A Computational Introduction to Number Theory and Algebra
by Victor Shoup
Publisher: Cambridge University Press 2005
Number of pages: 534
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.
Home page url
Download or read it online for free here:
by Edward A. Bender, S. Gill Williamson - Dover Publications
This text assists undergraduates in mastering the mathematical language to address problems in the field's many applications. It consists of 4 units: counting and listing, functions, decision trees and recursion, and basic concepts of graph theory.
by Leonard Soicher, Franco Vivaldi - Queen Mary University of London
This text is a course in mathematical algorithms, intended for second year mathematics students. It introduces the algorithms for computing with integers, polynomials and vector spaces. The course requires no computing experience.
by Thomas Hales - arXiv
Computers have rapidly become so pervasive in mathematics that future generations may look back to this day as a golden dawn. The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.
by Joseph O'Rourke - Oxford University Press
Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas.