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[Timeline]


This question has the same spirit of what papers should everyone read and what videos should everybody watch. It asks for remarkable books in different areas of theoretical computer science.

The books can be math-oriented, yet you may find it great for a computer scientist. Examples:

  • Probability
  • Inequalities
  • Logic
  • Graph Theory
  • Combinatorics
  • Design & Analysis of Algorithm
  • Theory of Computation / Computational Complexity Theory

Please devote each answer to books of the same subject (e.g. books on combinatorics).

Note: The title might be misleading. Here's a clarification: Let X and Y be two fields in computer science. There are books that everyone

  • in field X should read.
  • in field Y should read.
  • in both fields should read.

This question seeks all 3 cases. In other words, it is NOT specific to the latter case.

Edit: As suggested by Dai Le, please highlight the reason(s) you like the book as well.


Related topics:

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  • $\begingroup$ Since I can't answer to the question I'll do it here. Discrete Mathematics - TTC: Discrete Mathematics by Arthur T. Benjamin. It's a lectures bundle on various topics from Set Theory to Graphs and Probability. $\endgroup$ – Pithikos Sep 12 '14 at 13:31
  • $\begingroup$ It may be interesting to compare this list of remarkable books with the list of introductory book from the Is there a list of the canonical introductory textbooks covering the major branches of computer science? question on reddit/compsci. There is some overlap, but luckily the differences are sufficiently significant. $\endgroup$ – Thomas Klimpel Jun 8 '17 at 9:59

37 Answers 37

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Fundamental Algorithms in Algorithmic Algebra by Chee Yap (available online here).

This text covers (fast) integer multiplication, polynomial root finding, integer polynomial factorization, lattice reduction techniques (specifically LLL), elimination theory, Grobner bases and continued fractions, all from an algorithmic perspective. I found this text indispensable when learning about lattice reduction.

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6
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I've got to answer this question, even though it already has 30+ answers.

Out of Their Minds really is a must read for all computer scientists or people with a general interest in computer science. It introduces the reader to the life and work of 15 very important computer scientists, 8 of whom have won a Turing Award. I had read this book after it was recommended in my first university computer science course (almost two years ago now) and have since then skimmed through it again for 2 times. It is just brilliant.

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Writing Mathematics

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4
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Coloring Problems

The best book on the subject is The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of its Creators by Soifer et al.

There is also another book Graph Coloring Problems, by Tommy R. Jensen and Bjarne Toft.

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3
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Algebraic Geometry

Algebraic Geometry by Robin Hartshorne.

The book is, for me, challenging but covers a broad area of the field of algebraic geometry. I found this a good addition to the next book when learning about ellipc curve cryptography.

Elliptic curves

The Arithmetic of Elliptic Curves by Joseph H. Silverman.

The book is a good introduction into mathematics of elliptic as well as a suitable source for an extended insight of elliptic curve cryptography. Also it reads very well.

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  • 1
    $\begingroup$ Hartshorne a book "everyone" should read? That's a surprising recommendation in a computer-science context. $\endgroup$ – Martin Berger Jul 18 '15 at 15:54
  • $\begingroup$ According to the quesetion: ''The books can be math-oriented. [...] There are books that everyone in field X should read.'' So not all of the book might be interesting for people in the field ''elliptic curves'', but at least some of it. $\endgroup$ – Fleeep Jul 23 '15 at 13:15
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    $\begingroup$ I think Martin's point was not that the content of Hartshorne might not be suitable here, but that Hartshorne is notorious as an introductory book, which one might imagine is especially so for people outside of algebraic geometry (which includes most computer scientists)... $\endgroup$ – Joshua Grochow Feb 5 '16 at 18:39
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A new addition to the list is a book "Foundations of Data Science" by Blum, Hopcroft and Kannan: https://www.cs.cornell.edu/jeh/book.pdf

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Theory of Computation, Logic ( and also Music and Art )

When I was a young student I found this book really exciting. Maybe it is not so usefull in technical sense, but it's a good and funny way to understand hard concepts from Logic and Theory in general.

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protected by Kaveh May 10 '13 at 6:52

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