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This exploration of quadratic forms over rational numbers and rational integers offers an excellent elementary introduction to many aspects of a classical subject, including recent developments. The author, a Professor Emeritus at Trinity College, University of Cambridge, offers a largely self-contained treatment that develops most of the prerequisites.Topics include the theory of quadratic forms over local fields, forms with integral coefficients, genera and spinor genera, reduction theory for definite forms, and Gauss' composition theory. The final chapter explains how to formulate the proofs in earlier chapters independently of Dirichlet's theorems related to the existence of primes in arithmetic progressions. Specialists will particularly value the several helpful appendixes on class numbers, Siegel's formulas, Tamagawa numbers, and other topics. Each chapter concludes with many exercises and hints, plus notes that include historical remarks and references to the literature.
- Sales Rank: #5555315 in Books
- Brand: Brand: Academic Pr
- Published on: 1979-02
- Original language: English
- Binding: Hardcover
- 413 pages
- Used Book in Good Condition
About the Author
Biography of J.W.S. Cassels
J. W. S. Cassels (known to his friends by the Gaelic form "Ian" of his first name) was born of mixed English-Scottish parentage on 11 July 1922 in the picturesque cathedral city of Durham. With a first degree from Edinburgh, he commenced research in Cambridge in 1946 under L. J. Mordell, who had just succeeded G. H. Hardy in the Sadleirian Chair of Pure Mathematics. He obtained his doctorate and was elected a Fellow of Trinity College in 1949. After a year in Manchester, he returned to Cambridge and in 1967 became Sadleirian Professor. He was Head of the Department of Pure Mathematics and Mathematical Statistics from 1969 until he retired in 1984.
Cassels has contributed to several areas of number theory and written a number of other expository books:
- An introduction to diophantine approximations
- Rational quadratic forms
- Economics for mathematicians
- Local fields
- Lectures on elliptic curves
- Prolegomena to a middlebrow arithmetic of curves of genus 2 (with E. V. Flynn).
Most helpful customer reviews
8 of 8 people found the following review helpful.
A standard.
By David
The author is a master at writing and giving clear explanations. The
necessary tools needed are developed in the text which provide for
a self contained text. I recommend the book to the undergraduate
or graduate who is looking for a great read. It was a fun book to
study. The subject is beautiful.
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