Invitation to Geometry

Author: Z. A. Melzak

Publisher: Courier Corporation

ISBN: 0486789489

Category: Mathematics

Page: 240

View: 907

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Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. Only a slight acquaintance with mathematics beyond the high-school level is necessary, including some familiarity with calculus and linear algebra. This text's introductions to several branches of geometry feature topics and treatments based on memorability and relevance. The author emphasizes connections with calculus and simple mechanics, focusing on developing students' grasp of spatial relationships. Subjects include classical Euclidean material, polygonal and circle isoperimetry, conics and Pascal's theorem, geometrical optimization, geometry and trigonometry on a sphere, graphs, convexity, and elements of differential geometry of curves. Additional material may be conveniently introduced in several places, and each chapter concludes with exercises of varying degrees of difficulty.

Differential Geometry

Author: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 9780486667218

Category: Mathematics

Page: 352

View: 1418

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

Linear Geometry

Author: Rafael Artzy

Publisher: N.A

ISBN: 9780486466279

Category: Mathematics

Page: 273

View: 4671

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Most linear algebra texts neglect geometry in general and linear geometry in particular. This text for advanced undergraduates and graduate students stresses the relationship between algebra and linear geometry. It begins by using the complex number plane as an introduction to a variety of transformations and their groups in the Euclidean plane, explaining algebraic concepts as they arise. A brief account of Poincaré's model of the hyperbolic plane and its transformation group follow. Succeeding chapters contain a systematic treatment of affine, Euclidean, and projective spaces over fields that emphasizes transformations and their groups, along with an outline of results involving other geometries. An examination of the foundations of geometry starts from rudimentary projective incidence planes, then gradually adjoins axioms and develops various non-Desarguesian, Desarguesian, and Pappian planes, their corresponding algebraic structures, and their collineation groups. The axioms of order, continuity, and congruence make their appearance and lead to Euclidean and non-Euclidean planes. Lists of books for suggested further reading follow the third and fourth chapters, and the Appendix provides lists of notations, axioms, and transformation groups.

Geometry: A Comprehensive Course

Author: Dan Pedoe

Publisher: Courier Corporation

ISBN: 0486131734

Category: Mathematics

Page: 464

View: 4629

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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.

Introduction to Projective Geometry

Author: C. R. Wylie

Publisher: Courier Corporation

ISBN: 0486141705

Category: Mathematics

Page: 576

View: 9578

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This introductory volume offers strong reinforcement for its teachings, with detailed examples and numerous theorems, proofs, and exercises, plus complete answers to all odd-numbered end-of-chapter problems. 1970 edition.

Geometry of Complex Numbers

Author: Hans Schwerdtfeger

Publisher: Courier Corporation

ISBN: 0486135861

Category: Mathematics

Page: 224

View: 401

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Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Differential Geometry

Author: Heinrich W. Guggenheimer

Publisher: Courier Corporation

ISBN: 0486157202

Category: Mathematics

Page: 400

View: 8494

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This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.

Introductory Non-Euclidean Geometry

Author: Henry Parker Manning

Publisher: Courier Corporation

ISBN: 0486154645

Category: Mathematics

Page: 112

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This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.

Coordinate Geometry

Author: Luther Pfahler Eisenhart

Publisher: Courier Corporation

ISBN: 0486442616

Category: Mathematics

Page: 298

View: 3962

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A thorough, complete, and unified introduction, this volume affords exceptional insights into coordinate geometry. Invariants of conic sections and quadric surfaces receive full treatments. Algebraic equations on the first degree in two and three unknowns are carefully reviewed. Throughout the book, results are formulated precisely, with clearly stated theorems. More than 500 helpful exercises. 1939 edition.

Fundamental Concepts of Geometry

Author: Bruce E. Meserve

Publisher: Courier Corporation

ISBN: 048615226X

Category: Mathematics

Page: 336

View: 3811

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Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

Taxicab Geometry

An Adventure in Non-Euclidean Geometry

Author: Eugene F. Krause

Publisher: Courier Corporation

ISBN: 048613606X

Category: Mathematics

Page: 96

View: 6748

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Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problems.

A Geometric Introduction to Topology

Author: Charles Terence Clegg Wall

Publisher: Courier Corporation

ISBN: 0486678504

Category: Mathematics

Page: 168

View: 9699

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First course in algebraic topology for advanced undergraduates. Homotopy theory, the duality theorem, relation of topological ideas to other branches of pure mathematics. Exercises and problems. 1972 edition.

Invitation to Combinatorial Topology

Author: Maurice Fréchet,Ky Fan

Publisher: Courier Corporation

ISBN: 0486147886

Category: Mathematics

Page: 136

View: 4365

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Elementary text, accessible to anyone with a background in high school geometry, covers problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, topological polygons, more. Includes 108 figures. 1967 edition.

Mathematics and Logic

Author: Mark Kac,Stanislaw M. Ulam

Publisher: Courier Corporation

ISBN: 0486670856

Category: Philosophy

Page: 170

View: 4688

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Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

Mathematics and the Physical World

Author: Morris Kline

Publisher: Courier Corporation

ISBN: 0486136310

Category: Mathematics

Page: 512

View: 4148

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Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

Tensor Analysis on Manifolds

Author: Richard L. Bishop,Samuel I. Goldberg

Publisher: Courier Corporation

ISBN: 0486139239

Category: Mathematics

Page: 288

View: 8790

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DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div

Concepts of Modern Mathematics

Author: Ian Stewart

Publisher: Courier Corporation

ISBN: 0486134954

Category: Mathematics

Page: 368

View: 5630

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In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

Geometry, Relativity and the Fourth Dimension

Author: Rudolf Rucker

Publisher: Courier Corporation

ISBN: 0486140334

Category: Science

Page: 160

View: 4191

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Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.

The Beauty of Geometry

Twelve Essays

Author: H. S. M. Coxeter,Harold Scott Macdonald Coxeter

Publisher: Courier Corporation

ISBN: 0486409198

Category: Mathematics

Page: 274

View: 772

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Absorbing essays demonstrate the charms of mathematics. Stimulating and thought-provoking treatment of geometry's crucial role in a wide range of mathematical applications, for students and mathematicians.