Elementary Geometry of Algebraic Curves

An Undergraduate Introduction

Author: C. G. Gibson

Publisher: Cambridge University Press

ISBN: 9780521646413

Category: Mathematics

Page: 250

View: 2505

Here is an introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book is well illustrated and contains several hundred worked examples and exercises. From the familiar lines and conics of elementary geometry the reader proceeds to general curves in the real affine plane, with excursions to more general fields to illustrate applications, such as number theory. By adding points at infinity the affine plane is extended to the projective plane, yielding a natural setting for curves and providing a flood of illumination into the underlying geometry. A minimal amount of algebra leads to the famous theorem of Bezout, while the ideas of linear systems are used to discuss the classical group structure on the cubic.
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Elementary Geometry of Algebraic Curves, An Undergraduate Introduction

Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 149703308X

Category: Education

Page: 40

View: 7246

Facts101 is your complete guide to Elementary Geometry of Algebraic Curves, An Undergraduate Introduction. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.
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Ebene algebraische Kurven

Author: Egbert Brieskorn,Horst Knörrer

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 964

View: 1202

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Ebene algebraische Kurven

Author: Gerd Fischer

Publisher: Springer-Verlag

ISBN: 3322803112

Category: Mathematics

Page: 177

View: 7942

Neben den elementaren Dingen, wie Tangenten, Singularitäten und Wendepunkten werden auch schwierigere Begriffe wie lokale Zweige und Geschlecht behandelt. Höhepunkte sind die klassischen Formeln von Plücker und Clebsch, die Beziehungen zwischen verschiedenen globalen und lokalen Invarianten einer Kurve beschreiben.
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Algebraic Geometry

A Problem Solving Approach

Author: Thomas A. Garrity

Publisher: American Mathematical Soc.

ISBN: 0821893963

Category: Mathematics

Page: 335

View: 3459

Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of ex
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Elementary Geometry of Differentiable Curves

An Undergraduate Introduction

Author: C. G. Gibson

Publisher: Cambridge University Press

ISBN: 9780521011075

Category: Mathematics

Page: 216

View: 5396

An introductory text on the differential geometry of plane curves, first published in 2001.
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Using the Mathematics Literature

Author: Kristine K. Fowler

Publisher: CRC Press

ISBN: 9780824750350

Category: Language Arts & Disciplines

Page: 475

View: 6017

This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.
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Plane Algebraic Curves

Author: Gerd Fischer

Publisher: American Mathematical Soc.

ISBN: 0821821229

Category: Mathematics

Page: 231

View: 4670

This is an excellent introduction to algebraic geometry, which assumes only standard undergraduate mathematical topics: complex analysis, rings and fields, and topology. Reading this book will help establish the geometric intuition that lies behind the more advanced ideas and techniques used in the study of higher-dimensional varieties.
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Differentialgeometrie von Kurven und Flächen

Author: Manfredo P. do Carmo

Publisher: Springer-Verlag

ISBN: 3322850722

Category: Technology & Engineering

Page: 263

View: 7552

Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang
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Conics and Cubics

A Concrete Introduction to Algebraic Curves

Author: Robert Bix

Publisher: Springer Science & Business Media

ISBN: 038731802X

Category: Mathematics

Page: 347

View: 7263

Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout’s Theorem on the number of intersections of two curves. The subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course.
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Algorithmische Geometrie

Polyedrische und algebraische Methoden

Author: Michael Joswig,Thorsten Theobald

Publisher: Springer-Verlag

ISBN: 3834894400

Category: Mathematics

Page: 266

View: 1126

In dem Lehrbuch wird eine mathematisch orientierte Einführung in die algorithmische Geometrie gegeben. Im ersten Teil werden „klassische“ Probleme und Techniken behandelt, die sich auf polyedrische (= linear begrenzte) Objekte beziehen. Hierzu gehören beispielsweise Algorithmen zur Berechnung konvexer Hüllen und die Konstruktion von Voronoi-Diagrammen. Im zweiten Teil werden grundlegende Methoden der algorithmischen algebraischen Geometrie entwickelt und anhand von Anwendungen aus Computergrafik, Kurvenrekonstruktion und Robotik illustriert. Das Buch eignet sich für ein fortgeschrittenes Modul in den derzeit neu konzipierten Bachelor-Studiengängen in Mathematik und Informatik.
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Elementare Differentialgeometrie

Author: Christian Bär

Publisher: Walter de Gruyter

ISBN: 3110224593

Category: Mathematics

Page: 356

View: 6382

This textbook presents an introduction to the differential geometry of curves and surfaces. This second, revised edition has been expanded to include solutions and applications in cartography. Topics include Euclidean geometry, curve theory, surface theory, curvature concepts, minimal surfaces, Riemann geometry and the Gauss-Bonnet theorem.
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Elementary Algebraic Geometry

Author: Klaus Hulek

Publisher: American Mathematical Soc.

ISBN: 0821829521

Category: Mathematics

Page: 213

View: 8881

This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary.
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Einführung in die Geometrie und Topologie

Author: Werner Ballmann

Publisher: Springer-Verlag

ISBN: 3034809018

Category: Mathematics

Page: 162

View: 5630

Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik- und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein- oder zweisemestrige Vorlesungen geeignet.
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