
Notes on Computational Group Theory (2010) [pdf] - lainon
https://www.math.colostate.edu/~hulpke/CGT/cgtnotes.pdf
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ginnungagap
Having just finished a geometric group theory course I was hoping to see
something about the word problem for automatic groups, or 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/](https://shoup.net/ntb/)

~~~
harf
Nice! Similar recommendation: William Stein's "Algebraic Number Theory, A
Computational Approach" got me excited about studying math again. I would
recommend it to anybody reading this thread.

[https://github.com/williamstein/stein-
ant](https://github.com/williamstein/stein-ant)

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ianai
Please go easy on me, but is there a list of applications of CGT somewhere?

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ginnungagap
As far as I know CGT is mostly of interest to mathematicians, because there
are some groups whose study require calculations that are absolutely
impractical to carry out by hand, such as presentations of the sporadic
groups. Or maybe you need to know how many nonabelian groups of order 2652 are
there and throwing it to a computer is just the fastest way to find out or you
need to compute conjugacy classes or stuff like that.

Computational algebra more broadly however has many applications to
cryptography for example

