生作为教材使用，也可供教师及工程技术人员参考。

This is the first text in a generation to re-examine the purpose of the mathematical statistics course. The book's approach interweaves traditional topics with data analysis and reflects the use of the computer with close ties to the practice of statistics. The author stresses analysis of data, examines real problems with real data, and motivates the theory. The book's descriptive statistics, graphical displays, and realistic applications stand in strong contrast to traditional texts which are set in abstract settings.

《数学超入门》是《蜗牛科学系列》丛书中的一本，本套科普读物以传播基本的科学原理和最新的科学知识为已任，它所涉及的科学领域既包括数学、微积分、概率统计、物理学、生物学、化学等学科的基本原理，也引入了生化学、遗传 学、病理学等新兴学科的最新研究成果。本套科普读物将把读者引入一个色彩斑斓、绚丽芬芳的科学世界，读者置身于其中如同在碧草蓝天的旷野中感受科学之花的芳香；又如在烟波浩森的海洋中领略知识之源的浩瀚。

《好玩的数学(普及版):幻方与素数:娱乐数学两大经典名题》分为两部分，第一部分是百变幻方——娱乐数学第一名题，对古今中外在幻方研究中的发现和成果有极为详细的介绍；第二部分是娱乐数学其他经典名题，包括数学哑谜、数学金字塔、素数、完美数、自守数、累进可除数，以及“数学黑洞”现象、重排九宫等问题。

《好玩的数学(普及版):乐在其中的数学》分10个方面，就数与形、逻辑、游戏、古今名题、概率运筹、循环回归、映射反演、文学艺术、书法建筑等，一幕又一幕地尘埃落定，展开了万花筒般的数学画卷。作者尽了很大努力，企图将世界闻名的马丁·伽德纳的趣味数学与乔治·波利亚的发现技巧熔为一炉，尽可能将所有题材中国化、本土化，用行云流水的科学小品风格来拨动读者的心弦，引起读者的共鸣。

本书重点介绍生成函数的理论和应用，生成函数是计数组合学的基本工具。本书分四章介绍了计数、筛法、偏序集以及有理生成函数，并欢未包含在正文中的许多数学领域提供了入门知识。书中所选择的材料覆盖了计数组合学中应用范围最广以及与其他数学领域联系最密切的部分。另外，书中包含大量习题，并几乎对所有习题都提供了解答，有助于教学。 　　本书是两卷集计数组合学基础导论中的第1卷，适合于研究生和数学研究人员。

《无穷的玩艺:数学的探索与旅行》是著名数学家写的数学普及读物。一部引人入胜的名著，不用任何公式。着重讨论数学的思想方法。从原始的计数开始，到达数理逻辑这一现代数学分支为止。 《无穷的玩艺:数学的探索与旅行》语言平易、浅显、自然、流畅，伴有大量生动的比喻和图形，内容循序渐进，前后呼应，趣味盎然。 数学有两种品格，其一是工具品格，其二是文化品格。……数学之文化品格、文化理念与文化素质原则之深远意义和至高的价值在于：他们当年所受到的数学训练，一直会在他们的生存方式和思维方式中潜在地起着根本性的作用，并且受用终身。

《简明数论》是初等数论入门教材。全书共分三十六节，内容包括：整除、不定方程、同余、指数与原根、连分数、数论函数等。每节配备适量习题，书末附有提示与解答。《简明数论》积累了作者数十年的教学经验，它是在作者编写的《初等数论》（北京大学出版社，1992）基础上，经过几年的教学实践，认真听取各方面意见，将精选的内容加以重新组织并作必要的修改、补充而成。使其内容更成熟，结构更合理，具有选择面宽，适用范围广等特点。 《简明数论》选材精练，推理严谨，重点突出，例题丰富，习题难易适度，对重点内容从不同侧面和不同角度进行论述，使读者能在较短时间内窥见数论的一些真髓。 读者对象为综合性大学、中、高等师范学校数学系、计算机系及其相关专业师生、教师进修学院师生、数学爱好者、中学数学教师、高中学生。

If you know how to program with Python and also know a little about probability, you’re ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical notation, and use discrete probability distributions instead of continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer, and you’ll begin to apply these techniques to real-world problems. Bayesian statistical methods are becoming more common and more important, but not many resources are available to help beginners. Based on undergraduate classes taught by author Allen Downey, this book’s computational approach helps you get a solid start. Use your existing programming skills to learn and understand Bayesian statistics Work with problems involving estimation, prediction, decision analysis, evidence, and hypothesis testing Get started with simple examples, using coins, M&Ms, Dungeons & Dragons dice, paintball, and hockey Learn computational methods for solving real-world problems, such as interpreting SAT scores, simulating kidney tumors, and modeling the human microbiome.

《数论讲义(上册)(第2版)》是根据作者多年教学经验和科研成果写成的，内容除通常的初等数论教材中所包括的基本内容外，还包括三次、四次互反律，代数数论初步，有限域上某些不定方程的基础知识，第二版中还增加了素性判别和整数分解等内容，作者在介绍熟知的经典结果时，也注意介绍新的证明方法和近代进展，并尽可能介绍它们的应用，《数论讲义(上册)(第2版)》第二版仍分上、下两册出版，上册前五章可作为初等数论课教学内容，上册第六章及下册可作为选修课教学内容，《数论讲义(上册)(第2版)》可供数学专业、计算机专业及信息安全、数字信号处理、组合数学方面的学生和研究生用作教材或参考书，也可供从事上述这些方面的教学、科研人员参考。