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.
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by S. Basu, R. Pollack, M. Roy - Springer
The monograph gives a detailed exposition of the algorithmic real algebraic geometry. It is well written and will be useful both for beginners and for advanced readers, who work in real algebraic geometry or apply its methods in other fields.
by Justin Solomon - CRC Press
Using examples from a broad base of computational tasks, including data processing and computational photography, the book introduces numerical modeling and algorithmic design from a practical standpoint and provides insight into theoretical tools.
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.
by Cameron Davidson-Pilon - GitHub, Inc.
This book is designed as an introduction to Bayesian inference from a computational understanding-first, and mathematics-second, point of view. The book assumes no prior knowledge of Bayesian inference nor probabilistic programming.