Review2 of A Computational Introduction to Number Theory and Algebra by Victor Shoup Cambridge University Press, 2005, 534 pp., $55.00 Reviewed by Jonathan Katz Dept. of Computer Science, University of Maryland Increasingly, number theory and algebra have become useful tools for the well-rounded computer scientist. Historically, of course, number theory and algebra have been indispensable for cryptography, and nite elds (and, to a more limited extent, other algebraic structures) have been widely used in coding theory. More recently, though, these topics have begun to permeate other areas of theoretical computer science: nite elds and errorcorrecting codes are now pervasive in complexity theory; quantum computing relies heavily on abstract algebra (especially linear algebra) and coding theory; and, somewhat surprisingly, there have been recent explicit constructions of combinatorial objects such as extractors which rely on deep results from number theory. While there are numerous textbooks covering number theory, abstract algebra, and/or the basics of nite elds, there have not been many introductory-level books to approach the subject matter from a computer science perspective. A typical algebra textbook, for example, is more interested in proving that a certain function is well-de ned or that a certain algebraic structure exists than
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Review of A Computational Introduction to Number Theory and Algebra by Victor Shoup, Cambridge University Press, 2005
Katz, Jonathan
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, Volume 37 (1)
Association for Computing Machinery – Mar 1, 2006
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