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Jun 10, 2013 at 13:42 comment added S. Carnahan William Stein has a book about doing number theory with SAGE.
Jun 10, 2013 at 7:26 comment added duje You may find some suitable titles on this page web.math.pmf.unizg.hr/~duje/literatura.html#PFP
Jun 9, 2013 at 16:01 comment added Gerhard Paseman Two texts that would support such study, if not quite graduate level, are Hans Riesel's book on factorization and primality testing, and Crandall and Pomerance's book focusing on prime numbers. Mastering the contents of both books puts you well on the road to such study. Gerhard "Might Remember The Titles Someday" Paseman, 2013.06.09
Jun 9, 2013 at 15:21 history edited user9072 CC BY-SA 3.0
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Jun 9, 2013 at 15:14 comment added user9072 What do you mean by "explore". Should they learn the subject seriously or just get a bit of a vague idea. For the former I strongly endorse the suggestion of Henri Cohen's book "A course in computational algebraic number theory" (while it says 'algebraic' in the title also classical primetesting algos that have not much to do with alg. numb. theory are covered). For the latter with some guidance it could also work well; but then I think one should not read it in linear order.
Jun 9, 2013 at 15:12 comment added Chris Wuthrich Definitely Henri Cohen's "A course in computational algebraic number theory" is the best place to start. At a lower level David M. Bressoud "Factorization and Primality Testing" is a nice introduction.
Jun 9, 2013 at 14:56 comment added Chandan Singh Dalawat Henri Cohen's books ?
Jun 9, 2013 at 14:55 comment added Carlo Beenakker this looks like what you'd want: amazon.com/Algorithmic-Number-Theory-Cryptography-Mathematical/… This 2008 text provides a comprehensive introduction to algorithmic number theory for beginning graduate students, written by the leading experts in the field. It includes several articles that cover the essential topics in this area, and in addition, there are contributions pointing in broader directions, including cryptography, computational class field theory, zeta functions and L-series, discrete logarithm algorithms, and quantum computing.
Jun 9, 2013 at 14:49 history asked Chebolu CC BY-SA 3.0