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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:
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.
Donald E. Knuth is known throughout the world for his pioneering work on algorithms and programming techniques, for his invention of the Tex and Metafont systems for computer typesetting, and for his prolific and influential writing. Professor Emeritus of The Art of Computer Programming at Stanford University, he currently devotes full time to the completion of these fascicles and the seven volumes to which they belong.
This may sound like a lot, but trust me when I say you will know all the tricks of the trade when you're finished.
It is a book on hard math, done in a concise manner by brilliant teachers who assume students are very comfortable with calculus, probability, etc.
I read this book as my introduction to computer science and discrete mathematics in my re-education as a physicist to a computer scientist.
I originally bought this book as a source of remedial study following the end of my US state school CS undergrad experience (I completed a BS Computer Science in 2013, > 3. Read morePublished 6 months ago by Unbroken
Perhaps I had it coming, but this book really means concrete, as in "not abstract", by "concrete". Read morePublished 6 months ago by Darius Jahandarie
I've read a lot of math books: I majored in math in college, got a PhD in CS (in cryptography, specifically) and I love doing math recreationally. Read morePublished 10 months ago by JJ
This is a wonderful and desk reference, proving holistic coverage of all the math-oriented themes in CS study and practice. Read morePublished 12 months ago by CHAD D WOOD
I was lucky enough to find this book for a dollar. It became very quickly one of my 5 favorite math books (out of 100 or so. Read morePublished 18 months ago by S.Z.
It simply teaches you how to think in a simple way without complex unproven theorems. I really recommend this book.Published 21 months ago by M. Majid Khonji
This is exactly what I was looking for. This book is really challenging and provides the reader all the tools he will need to enjoy learning the topics presented.Published 22 months ago by mauricio
I read this book as my introduction to computer science and discrete mathematics in my re-education as a physicist to a computer scientist. It was invaluable. Read morePublished on April 5, 2012 by Malik Magdon-Ismail
This book isn't about mathematical thinking per se, but it's one of the books I read early on in my studies that really helped me with my mathematical thinking and notation. Read morePublished on January 18, 2012 by Upunder