Concrete Mathematics: A Foundation for Computer Science

by Ronald Graham, Donald Knuth, Oren Patashnik

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."

Genres: Mathematics, Computer Science, Programming, Science, Nonfiction, Technology, Computers

672 pages, Hardcover

First published January 1, 1988

Reviews

[Kevin K. Gillette]

I had the great fortune to take this course at Stanford from Ron Graham, with Oren Patashnik as my TA, and we used Don Knuth's "Art Of Computer Programming: Vol. 1 - Fundamental Algorithms" as our textbook. All of the course notes and problem set solutions were written up using TEX. It didn't get any better than that! When I saw that this book had been released, I rushed to my nearest technical bookstore to buy it. 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.

If you've ever wondered what sort of mathematics course could actually inspire someone to continue learning mathematics, check this book out! And if you're *really* lucky, try attending a course, colloquium, seminar, or conference session with any of these three gentlemen presenting - you'll be glad you did!

[Thore Husfeldt]

Incredibly well written, utterly idiosyncratic, and remarkably useless. Somewhere between masterpiece and complete failure. I love every comma of it.

[Jigar Brahmbhatt]

A wonderful, wonderful exploration of a mathematical system that according to its authors is a blend of "continuous and discreet mathematics". It also forms a foundation to understand Donald Knuth's epic exploration of algorithms, the seven-books series on the "Art of Computer Programming". Like with all the books by Knuth, if the reader is able to find an error which is "technically, historically, typographically, or politically incorrect", he/she will be rewarded with 2.56 US dollars, which according to Knuth is "one hexadecimal dollar"! Such playful rigor is found throughout this book, which explains number theory, recursion, discrete probability et al with elan. It is also one of the few books from my Engineering days that I will cherish and keep returning to, just for the infotainment it provides.

[Joshua]

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. The explanations are clear and the exercises are great.

[Mcbear Holden]

Great book, this really helps clarify the problems we see in algorithms.

There's a great youtube class that basically use this book as reference.
https://www.youtube.com/playlist?list...

Instructor: Shai Simonson

[shishir]

This is an odd maths book. All chapters are interesting, explored in depth and the problem set is challanging. A big chunk of content (explanations and unsolved problems) were beyond my reach. My favourite chapters are recurrences, binomial coefficients and generating functions. I keep coming back to re-read them. This book is for anyone who is interested in maths puzzles. It can help in building necessary tools for problem solving.

[Nick Black]

The best overall set of discrete exercises I've ever seen, well worth the price of admission alone.

[Joe Cole]

I really recommend this book. It simply teaches you how to think in a simple way without complex unproven theorems. This book is really challenging and provides the reader all the tools he will need to enjoy learning the topics presented.

[Ayush Bhat]

A Concrete Math book from the God Himself.

[Szymon Różański]

Jako chemik, książka ta była dla mnie trudna, i mimo jej czytania na bieżąco, nie poradziłem sobie z matematyką dyskretną.
Jednakże nie poddaję się i podejrzewam że w przyszłości, razem z większym zrozumieniem, odkryję piękno tej książki

[Jeff]

Very good book. 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). It's worth noting that this is a challenging book and if you haven't had some exposure to mathematics before and developed some degree of mathematical maturity you'll likely find this book too hard and trying to work through it discouraging. I first took a look at it in high school, couldn't make much progress, and put it down. It wasn't until my junior year of college that I started to get much out of it.

[Avinash K]

Really good! Well written. But really, a very good text book. If you don't want to solve the exercises (at least 40% what is called the Warm Ups and The Basics) you are better of with a book meant for popular reading. If you would like to solve the exercises, then here's to many a rainy Sunday afternoons!

[Gary]

Of course I barely scraped the surface of all that this book contains. I did find an error and wrote to the authors and received a reply from Knuth and Ron Graham, but didn't get a cheque for $2.56 as they already knew about it.

[Paul Floyd]

The first three chapters were OK, but by the time I got to hypergeometric generating functions I was feeling a bit out of my depth. The last couple of chapters on probability and asymptotics were a bit easier to follow.

[David]

Insanely fun and challenging, a great Friday night hobby.

[Colin Lamont]

Pretty mindbending to see the discrete analogs of calculus, "integrating" finite difference operators, moving between regular powers and "factorial" powers with Stirling numbers, "finite differentiating" polynomials. Then there's the fact that hypergeometric functions can be fun and useful. With Riordan's Introduction to Combinatorics this book makes you feel like there is a much bigger mathematical world out there, sonny boy, that lives and breaths and solves real problems.

