Rudiments of Algebraic Geometry

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Author: W.E. Jenner

Publisher: Courier Dover Publications

ISBN: 0486818063

Category: Mathematics

Page: 112

View: 3373

Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.

Elementary Algebraic Geometry

Second Edition

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Author: Keith Kendig

Publisher: Courier Dover Publications

ISBN: 048680187X

Category: Mathematics

Page: 320

View: 5034

Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring theory and algebraic geometry as well as varieties of arbitrary dimension and some elementary mathematics on curves. Upon finishing the text, students will have a foundation for advancing in several different directions, including toward a further study of complex algebraic or analytic varieties or to the scheme-theoretic treatments of algebraic geometry. 2015 edition.

Algebraic Geometry

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Author: Solomon Lefschetz

Publisher: Courier Corporation

ISBN: 0486154726

Category: Mathematics

Page: 256

View: 7984

An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

Ebene algebraische Kurven

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Author: Gerd Fischer

Publisher: Springer-Verlag

ISBN: 3322803112

Category: Mathematics

Page: 177

View: 6295

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.

Algebraic Topology

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Author: C. R. F. Maunder

Publisher: Courier Corporation

ISBN: 9780486691312

Category: Mathematics

Page: 375

View: 6930

Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.

Introduction to Algebraic Geometry

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Author: Serge Lang

Publisher: Courier Dover Publications

ISBN: 0486834220

Category: Mathematics

Page: 272

View: 1837

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.

Geometric Algebra

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Author: Emil Artin

Publisher: Courier Dover Publications

ISBN: 048680920X

Category: Mathematics

Page: 224

View: 1613

This concise classic presents advanced undergraduates and graduate students in mathematics with an overview of geometric algebra. The text originated with lecture notes from a New York University course taught by Emil Artin, one of the preeminent mathematicians of the twentieth century. The Bulletin of the American Mathematical Society praised Geometric Algebra upon its initial publication, noting that "mathematicians will find on many pages ample evidence of the author's ability to penetrate a subject and to present material in a particularly elegant manner." Chapter 1 serves as reference, consisting of the proofs of certain isolated algebraic theorems. Subsequent chapters explore affine and projective geometry, symplectic and orthogonal geometry, the general linear group, and the structure of symplectic and orthogonal groups. The author offers suggestions for the use of this book, which concludes with a bibliography and index.

Differentialgeometrie von Kurven und Flächen

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Author: Manfredo P. do Carmo

Publisher: Springer-Verlag

ISBN: 3322850722

Category: Technology & Engineering

Page: 263

View: 3380

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

Geometry: A Comprehensive Course

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Author: Dan Pedoe

Publisher: Courier Corporation

ISBN: 0486131734

Category: Mathematics

Page: 464

View: 2890

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Linear Algebra and Projective Geometry

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Author: Reinhold Baer

Publisher: Courier Corporation

ISBN: 0486154661

Category: Mathematics

Page: 336

View: 7993

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.

Linear Algebra and Geometry

A Second Course

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Author: Irving Kaplansky

Publisher: Courier Corporation

ISBN: 9780486432335

Category: Mathematics

Page: 143

View: 1910

The author of this text seeks to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. Focusing on inner product spaces, orthogonal similarity, and elements of geometry, this volume is illustrated with an abundance of examples, exercises, and proofs and is suitable for both undergraduate and graduate courses. 1974 edition.

Challenging Problems in Geometry

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Author: Alfred S. Posamentier,Charles T. Salkind

Publisher: Courier Corporation

ISBN: 0486134865

Category: Mathematics

Page: 256

View: 5366

Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and more. Arranged in order of difficulty. Detailed solutions.

Lectures on Linear Algebra

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Author: I. M. Gelfand

Publisher: Courier Corporation

ISBN: 9780486660820

Category: Mathematics

Page: 185

View: 9087

Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector.

Algebraische Zahlentheorie

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Author: Jürgen Neukirch

Publisher: Springer-Verlag

ISBN: 3540376631

Category: Mathematics

Page: 595

View: 3362

Algebraische Zahlentheorie: eine der traditionsreichsten und aktuellsten Grunddisziplinen der Mathematik. Das vorliegende Buch schildert ausführlich Grundlagen und Höhepunkte. Konkret, modern und in vielen Teilen neu. Neu: Theorie der Ordnungen. Plus: die geometrische Neubegründung der Theorie der algebraischen Zahlkörper durch die "Riemann-Roch-Theorie" vom "Arakelovschen Standpunkt", die bis hin zum "Grothendieck-Riemann-Roch-Theorem" führt.

Challenging Problems in Algebra

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Author: Alfred S. Posamentier,Charles T. Salkind

Publisher: Courier Corporation

ISBN: 0486131548

Category: Mathematics

Page: 288

View: 2473

Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.

Differential Geometry

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Author: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 9780486667218

Category: Mathematics

Page: 352

View: 7125

Text from preface: "This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space"

History of Mathematics

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Author: David E. Smith

Publisher: Courier Corporation

ISBN: 9780486204307

Category: Mathematics

Page: 736

View: 874

Within this two-volume edition, Professor Smith covers the entire history of mathematics in the Near and Far East and the West, from primitive number concepts to the calculus. His account is distinguished by impeccable scholarship combined with unusual clarity and readability. Footnotes add many technical points outside the book's actual line of development and direct the reader to disputed matters and source readings. Hundreds of illustrations from Egyptian papyri, Hindu, Chinese, and Japanese manuscripts, Greek and Roman texts, Medieval treatises, maps, portraits, etc. are used along with modern graphs and diagrams. Every major figure from Euclid to Descartes, Gauss, and Riemann and hundreds of lesser-known figures — Theon of Smyrna, Rabbi ben Ezra, Radulph of Laon, Mersenns, Benedetti, and more — are considered both with respect to specific problems and with an awareness of their overall influence on mathematics. Volume II: Special Topics, considering mathematics in terms of arithmetic geometry, algebra, trig, calculus, calculating machines, and other specific fields and problems. 192 Topics for Discussion. 195 illustrations. Index.