Links
Books, LectureS
Book, Algorithmic Number Theory (Lattices, Number Fields, Curves and Cryptography), Edited by Joseph P. Buhler and Peter Stevenhagen.
Book, Modern Computer Algebra, von zur Gathen & Gerhard.
Book, Algorithmic Number Theory, Bach & Shallit.
Book, Finite Fields, Lidl & Niederreiter.
Course, Algebra and Computation, Madhu Sudan.
Course, Computational Number Theory and Algebra, Manindra Agrawal.
Online Stuff
Computational number theory, algebra.
Open problems, Adleman & McCurley.
History: Algebra.
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``Nowadays we can do computer experiments using Mathematica, and even solve a system of 42 equations. This offers another route to knowledge, rather than mere ideas.''
-- John F. Nash, Jr. (ICM 2002 public lecture).