Using Algebraic Geometry

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Using Algebraic Geometry

David A. Cox,John Little,DONAL OSHEA
Using Algebraic Geometry Book PDF

Author : David A. Cox,John Little,DONAL OSHEA
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 53,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475769111

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Using Algebraic Geometry by David A. Cox,John Little,DONAL OSHEA Pdf

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.

Using Algebraic Geometry

David A Cox,John Little,Donal O'Shea
Using Algebraic Geometry Book PDF

Author : David A Cox,John Little,Donal O'Shea
Publisher : Springer Science & Business Media
Page : 596 pages
File Size : 43,9 Mb
Release : 2005-03-17
Category : Mathematics
ISBN : 0387207333

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Using Algebraic Geometry by David A Cox,John Little,Donal O'Shea Pdf

The discovery of new algorithms for dealing with polynomial equations, and their implementation on fast, inexpensive computers, has revolutionized algebraic geometry and led to exciting new applications in the field. This book details many uses of algebraic geometry and highlights recent applications of Grobner bases and resultants. This edition contains two new sections, a new chapter, updated references and many minor improvements throughout.

Using Algebraic Geometry

David A. Cox,John B. Little,Donal O'Shea
Using Algebraic Geometry Book PDF

Author : David A. Cox,John B. Little,Donal O'Shea
Publisher : Springer Verlag
Page : 499 pages
File Size : 45,6 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 9780387984926

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Using Algebraic Geometry by David A. Cox,John B. Little,Donal O'Shea Pdf

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gr"obner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility. The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Gr"obner bases. The book does not assume the reader is familiar with more advanced concepts such as modules.

Introduction to Algebraic Geometry

Serge Lang
Introduction to Algebraic Geometry Book PDF

Author : Serge Lang
Publisher : Courier Dover Publications
Page : 273 pages
File Size : 51,6 Mb
Release : 2019-03-20
Category : Mathematics
ISBN : 9780486839806

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Introduction to Algebraic Geometry by Serge Lang Pdf

Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.

Introduction to Algebraic Geometry

Steven Dale Cutkosky
Introduction to Algebraic Geometry Book PDF

Author : Steven Dale Cutkosky
Publisher : American Mathematical Soc.
Page : 484 pages
File Size : 49,9 Mb
Release : 2018-06-01
Category : Geometry, Algebraic
ISBN : 9781470435189

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Introduction to Algebraic Geometry by Steven Dale Cutkosky Pdf

This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.

Algebraic Geometry

Robin Hartshorne
Algebraic Geometry Book PDF

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 54,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475738490

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Algebraic Geometry by Robin Hartshorne Pdf

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.

Computing in Algebraic Geometry

Wolfram Decker,Christoph Lossen
Computing in Algebraic Geometry Book PDF

Author : Wolfram Decker,Christoph Lossen
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 46,8 Mb
Release : 2006-03-02
Category : Mathematics
ISBN : 9783540289920

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Computing in Algebraic Geometry by Wolfram Decker,Christoph Lossen Pdf

This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.

Ideals, Varieties, and Algorithms

David Cox,John Little,DONAL OSHEA
Ideals Varieties and Algorithms Book PDF

Author : David Cox,John Little,DONAL OSHEA
Publisher : Springer Science & Business Media
Page : 523 pages
File Size : 44,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475721812

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Ideals, Varieties, and Algorithms by David Cox,John Little,DONAL OSHEA Pdf

Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.

Algebraic Geometry

Ulrich Görtz,Torsten Wedhorn
Algebraic Geometry Book PDF

Author : Ulrich Görtz,Torsten Wedhorn
Publisher : Springer Science & Business Media
Page : 615 pages
File Size : 44,7 Mb
Release : 2010-08-09
Category : Mathematics
ISBN : 9783834897220

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Algebraic Geometry by Ulrich Görtz,Torsten Wedhorn Pdf

This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.

