This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform.

The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.

Author: Frazer Jarvis
Binding Type: Paperback
Publisher: Springer
Published: 07/04/2014
Series: Springer Undergraduate Mathematics
Pages: 292
Weight: 0.96lbs
Size: 9.21h x 6.14w x 0.65d
ISBN: 9783319075440
2014 Edition


Review Citation(s):
Choice 04/01/2015 pg. 1356

About the Author
Frazer Jarvis obtained his PhD from the University of Cambridge under the supervision of Richard Taylor in 1995. After postdoctoral periods in Strasbourg, Durham and Oxford, he has been a lecturer at Sheffield since 1998. His research has focused on modular forms and Galois representations over totally real fields, and he is currently interested in GSp(4).