Concrete Mathematics

Name: Concrete Mathematics
Availability: InStock
Rating: 9.8 (149 reviews)
ISBN: 9780201558029

Ronald L. Graham

出版社

Addison-Wesley Professional

出版时间

1994-03-10

ISBN

9780201558029

评分

★★★★★

标签

计算机科学与技术数学算法

书籍介绍

这不是一本用来'学数学'的书，而是一套教人如何'玩弄公式'的工具箱。读者反复提到的，是它把离散与连续揉捏在一起的能力：爬梯子式的数学归纳法、'一半百分之一纯酒精'式的证明观、以及'把艺术变成科学就是以汗水替代灵感'的执拗。它不追求严谨到无菌，反而坦承'正确规则往往与直觉相反'，让读者在 Murphy's Law 式的反转里体会发现的惊喜。多位读者强调'不做习题等于白看'，因为它教的是受控地操纵公式、算出骇人的求和、从数据里嗅出隐秘模式——一种近乎魔术的'能工巧匠'手艺。适合愿意花时间和耐心、把解题当乐趣的人；若只求速成或想要无菌教科书，它未必合意。

AI导读

核心看点

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。

读者共识

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。

精彩摘录

"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"