Algebraic Geometry and Commutative Algebra

Siegfried Bosch
Algebraic Geometry and Commutative Algebra Book PDF

Author : Siegfried Bosch
Publisher : Springer Nature
Page : 504 pages
File Size : 47,6 Mb
Release : 2022-04-22
Category : Mathematics
ISBN : 9781447175230

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Algebraic Geometry and Commutative Algebra by Siegfried Bosch Pdf

Algebraic Geometry is a fascinating branch of Mathematics that combines methods from both Algebra and Geometry. It transcends the limited scope of pure Algebra by means of geometric construction principles. Putting forward this idea, Grothendieck revolutionized Algebraic Geometry in the late 1950s by inventing schemes. Schemes now also play an important role in Algebraic Number Theory, a field that used to be far away from Geometry. The new point of view paved the way for spectacular progress, such as the proof of Fermat's Last Theorem by Wiles and Taylor. This book explains the scheme-theoretic approach to Algebraic Geometry for non-experts, while more advanced readers can use it to broaden their view on the subject. A separate part presents the necessary prerequisites from Commutative Algebra, thereby providing an accessible and self-contained introduction to advanced Algebraic Geometry. Every chapter of the book is preceded by a motivating introduction with an informal discussion of its contents and background. Typical examples, and an abundance of exercises illustrate each section. Therefore the book is an excellent companion for self-studying or for complementing skills that have already been acquired. It can just as well serve as a convenient source for (reading) course material and, in any case, as supplementary literature. The present edition is a critical revision of the earlier text.

Computations in Algebraic Geometry with Macaulay 2

David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels
Computations in Algebraic Geometry with Macaulay 2 Book PDF

Author : David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 50,6 Mb
Release : 2001-09-25
Category : Mathematics
ISBN : 3540422307

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Computations in Algebraic Geometry with Macaulay 2 by David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels Pdf

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

Algorithms in Real Algebraic Geometry

Saugata Basu,Richard Pollack,Marie-Françoise Coste-Roy
Algorithms in Real Algebraic Geometry Book PDF

Author : Saugata Basu,Richard Pollack,Marie-Françoise Coste-Roy
Publisher : Springer Science & Business Media
Page : 602 pages
File Size : 50,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662053553

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Algorithms in Real Algebraic Geometry by Saugata Basu,Richard Pollack,Marie-Françoise Coste-Roy Pdf

In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.

The Geometry of Schemes

David Eisenbud,Joe Harris
The Geometry of Schemes Book PDF

Author : David Eisenbud,Joe Harris
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 47,9 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387226392

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The Geometry of Schemes by David Eisenbud,Joe Harris Pdf

Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Algebraic Geometry for Scientists and Engineers

Shreeram Shankar Abhyankar
Algebraic Geometry for Scientists and Engineers Book PDF

Author : Shreeram Shankar Abhyankar
Publisher : American Mathematical Soc.
Page : 295 pages
File Size : 43,8 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821815359

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Algebraic Geometry for Scientists and Engineers by Shreeram Shankar Abhyankar Pdf

This book, based on lectures presented in courses on algebraic geometry taught by the author at Purdue University, is intended for engineers and scientists (especially computer scientists), as well as graduate students and advanced undergraduates in mathematics. In addition to providing a concrete or algorithmic approach to algebraic geometry, the author also attempts to motivate and explain its link to more modern algebraic geometry based on abstract algebra.The book covers various topics in the theory of algebraic curves and surfaces, such as rational and polynomial parametrization, functions and differentials on a curve, branches and valuations, and resolution of singularities. The emphasis is on presenting heuristic ideas and suggestive arguments rather than formal proofs. Readers will gain new insight into the subject of algebraic geometry in a way that should increase appreciation of modern treatments of the subject, as well as enhance its utility in applications in science and industry.

Algebraic Geometry

Joe Harris
Algebraic Geometry Book PDF

Author : Joe Harris
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 43,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475721898

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Algebraic Geometry by Joe Harris Pdf

"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS