Assumes knowledge of discrete mathematics. Però il modo in cui ti insegna a trovare il risultato in somma chiusa delle sommatorie è favoloso... anche se dopo i primi capitoli bisogna togliersi dalla testa di riuscire a leggerlo e capirlo al volo.Of course I barely scraped the surface of all that this book contains. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. 【思维方法】Smart mathematicians are not ashamed to think small, because general patterns are easier to perceive when the extreme cases are well understood (even when they are trivial). cara penyampaiannya seperti ngobrol santai tapi sambil mengajarkan pola pikir kreatif ttg problem solving dengan matematika. 我在06年的时候买的这本书，买的时候并没有参考别人的书评，只是觉得这本书的标题很酷，那时才工作2年，也曾经静下心来花了几个月的时间去学习，但是发现与每天的编码工作没有太大的关系，更重要的是想读懂这本书绝对不是易事，后来就放在书架上。 时间一晃过去了3年，随着经验... Concrete Mathematics a pour objectif d'exposer les connaissances et les compétences mathématiques nécessaires en informatique (théorique), et plus particulièrement celles permettant l'analyse de l'efficacité des algorithmes. 42.10元 I am not sure about Patashnik, but Ronald Graham and Donald Knuth are power houses of mathematics (and CS), which shows in this book. 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. Still, it is amazing what the authors manage to convey in such a leisurely way. It also forms a foundation to understand Donald Knuth's epic exploration of algorithms, the seven-books series on the "Art of Computer Programming". 6 "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." I am not sure about Patashnik, but Ronald Graham and Donald Knuth are power houses of mathematics (and CS), which shows in this book. 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. I haven't read the whole thing, but have read a number of the sections that were of particular interest to me (especially the chapter on generating functions). 把上面L(n)展开（注意，和第一节用到的方法不同），最后得到L(0)+S(n)，L(0)当然等于1，S(n)就是高斯同学的等差数列求和。 It's every bit as fun and whimsical as the class was, but it is by no means any sort of satire or spoof - this book is very deep, and covers a vast array of problems and methodologies.I'm still working my way through this book -- it's supposed to be a precursor to the Art of Computer Programming, to give you the math foundation you need. If you enjoy that class of reading and you are a computer scientist, software engineer, or either with a serious dedication to your craft, pick it up.
This is good if you can manage to fill the details yourself, but I had to give up at times. 汉诺塔问题的解答，关系宇宙的生灭，不可不谨慎啊：） 所以，《Concrete Mathematics》开宗明义，第一节就讲汉诺塔问题，是非常正确的。另外，九连环是中国的汉诺塔，同样是一种递归玩具，其实并没用什么训练智力的作用，熟悉之后就是机械的重复。 把上...1.1 The Tower of Hanoi 不知道汉诺塔的人是有罪的，愿大梵天宽恕你们。 汉诺塔问题的解答，关系宇宙的生灭，不可不谨慎啊：） 所以，《Concrete Mathematics》开宗明义，第一节就讲汉诺塔问题，是非常正确的。另外，九连环是中国的汉诺塔，同样是一种递归玩具，其实并没用什么训练智力的作用，熟悉之后就是机械的重复。 【思维方法】Smart mathematicians are not ashamed to think small, because general patterns are easie...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.1.2 Lines in the Plane 我们小时候几乎都遇到过这样的问题：一个西瓜切3刀，最多能切成几块？书里用的例子是Pizza. 13 见缝插针，随即又讨论了什么是closed forms：An expression for a quantity f(n) is in closed form if we can compute it using at most a fixed number of “well known” standard operations, independent of n.
Don’t you just hate that feeling of falling head over heels for a new series...and then having to wait anxiously (sometimes for years!)
Des milliers de livres avec la livraison chez vous en 1 jour ou en magasin avec -5% de réduction . "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems. La préface précise que les sujets abordés « combinent des mathématiques CONtinues et disCRÈTES. 30位读者评价了这条书评，30位认为有价值 [5星评价] 我最喜爱的数学书，毫无疑问 2011.05.16 作者：A Studious Student（一位勤奋好学的学生） 原文：http://www.amazon.com/review/R29RP5TLX8P90K 这是迄今为止我最喜爱的数学书。我在普特南(Putnam)数学竞赛预备课程... 不知道汉诺塔的人是有罪的，愿大梵天宽恕你们。 Start by marking “Concrete Mathematics: A Foundation for Computer Science” as Want to Read: 1
言下之意，人应该比电脑要聪明，算法是人发明的，不是计算机。 It also forms a foundation to understand Donald Knuth's epic exploration of algorithms, the seven-books series on the "Art of Computer Programming".
Concrete Mathematics is an amazing book, but it assumes you already know the basics that would be taught in a 1-semester course on the subject.
Otherwise, mathematical annotations coupled with side annotations are exceedingly useful. 37 【思维方法】平面上已经有n-1条直线，最多把平面分成L(n-1)个区域，如果这n-1条直线互相都不平行，且没有三条直线共点；则第n条直线最多可以和前面的n-1条直线每条都相交（同样没有三条直线共点），可以增加n-1个交点，每增加一个交点就会增加一个区域，但第一个交点会增加2个区域，所以，L(n)=L(n-1)+n. Welcome back. 3 Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics.
2 但对于什么是“well known” standard operations，作者又说道When such recurrences turn out to be important, because they arise repeatedly, we add new operations to our repertoire; this can greatly extend the range of problems solvable in “simple” closed form.
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