Using Algebraic Geometry

Author: David A. Cox,John Little,DONAL OSHEA

Publisher: Springer Science & Business Media

ISBN: 1475769113

Category: Mathematics

Page: 503

View: 761

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.
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Commutative Algebra

With a View Toward Algebraic Geometry

Author: David Eisenbud,Professor David Eisenbud

Publisher: Springer Science & Business Media

ISBN: 9780387942698

Category: Mathematics

Page: 785

View: 2127

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.
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Algebraic Geometry

A Concise Dictionary

Author: Elena Rubei

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110316234

Category: Mathematics

Page: 239

View: 4735

Algebraic geometry has a complicated, difficult language. This book contains a definition, several references and the statements of the main theorems (without proofs) for every of the most common words in this subject. Some terms of related subjects are included. It helps beginners that know some, but not all, basic facts of algebraic geometry to follow seminars and to read papers. The dictionary form makes it easy and quick to consult.
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Algebraic Geometry

Author: Robin Hartshorne

Publisher: Springer Science & Business Media

ISBN: 1475738498

Category: Mathematics

Page: 496

View: 9011

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.
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An Invitation to Algebraic Geometry

Author: Karen E. Smith,Lauri Kahanpää,Pekka Kekäläinen,William Traves

Publisher: Springer Science & Business Media

ISBN: 1475744978

Category: Mathematics

Page: 164

View: 3452

This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.
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Computational Commutative and Non-commutative Algebraic Geometry

Author: Svetlana Cojocaru,Gerhard Pfister,Victor Ufnarovski

Publisher: IOS Press

ISBN: 1586035053

Category: Mathematics

Page: 325

View: 6872

This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in Commutative and Non-Commutative Algebraic Geometry and Algebra. The contributors to this publication present the most recent and state-of-the-art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of information on commutative and non-commutative algebraic geometry.
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Topics in Algebraic Geometry and Geometric Modeling

Workshop on Algebraic Geometry and Geometric Modeling, July 29-August 2, 2002, Vilnius University, Lithuania

Author: Ron Goldman,Rimvydas Krasauskas

Publisher: American Mathematical Soc.

ISBN: 0821834207

Category: Mathematics

Page: 366

View: 3884

Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise polynomial, and rational curves and surfaces to build computer models of mechanical components and assemblies for industrial design and manufacture. The NSF sponsored the four-day ``Vilnius Workshop on Algebraic Geometry and Geometric Modeling'', which brought together some of the top experts in the two research communities to examine a wide range of topics of interest to both fields. This volume is an outgrowth of that workshop. Included are surveys, tutorials, and research papers. In addition, the editors have included a translation of Minding's 1841 paper, ``On the determination of the degree of an equation obtained by elimination'', which foreshadows the modern application of mixed volumes in algebraic geometry. The volume is suitable for mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.
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Elementare Algebraische Geometrie

Grundlegende Begriffe und Techniken mit zahlreichen Beispielen und Anwendungen

Author: Klaus Hulek

Publisher: Springer-Verlag

ISBN: 3322802213

Category: Mathematics

Page: 167

View: 339

Dieses Buch gibt eine Einführung in die Algebraische Geometrie. Ziel ist es, die grundlegenden Begriffe und Techniken der algebraischen Geometrie zusammen mit einer Reihe von Beispielen darzustellen.
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An Introduction to Algebraic Geometry and Algebraic Groups

Author: Meinolf Geck

Publisher: OUP Oxford

ISBN: 0191663727

Category: Mathematics

Page: 320

View: 817

An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results. The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks.
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Algebraic Geometry

A First Course

Author: Joe Harris

Publisher: Springer Science & Business Media

ISBN: 1475721897

Category: Mathematics

Page: 330

View: 2908

"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
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Poincarés Vermutung

die Geschichte eines mathematischen Abenteuers

Author: Donal O'Shea

Publisher: N.A

ISBN: 9783596176632

Category:

Page: 376

View: 3587

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Elementare Algebraische Geometrie

Grundlegende Begriffe und Techniken mit zahlreichen Beispielen und Anwendungen

Author: Klaus Hulek

Publisher: Springer-Verlag

ISBN: 3834823481

Category: Mathematics

Page: 194

View: 5241

Dieses Buch gibt eine Einführung in die Algebraische Geometrie. Ziel ist es, die grundlegenden Begriffe und Techniken der algebraischen Geometrie zusammen mit einer Reihe von Beispielen darzustellen.
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Newsletter

Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1233

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The Geometry of Schemes

Author: David Eisenbud,Joe Harris

Publisher: Springer Science & Business Media

ISBN: 0387226397

Category: Mathematics

Page: 300

View: 1189

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.
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Ebene algebraische Kurven

Author: Egbert Brieskorn,Horst Knörrer

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 964

View: 6282

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Maß und Kategorie

Author: J.C. Oxtoby

Publisher: Springer-Verlag

ISBN: 364296074X

Category: Mathematics

Page: 112

View: 9852

Dieses Buch behandelt hauptsächlich zwei Themenkreise: Der Bairesche Kategorie-Satz als Hilfsmittel für Existenzbeweise sowie Die "Dualität" zwischen Maß und Kategorie. Die Kategorie-Methode wird durch viele typische Anwendungen erläutert; die Analogie, die zwischen Maß und Kategorie besteht, wird nach den verschiedensten Richtungen hin genauer untersucht. Hierzu findet der Leser eine kurze Einführung in die Grundlagen der metrischen Topologie; außerdem werden grundlegende Eigenschaften des Lebesgue schen Maßes hergeleitet. Es zeigt sich, daß die Lebesguesche Integrationstheorie für unsere Zwecke nicht erforderlich ist, sondern daß das Riemannsche Integral ausreicht. Weiter werden einige Begriffe aus der allgemeinen Maßtheorie und Topologie eingeführt; dies geschieht jedoch nicht nur der größeren Allgemeinheit wegen. Es erübrigt sich fast zu erwähnen, daß sich die Bezeichnung "Kategorie" stets auf "Bairesche Kategorie" be zieht; sie hat nichts zu tun mit dem in der homologischen Algebra verwendeten Begriff der Kategorie. Beim Leser werden lediglich grundlegende Kenntnisse aus der Analysis und eine gewisse Vertrautheit mit der Mengenlehre vorausgesetzt. Für die hier untersuchten Probleme bietet sich in natürlicher Weise die mengentheoretische Formulierung an. Das vorlie gende Buch ist als Einführung in dieses Gebiet der Analysis gedacht. Man könnte es als Ergänzung zur üblichen Grundvorlesung über reelle Analysis, als Grundlage für ein Se minar oder auch zum selbständigen Studium verwenden. Bei diesem Buch handelt es sich vorwiegend um eine zusammenfassende Darstellung; jedoch finden sich in ihm auch einige Verfeinerungen bekannter Resultate, namentlich Satz 15.6 und Aussage 20.4. Das Literaturverzeichnis erhebt keinen Anspruch auf Vollständigkeit. Häufig werden Werke zitiert, die weitere Literaturangaben enthalten.
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Topics in Combinatorial Group Theory

Author: Gilbert Baumslag

Publisher: Springer Science & Business Media

ISBN: 9783764329211

Category: Mathematics

Page: 170

View: 5037

Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. With surprising frequency, problems in a wide variety of disciplines, including differential equations, automorphic functions and geometry, have been distilled into explicit questions about groups, typically of the following kind: Are the groups in a given class finite (e.g., the Burnside problem)? Finitely generated? Finitely presented? What are the conjugates of a given element in a given group? What are the subgroups of that group? Is there an algorithm for deciding for every pair of groups in a given class whether they are isomorphic or not? The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions. In view of the scope of the subject and the extraordinary variety of groups involved, it is not surprising that no really general theory exists. These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level.
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Moderne Algebra

Author: Bartel Eckmann L. Van der van der Waerden,Emil Artin,Emmy Noether

Publisher: Springer-Verlag

ISBN: 3662364344

Category: Mathematics

Page: 274

View: 9284

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
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The American Mathematical Monthly

The Official Journal of the Mathematical Association of America

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematicians

Page: N.A

View: 7287

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Schloss aus Glas

Author: Jeannette Walls

Publisher: Hoffmann und Campe

ISBN: 3455810519

Category: Fiction

Page: 382

View: 8410

Jeannette Walls ist ein glückliches Kind: Sie hat einen Vater, der mit ihr auf Dämonenjagd geht, ihr die Physik erklärt und die Sterne vom Himmel holt. Da nimmt sie gerne in Kauf, immer mal wieder mit leerem Bauch ins Bett zu gehen, ihre egomanische Künstlermutter zu ertragen oder in Nacht-und-Nebel-Aktionen den Wohnort zu wechseln. Mit den Jahren allerdings werden die sozialen Verhältnisse schlimmer, die Sprüche des Vaters schaler und das Lügengebäude der Eltern so zerbrechlich wie das Schloss aus Glas, das der Vater jahrelang zu bauen versprochen hatte.
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