geometry from euclid to knots dover books on mathematics

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Geometry From Euclid To Knots

Author : Saul Stahl
ISBN : 9780486134987
Genre : Mathematics
File Size : 32. 86 MB
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This text provides a historical perspective on plane geometry and covers non-neutral Euclidean geometry, circles and regular polygons, projective geometry, symmetries, inversions, informal topology, and more. Includes 1,000 practice problems. Solutions available. 2003 edition.

Mathematics Old And New

Author : Saul Stahl
ISBN : 9780486807386
Genre : Mathematics
File Size : 73. 59 MB
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Introductory treatment for undergraduates provides insightful expositions of specific applications of mathematics and elements of mathematical history and culture. Topics include probability, statistics, voting systems game theory, geometry, Egyptian arithmetic, and more. 2016 edition.

A First Course In Geometry

Author : Edward T Walsh
ISBN : 9780486796680
Genre : Mathematics
File Size : 89. 52 MB
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Suitable for college courses, this introductory text covers the language of mathematics, geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, and space and coordinate geometry. 1974 edition.

Differential Geometry

Author : Erwin Kreyszig
ISBN : 9780486318622
Genre : Mathematics
File Size : 58. 5 MB
Format : PDF
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An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.

Differential Geometry

Author : Heinrich W. Guggenheimer
ISBN : 9780486157207
Genre : Mathematics
File Size : 38. 61 MB
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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.

Fundamental Ideas Of Analysis

Author : Michael C. Reed
ISBN : 0471159964
Genre : Mathematics
File Size : 35. 11 MB
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The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.

Foundations Of Hyperbolic Manifolds

Author : John Ratcliffe
ISBN : 9781475740134
Genre : Mathematics
File Size : 71. 55 MB
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This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.

An Interactive Introduction To Knot Theory

Author : Inga Johnson
ISBN : 9780486818740
Genre : Mathematics
File Size : 59. 6 MB
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This well-written and engaging volume, intended for undergraduates, introduces knot theory, an area of growing interest in contemporary mathematics. The hands-on approach features many exercises to be completed by readers. Prerequisites are only a basic familiarity with linear algebra and a willingness to explore the subject in a hands-on manner. The opening chapter offers activities that explore the world of knots and links — including games with knots — and invites the reader to generate their own questions in knot theory. Subsequent chapters guide the reader to discover the formal definition of a knot, families of knots and links, and various knot notations. Additional topics include combinatorial knot invariants, knot polynomials, unknotting operations, and virtual knots.

A Vector Space Approach To Geometry

Author : Melvin Hausner
ISBN : 9780486137858
Genre : Mathematics
File Size : 77. 39 MB
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This examination of geometry's correlation with other branches of math and science features a review of systematic geometric motivations in vector space theory and matrix theory; more. 1965 edition.

Deductive Geometry

Author : E.A. Maxwell
ISBN : 9780486809250
Genre : Mathematics
File Size : 55. 46 MB
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This concise review examines the geometry of the straight line, circle, plane, and sphere as well as their associated configurations, including the triangle and the cylinder. Aimed at university undergraduates, the treatment is also useful for advanced students at the secondary level. The straightforward approach begins with a recapitulation of previous work on the subject, proceeding to explorations of advanced plane geometry, solid geometry with some reference to the geometry of the sphere, and a chapter on the nature of space, including considerations of such properties as congruence, similarity, and symmetry. The text concludes with a brief account of the elementary transformations of projection and inversion. Numerous examples appear throughout the book.

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