Author : Wolfram Decker
Publisher : Cambridge University Press
Page : 127 pages
File Size : 34,88 MB
Release : 2013-02-07
Category : Computers
ISBN : 1107612535
A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.
Author : Wolfram Decker
Publisher : Cambridge University Press
Page : 127 pages
File Size : 10,81 MB
Release : 2013-02-07
Category : Mathematics
ISBN : 1107311489
A First Course in Computational Algebraic Geometry is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the freely available computer algebra system, Singular. Readers will quickly gain the confidence to begin performing their own experiments.
Author : Huishi Li
Publisher : CRC Press
Page : 393 pages
File Size : 13,34 MB
Release : 2017-12-19
Category : Mathematics
ISBN : 1482270331
"Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory, curves and elliptic curves, and more."
Author : David A. Cox
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 50,97 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 1475769113
An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.
Author : Ihsen Yengui
Publisher : World Scientific
Page : 283 pages
File Size : 31,13 MB
Release : 2021-05-17
Category : Mathematics
ISBN : 981123826X
This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry.This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Experience has shown that beginners who want to take their first steps in algebraic geometry are usually discouraged by the difficulty of the proposed exercises and the absence of detailed answers. Therefore, exercises (and their solutions) as well as examples occupy a prominent place in this course.This book is not designed as a comprehensive reference work, but rather as a selective textbook. The many exercises with detailed answers make it suitable for use in both a math or computer science course.
Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 20,79 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 1475738498
An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Author : David Eisenbud
Publisher : Springer Science & Business Media
Page : 784 pages
File Size : 11,38 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461253500
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 38,34 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 3662029456
A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 591 pages
File Size : 26,68 MB
Release : 2012-10-29
Category : Mathematics
ISBN : 1441984895
Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.
Author : Miles Reid
Publisher : Cambridge University Press
Page : 144 pages
File Size : 16,80 MB
Release : 1988-12-15
Category : Mathematics
ISBN : 9780521356626
Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to the basic concepts of algebraic geometry including: plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. He is at pains to stress the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book arises from an undergraduate course given at the University of Warwick and contains numerous examples and exercises illustrating the theory.
