This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories.Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: *Sums *Recurrences *Integer functions *Elementary number theory *Binomial coefficients *Generating functions *Discrete probability *Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them. 0201558025B04062001
- 融合连续与离散数学，为算法分析提供坚实基础。
- 教授求和、递归等技巧，培养解决复杂问题的能力。
- 风格幽默睿智，被誉为计算机科学的数学基石。
- 计算机科学专业学生，尤其是准备阅读TAOCP者。
- 从事算法设计与分析，需提升数学功底的研究者。
- 对数学之美感兴趣，喜欢挑战思维深度的读者。
- 务必动手做习题，否则等于白看，需极大耐心。
- 建议先阅读TAOCP前几章，作为前置知识准备。
- 不必追求速成，享受推导过程，体会数学优雅。
- 必读经典，所有CS学生都应阅读，提升思维深度。
- 内容虽难但有趣，排版精美，被赞为数学艺术品。
- 自学难度较大，需配合习题训练，不可浅尝辄止。
本导读基于书籍简介、目录、原文摘录、短评和书评生成，不等同于全文精读。
- "By the way, there's a mnemonic for remembering which case uses floors and which uses ceilings: Half-open intervals that include the left endpoint but not the right (such as 0 ≤ θ < 1) are slightly more common than those that include the right endpoint but not the left; and floors are slightly more c"
- "通过证明我们可以爬到提子的最底一级（基础），并能从一个阶梯爬到上一个阶梯（递归），数学归纳法就证明了：我们可以在一架梯子上想爬多高就爬多高。"
- "When we transform an art into a science, we aim to replace inspiration by perspiration."
- ""There are two kinds of generalizations. One is cheap and the other is valuable. It is easy to generalize by diluting a little idea with a big terminology. It is much more difficult to prepare a refined and condensed extract from several good ingredients." --G. Polya"
- "What is a proof? "One half of one percent pure alcohol.""
- "So we think the book has turned out to be a tale of mathematical beauty and surprise, and we hope that our readers will share at least ε of the pleasure we had while writing it."
- "Algebraically, if we have a double sum whose terms involve k + f(j), where f is an arbitrary function, it's a good idea to tray replacing k by k - f(j) and summing on j."
- "P2 In fact, we'll see repeatedly in this book that it's advantageous to look at small cases first. The next step in solving the problem is to introduce appropriate notation: name and conquer. Smart mathematicians are not ashamed to think small, because general patterns are easier to perceive when th"
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