A Computational Introduction to Number Theory and Algebra
by Victor Shoup · first published 2005
4mentions
4recommended by
4HN commenters
2015–2020first – last mentioned
100% recommend
Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus is presumed, other than some experience in doing proofs - everything else is developed from scratch. Thus the book can serve sev
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…rewarding. I can't do many of them, but reading the problem statements is usually enough to make me realize I don't understand something. When I started learning crypto, I spent a lot of time reading A Computational Introduction to Number Theory and Algebra [1] another free, high-quality book by Shoup. I did a lot of exercises, even corrected some results in the book, and at one point thought that I wanted to publish a solution manual. I emailed professor…
on “A Graduate Course in Applied Cryptography” ↗…neither Rotman nor Birkhoff/MacLane are ideal places to start learning algebra. There are plenty of gentler, more modern books. In terms of tomes that are available online, I can recommend Shoup's "A Computational Introduction to Number Theory and Algebra" [1]. As an aside, note that category theory is used only in the part of programming language research that is about (pure) functional programming. In other sub-fields (e.g. OO, logic programming and…
on “A Path to Enlightenment in Programming Language Theory” ↗Perhaps "A Computational Introduction to Number Theory and Algebra" by Victor Shoup? This was recommended by Dan Boneh in his crypto course.
on “The Periodic Table of Data Structures [pdf]” ↗…at least an algorithm to compute Dehn presentations of f.g. hyperbolic groups, but it looks like a cool resource with plenty of interesting topics. Another book the HN crowd might like is Shoup's "a computational introduction to number theory and algebra"[0], it is much more broad and with litte focus on implementations, but a very interesting book nonetheless [0]https://shoup.net/ntb/
on “Notes on Computational Group Theory (2010) [pdf]” ↗