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LMSST: 24 Lectures on Elliptic Curves (London Mathematical Society Student Texts), by J. W. S. Cassels
Free Ebook LMSST: 24 Lectures on Elliptic Curves (London Mathematical Society Student Texts), by J. W. S. Cassels
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The study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. This book, addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Wei finite basis theorem, points of finite order (Nagell-Lutz), etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the "Riemann hypothesis for function fields") and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch. Many examples and exercises are included for the reader, and those new to elliptic curves, whether they are graduate students or specialists from other fields, will find this a valuable introduction.
- Sales Rank: #16400283 in Books
- Published on: 1991-11-29
- Original language: English
- Dimensions: 9.33" h x .51" w x 6.18" l, .74 pounds
- Binding: Hardcover
- 143 pages
Review
'... an excellent introduction ... written with humour.' Monatshefte für Mathematik
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).
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