Serre's A Course in Arithmetic is a concentrated, modern introduction to basically three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms. The first edition was very well accepted and is now one of the leading introductory texts on the advanced undergraduate or beginning graduate level.
From the reviews: .,." The book is carefully written - in particular very much self-contained. As was the intention of the author, it is easily accessible to graduate or even undergraduate students, yet even the advanced mathematician will enjoy reading it. The last chapter, more difficult for the beginner, is an introduction to contemporary problems." "American Scientist"
"The book is a showcase of how some results in classical number theory (the Arithmetic of the title) can be derived quickly using abstract algebra. ... There are a reasonable number of worked examples, and they are very well-chosen. ... this book will expand your horizons, but you should already have a good knowledge of algebra and of classical number theory before you begin." (Allen Stenger, MAA Reviews, maa.org, July, 2016)
|Algebraic Methods: Finite fields|
|Quadratic forms over Qp, and over Q|
|Integral quadratic forms with discriminant -1|
|Analytic Methods: The theorem on arithmetic progressions|
|Table of Contents provided by Publisher. All Rights Reserved.|
Series: Graduate Texts in Mathematics
Tertiary; University or College
Number Of Pages: 119
Published: 7th November 1996
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5
Weight (kg): 0.34
Edition Number: 5