[PDF] Selected Papers On Number Theory And Algebraic Geometry eBook

Author : Katsumi Nomizu
Publisher : American Mathematical Soc.
Page : 170 pages
File Size : 21,86 MB
Release : 1994
Category : Geometry, Algebraic
ISBN : 9780821875117

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This book presents papers that originally appeared in the Japanese journal Sugaku. The papers explore the relationship between number theory, algebraic geometry, and differential geometry.

Author : Katsumi Nomizu
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 26,10 MB
Release : 1996
Category : Geometry, Algebraic
ISBN : 9780821804452

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This book presents papers that originally appeared in the Japanese journal Sugaku from the Mathematical Society of Japan. The papers explore the relationship between number theory and algebraic geometry.

Author : Miles Reid
Publisher : Cambridge University Press
Page : 312 pages
File Size : 18,60 MB
Release : 2003
Category : Mathematics
ISBN : 9780521545181

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This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.

Author : Álvaro Lozano-Robledo
Publisher : American Mathematical Soc.
Page : 488 pages
File Size : 24,77 MB
Release : 2019-03-21
Category : Arithmetical algebraic geometry
ISBN : 147045016X

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Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.

Author : B.Heinrich Matzat
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 41,85 MB
Release : 2012-12-06
Category : Computers
ISBN : 364259932X

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This book contains 22 lectures presented at the final conference of the Ger man research program (Schwerpunktprogramm) Algorithmic Number The ory and Algebra 1991-1997, sponsored by the Deutsche Forschungsgemein schaft. The purpose of this research program and of the meeting was to bring together developers of computer algebra software and researchers using com putational methods to gain insight into experimental problems and theoret ical questions in algebra and number theory. The book gives an overview on algorithmic methods and on results ob tained during this period. This includes survey articles on the main research projects within the program: • algorithmic number theory emphasizing class field theory, constructive Galois theory, computational aspects of modular forms and of Drinfeld modules • computational algebraic geometry including real quantifier elimination and real algebraic geometry, and invariant theory of finite groups • computational aspects of presentations and representations of groups, especially finite groups of Lie type and their Heeke algebras, and of the isomorphism problem in group theory. Some of the articles illustrate the current state of computer algebra sys tems and program packages developed with support by the research pro gram, such as KANT and LiDIA for algebraic number theory, SINGULAR, RED LOG and INVAR for commutative algebra and invariant theory respec tively, and GAP, SYSYPHOS and CHEVIE for group theory and representation theory.

Author : Yu I Manin
Publisher : World Scientific
Page : 614 pages
File Size : 49,44 MB
Release : 1996-06-28
Category : Mathematics
ISBN : 9814499552

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The book is a collection of research and review articles in several areas of modern mathematics and mathematical physics published in the span of three decades. The ICM Kyoto talk “Mathematics as Metaphor” summarises the author's view on mathematics as an outgrowth of natural language.