Algebra Geometry

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Algebraic Geometry

Robin Hartshorne
Algebraic Geometry Book PDF

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 52,8 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.

Algebra & Geometry

Mark V. Lawson
Algebra Geometry Book PDF

Author : Mark V. Lawson
Publisher : CRC Press
Page : 383 pages
File Size : 46,6 Mb
Release : 2016-11-25
Category : Mathematics
ISBN : 9781482246506

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Algebra & Geometry by Mark V. Lawson Pdf

Algebra & Geometry: An Introduction to University Mathematics provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first several chapters cover foundational topics, including the importance of proofs and properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solution of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra

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 : 42,5 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.

Algebra and Geometry

Alan F. Beardon
Algebra and Geometry Book PDF

Author : Alan F. Beardon
Publisher : Cambridge University Press
Page : 340 pages
File Size : 54,7 Mb
Release : 2005-05-12
Category : Mathematics
ISBN : 9781139443494

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Algebra and Geometry by Alan F. Beardon Pdf

Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources.

Linear Algebra, Geometry and Transformation

Bruce Solomon
Linear Algebra Geometry and Transformation Book PDF

Author : Bruce Solomon
Publisher : CRC Press
Page : 474 pages
File Size : 47,6 Mb
Release : 2014-12-12
Category : Mathematics
ISBN : 9781482299304

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Linear Algebra, Geometry and Transformation by Bruce Solomon Pdf

The Essentials of a First Linear Algebra Course and MoreLinear Algebra, Geometry and Transformation provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem.An Engaging Treatment of the Interplay amo

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 : 53,7 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.

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 : 43,8 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.

Linear Algebra and Geometry

Igor R. Shafarevich,Alexey O. Remizov
Linear Algebra and Geometry Book PDF

Author : Igor R. Shafarevich,Alexey O. Remizov
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 41,5 Mb
Release : 2012-08-23
Category : Mathematics
ISBN : 9783642309946

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Linear Algebra and Geometry by Igor R. Shafarevich,Alexey O. Remizov Pdf

This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.

Geometric Algebra for Computer Science

Leo Dorst,Daniel Fontijne,Stephen Mann
Geometric Algebra for Computer Science Book PDF

Author : Leo Dorst,Daniel Fontijne,Stephen Mann
Publisher : Elsevier
Page : 664 pages
File Size : 54,5 Mb
Release : 2010-07-26
Category : Juvenile Nonfiction
ISBN : 9780080553108

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Geometric Algebra for Computer Science by Leo Dorst,Daniel Fontijne,Stephen Mann Pdf

Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full colour book includes a website with GAViewer, a program to experiment with GA

Introduction to Algebraic Geometry

Serge Lang
Introduction to Algebraic Geometry Book PDF

Author : Serge Lang
Publisher : Courier Dover Publications
Page : 273 pages
File Size : 44,6 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.

Linear Algebra and Projective Geometry

Reinhold Baer
Linear Algebra and Projective Geometry Book PDF

Author : Reinhold Baer
Publisher : Courier Corporation
Page : 338 pages
File Size : 40,7 Mb
Release : 2012-06-11
Category : Mathematics
ISBN : 9780486154664

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Linear Algebra and Projective Geometry by Reinhold Baer Pdf

Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.

Foundations of Algebraic Geometry. --; 29

André 1906- Weil
Foundations of Algebraic Geometry 29 Book PDF

Author : André 1906- Weil
Publisher : Hassell Street Press
Page : 392 pages
File Size : 41,6 Mb
Release : 2021-09-10
Category : Electronic
ISBN : 1015107672

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Foundations of Algebraic Geometry. --; 29 by André 1906- Weil Pdf

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Algebra and Geometry with Python

Sergei Kurgalin,Sergei Borzunov
Algebra and Geometry with Python Book PDF

Author : Sergei Kurgalin,Sergei Borzunov
Publisher : Springer Nature
Page : 429 pages
File Size : 51,5 Mb
Release : 2021-01-18
Category : Computers
ISBN : 9783030615413

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Algebra and Geometry with Python by Sergei Kurgalin,Sergei Borzunov Pdf

This book teaches algebra and geometry. The authors dedicate chapters to the key issues of matrices, linear equations, matrix algorithms, vector spaces, lines, planes, second-order curves, and elliptic curves. The text is supported throughout with problems, and the authors have included source code in Python in the book. The book is suitable for advanced undergraduate and graduate students in computer science.

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 : 41,7 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.

Introduction to Commutative Algebra and Algebraic Geometry

Ernst Kunz
Introduction to Commutative Algebra and Algebraic Geometry Book PDF

Author : Ernst Kunz
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 51,7 Mb
Release : 2012-11-06
Category : Mathematics
ISBN : 9781461459873

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Introduction to Commutative Algebra and Algebraic Geometry by Ernst Kunz Pdf

Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.