Herman Weyl said something like: Geometry is the Angel and Algebra is the Devil and they war for the soul of every mathematician. This book had me lost forever to the dark gods of formal notational development and the unholy algebraic machine.

[Amir Keyvani]

ریاضیات را در روش تقسیم بندی دوگانه یا پیوسته و یا گسسته می‌دانند ولی در این کتاب ترکیب روشهای دو نوع پیوسته و گسسته بگونه ای یاری رسان بهمدیگر،طوری که مبحثی در شناسایی ذات ریاضیات می‌گشاید مطرح می‌شود.اینکه هر جا مطلب به ذات و باطن یک علم مربوط باشد پای گفتگو باز می‌شود در اینجا هم با ارائه حاشیه نویسیها بر کتاب جلوه کرده است. نویسندگان دانشمند کتاب مثل هر کتاب سطح بالای دیگر جای تحقیق بر روی مسائل نو و قدیمی را با مطرح نمودن آنها برای خواننده باز گذاشته اند،واقعا جذبه کتاب برای خواننده طوری است که محو نگاه به آن میشوید.با کیفیت و عالی🤑

[Ram Bharadwaj]

the title is somewhat misleading , you don't need to learn all these concepts in this to master algorithm analysis , the only thing i liked in this book is the "research problems" section just like in other knuth's books , and the graffiti. wont recommend this unless you are on a mission to read TAOCP

[Ijal]

Quality book, but the introduction was somewhat vague. Otherwise, mathematical annotations coupled with side annotations are exceedingly useful. Could make content a bit more presentable though.

[Manoj Khatri]

Hands down best for computer science. Great exercises. Loved the side notes.

[Thom]

One of the most entertaining and well put together textbooks I have read. Highly recommend for computer scientists, mathematicians and anyone else with mathematically curiosity.

[amvxn1]

Lowkey helpful dawg

[Emil Petersen]

I read the first couple hundred pages in detail, and the remaining less so. Some of it I already knew, so I felt confident that I could skim it, but most of all, a lot of the content was out of my reach without putting a lot of time into it. Still, it is amazing what the authors manage to convey in such a leisurely way. I am not sure about Patashnik, but Ronald Graham and Donald Knuth are power houses of mathematics (and CS), which shows in this book. Their command of the content is incredible. That being said, being a mere mortal, it took me a lot of work to verify some of the skipped details in the proofs. This is good if you can manage to fill the details yourself, but I had to give up at times. Also, some of the stuff seems less essential to computer science now as it might have been when the book was written. I have maybe seen generating functions mentioned explicitly once or twice in my studies, but that is it. Nor Catalan numbers, or other sequences mentioned in CM. This is however not that big of a deal, as the method of analysis and the reasoning is what makes this book great. So do not worry if you are never going to use the stuff; if you could understand it, then you are well set to master any concept more frequently used in CS.

Also, there are tons of exercises, most of which I did not do (my loss). As with most text books, the exercises are where you can really master the content, and CM gives you A LOT of potential mastering to do. I found them difficult, however. Even some of the warm-ups. There are solutions in the back.

[Peb]

buku yang menyenangkan, terutama bwt gw yang rada alergi sama matematik. cara penyampaiannya seperti ngobrol santai tapi sambil mengajarkan pola pikir kreatif ttg problem solving dengan matematika. buku pertama yang bikin gw ketawa sambil baca buku teks.. :D

learning math would never be this fun..

[Colby-Tait Africa]

I read it because Knuth's name was on it and I wasn't disappointed. It's dense, it's hard thinking, it's studying. 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. If you are lazy, forget about it. You might as well read the Wiki articles on the subject.

[Maurizio Codogno]

È un libro di testo, per quanto possa esserlo un libro in cui DEK è uno degli autori. 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.

[Bishu]

Reading it as a reference. Very well written. I mean, Donald Knuth is by far the most amazing computer scientist in my mind so considering I am such a huge fanboi of his work, I HAD to read this to refresh my math. Awesome stuff.

[Tomasz]

Good source of condensed knowledge on topic. While the book feels quite heavy (both physically and experience-wise), I refuse to believe this material could have been presented in a more accessible way.

[Volodymyr]

This great classical book gives very strong mathematical foundation for computer programming and algorithms, showing how to solve complex problems in a mathematical way

[Rodrigo Rivera]

One of the best CS math books available. 20 years later it is still current. A must for any CS student.