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 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 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 Jean Gallier - Morgan Kaufmann
This book offers both a theoretically unifying understanding of polynomial curves and surfaces and an effective approach to implementation that you can bring to bear on your own work -- whether you are a graduate student, scientist, or practitioner.
by T. Nipkow, L.C. Paulson, M. Wenzel - Springer
This book is a self-contained introduction to interactive proof in higher-order logic, using the proof assistant Isabelle. It is a tutorial for potential users. The book has three parts: Elementary Techniques; Logic and Sets; Advanced Material.