Authors:
Presents the historical background of various topics in number theory;
Provides a self-contained introduction to classical number theory;
Includes step-by-step proofs of theorems and solutions to exercises;
Designed for undergraduate students, particularly those who would like to prepare for mathematical competitions.
Includes supplementary material: sn.pub/extras
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (12 chapters)
-
Front Matter
-
Back Matter
About this book
The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).
Reviews
From the reviews:
"Opening at random any page of this delightful book, the reader will almost certainly find something intriguing and interesting on the page. The book is an excellent "training manual'' to use in preparation for (the number theoretic portions of) mathematical competitions and olympiads. The dedicated problem-solver would do well to avoid too early reference to the "Solutions'' chapter. At the proper time, however, carefully studying this chapter is as rewarding as the earlier part of the book. This is a book that belongs in all academic libraries—from high school through graduate level."
— F. J. Papp, Mathematical Reviews
“The book under review is not the only book which focuses on olympiad problems in number theory, but because of its structure (containing topics and problems), it is also useful for teaching. I highly recommend this book for students and teachers of MOs.”
—Mehdi Hassani, MAA Reviews
"[This book] appears like a confession of a young mathematician to students of his age, revealing to them some of his preferred topics in number theory based on solutions of particular problems... Michael does not limit himself to those particular problems. He also deals with topics in classical number theory and provided extensive proofs of the results...It offers pleasant reading for young people who are interested in mathematics. They will be guided to easy comprehension of some of the jewels of number theory."
—Preda Mihăilescu, EMS Newsletter March 2011
“The present book provides a wonderful presentation of concepts and ideas as well as problems with their solutions in Number Theory. Although most of the problems solved in this book were given in international mathematical contests and hence are of high level of complexity, the author has succeeded in providing solutions and extensive step-by-step proofs in a rigorous yet very simple and fascinating way. Even though the author is a very young mathematician (of only 23 years), he is an outstanding specialist in this field."
—Dorin Andrica, Zentralblatt MATH
“Containing all of the things he suggests one should know to compete successfully in an IMO competition. The book is based on his undergraduate thesis on computational number theory … . it is so much more than basic things one should know, providing a rich overview of the many beautiful ideas in number theory. … Plus, the text is enriched with historical comments, special problem-solving techniques, and a wealth of problems to investigate. … Summing Up: Recommended. Academic readership, all levels.”
—Johnson, Choice, Vol. 49 (4), December, 2011
Authors and Affiliations
-
, Department of Pure Mathematics and Mathe, University of Cambridge, Cambridge, United Kingdom
Michael Th. Rassias
About the author
Bibliographic Information
Book Title: Problem-Solving and Selected Topics in Number Theory
Book Subtitle: In the Spirit of the Mathematical Olympiads
Authors: Michael Th. Rassias
DOI: https://doi.org/10.1007/978-1-4419-0495-9
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Hardcover ISBN: 978-1-4419-0494-2Published: 02 December 2010
Softcover ISBN: 978-1-4899-8194-3Published: 02 September 2014
eBook ISBN: 978-1-4419-0495-9Published: 16 November 2010
Edition Number: 1
Number of Pages: XIV, 324
Topics: Number Theory