{"title":"J W S Cassels","description":"\u003cp\u003eDelve into the mathematical mind of J.W.S. Cassels. Explore his contributions to number theory and geometry, where precision meets profound insight. A must for enthusiasts of pure mathematics.\u003c\/p\u003e","products":[{"product_id":"lmsst-24-lectures-on-elliptic-curves-book-j-w-s-cassels-9780521425308","title":"LMSST: 24 Lectures on Elliptic Curves","description":"The study of (special cases of) elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centres of research in number theory. This book, which is 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-Weil 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, as is the little that is needed on Galois cohomology. Many examples and exercises are included for the reader. For those new to elliptic curves, whether they are graduate students or specialists from other fields, this will be a fine introductory text.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50114627567889,"sku":"GOR008255541","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":50400141148433,"sku":"CIN0521425301G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52146999918865,"sku":"NLS9780521425308","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52735410209041,"sku":"NIN9780521425308","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0521425301.jpg?v=1751135110"},{"product_id":"rational-quadratic-forms-book-j-w-s-cassels-9780486466705","title":"Rational Quadratic Forms","description":"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.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51002899005713,"sku":"NIN9780486466705","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ GOOD \/ SBYB","offer_id":51141229248785,"sku":"CIN0486466701G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0486466701.jpg?v=1750814871"},{"product_id":"algebraic-number-theory-book-j-w-s-cassels-9780950273426","title":"Algebraic Number Theory","description":"First printed in 1967, this book has been essential reading for aspiring algebraic number theorists for more than forty years. It contains the lecture notes from an instructional conference held in Brighton in 1965, which was a milestone event that introduced class field theory as a standard tool of mathematics. There are landmark contributions from Serre and Tate. The book is a standard text for taught courses in algebraic number theory. This Second Edition includes a valuable list of errata compiled by mathematicians who have read and used the text over the years.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51009638170897,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51009641840913,"sku":"NIN9780950273426","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52591752085777,"sku":"NLS9780950273426","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0950273422.jpg?v=1750916228"},{"product_id":"introduction-to-the-geometry-of-numbers-book-j-w-s-cassels-9781015319660","title":"An Introduction to the Geometry of Numbers","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51013138252049,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51013140971793,"sku":"NIN9781015319660","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1015319661.jpg?v=1751141724"},{"product_id":"diophant-approx-book-j-w-s-cassels-9780521045872","title":"Diophant Approx","description":"This tract sets out to give some idea of the basic techniques and of some of the most striking results of Diophantine approximation. A selection of theorems with complete proofs are presented, and Cassels also provides a precise introduction to each chapter, and appendices detailing what is needed from the geometry of numbers and linear algebra. Some chapters require knowledge of elements of Lebesgue theory and algebraic number theory. This is a valuable and concise text aimed at the final-year undergraduate and first-year graduate student.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51092588003601,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51092591968529,"sku":"NIN9780521045872","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52401704435985,"sku":"NLS9780521045872","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0521045878.jpg?v=1750975922"},{"product_id":"local-fields-book-j-w-s-cassels-9780521315258","title":"Local Fields","description":"The p-adic numbers, the earliest of local fields, were introduced by Hensel some 70 years ago as a natural tool in algebra number theory. Today the use of this and other local fields pervades much of mathematics, yet these simple and natural concepts, which often provide remarkably easy solutions to complex problems, are not as familiar as they should be. This book, based on postgraduate lectures at Cambridge, is meant to rectify this situation by providing a fairly elementary and self-contained introduction to local fields. After a general introduction, attention centres on the p-adic numbers and their use in number theory. There follow chapters on algebraic number theory, diophantine equations and on the analysis of a p-adic variable. This book will appeal to undergraduates, and even amateurs, interested in number theory, as well as to graduate students.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51820549275921,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51820549800209,"sku":"GOR014412091","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":51855762030865,"sku":"CIN0521315255G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52148612694289,"sku":"NLS9780521315258","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521315258.jpg?v=1752576973"},{"product_id":"prolegomena-to-a-middlebrow-arithmetic-of-curves-of-genus-2-book-j-w-s-cassels-9780521483704","title":"Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2","description":"The number theoretic properties of curves of genus 2 are attracting increasing attention. This book provides new insights into this subject; much of the material here is entirely new, and none has appeared in book form before. The authors include an explicit treatment of the Jacobian, which throws new light onto the geometry of the Kummer surface. Mathematicians can then determine the Mordell-Weil group for many curves, and in many nontrivial cases they can find all rational points. The results exemplify the power of computer algebra in diophantine contexts, but computer expertise is not assumed in the main text. Number theorists, algebraic geometers and workers in related areas will find that this book offers unique insights.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52333499547921,"sku":"NLS9780521483704","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52735427576081,"sku":"NIN9780521483704","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521483704.jpg?v=1758154973"},{"product_id":"economics-for-mathematicians-book-j-w-s-cassels-9780521286145","title":"Economics for Mathematicians","description":"This is the expanded notes of a course intended to introduce students specializing in mathematics to some of the central ideas of traditional economics. The book should be readily accessible to anyone with some training in university mathematics; more advanced mathematical tools are explained in the appendices. Thus this text could be used for undergraduate mathematics courses or as supplementary reading for students of mathematical economics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52343867900177,"sku":"NLS9780521286145","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52735406539025,"sku":"NIN9780521286145","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521286145.jpg?v=1758174123"},{"product_id":"introduction-to-the-geometry-of-numbers-book-j-w-s-cassels-9781014409874","title":"An Introduction to the Geometry of Numbers","description":"Reihentext + Geometry of Numbers From the reviews: The work is carefully written. It is well motivated, and interesting to read, even if it is not always easy. historical material is included. the author has written an excellent account of an interesting subject. (Mathematical Gazette) A well-written, very thorough account . Among the topics are lattices, reduction, Minkowski's Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references. (The American Mathematical Monthly)","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":52742573228305,"sku":"NIN9781014409874","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781014409874.jpg?v=1763492165"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-j-w-s-cassels.oembed","provider":"World of Books ","version":"1.0","type":"link"}