Overview
- Explores the multi-faceted nature of number theory, spanning several areas of research in one text
- Begins at undergraduate level and takes the reader through to graduate level
- Includes recent proofs, such as the polynomial primality algorithm
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (6 chapters)
Reviews
From the reviews:
“It gives an overview of various parts of number theory which should be studied after its basics have been mastered. … This book is extremely well written and a pleasure to read. It is well suited to whet a curious student’s appetite and to induce him or her to embark on an in-depth study of number theory.” (Ch. Baxa, Monatshefte für Mathematik, 2014)
“This is a detailed presentation of modern number theory, complete with overviews of current research problems. … Hindry (Univ. Paris 7, France) includes the standard topics in undergraduate number theory courses … . Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (J. Johnson, Choice, Vol. 49 (6), February, 2012)
“Geared toward graduate students at the masters level (M1 and M2), the book provides a thorough and lively introduction to various fundamental aspects of both classical and contemporary arithmetical theories, together with some of their most important applications and current research developments. … the book under review is both an excellent introduction and a truly irresistible invitation to number theory in its various fascinating aspects. … Its current translation into English will certainly augment both the worldwide popularity and usefulness of this remarkable textbook.” (Werner Kleinert, Zentralblatt MATH, Vol. 1233, 2012)
“This is a very modern text for a second course in number theory, slanted towards algebraic number theory and Diophantine equations, and using the language and concepts of abstract algebra throughout. … The book attempts, usually successfully, to cover not only modern methods but the most recent results as well. … The exercises are especially good, and supplement the exposition with a number of important results.” (Allen Stenger, The Mathematical Association of America, October, 2011)
Authors and Affiliations
Bibliographic Information
Book Title: Arithmetics
Authors: Marc Hindry
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4471-2131-2
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London Limited 2011
Softcover ISBN: 978-1-4471-2130-5Published: 05 August 2011
eBook ISBN: 978-1-4471-2131-2Published: 05 August 2011
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XVIII, 322
Number of Illustrations: 5 b/w illustrations
Additional Information: Translation from the French language edition: ‘Arithmétique’ by Marc Hindry Copyright © 2008 Calvage et Mounet, France
Topics: Number Theory, Algebra, Algebraic Geometry, Field Theory and Polynomials, Algorithms