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 : 57. 24 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 : 59. 32 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.

Advanced Euclidean Geometry

Author : Roger A. Johnson
ISBN : CORNELL:31924107164471
Genre : Mathematics
File Size : 25. 95 MB
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For many years, this elementary treatise on advanced Euclidean geometry has been the standard textbook in this area of classical mathematics; no other book has covered the subject quite as well. It explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. Several hundred theorems and corollaries are formulated and proved completely; numerous others remain unproved, to be used by students as exercises. The author makes liberal use of circular inversion, the theory of pole and polar, and many other modern and powerful geometrical tools throughout the book. In particular, the method of "directed angles" offers not only a powerful method of proof but also furnishes the shortest and most elegant form of statement for several common theorems. This accessible text requires no more extensive preparation than high school geometry and trigonometry.

Problems And Solutions In Euclidean Geometry

Author : M. N. Aref
ISBN : 9780486477206
Genre : Mathematics
File Size : 56. 69 MB
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Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. Each chapter covers a different aspect of Euclidean geometry, lists relevant theorems and corollaries, and states and proves many propositions. Includes more than 200 problems, hints, and solutions. 1968 edition.

A First Course In Geometry

Author : Edward T Walsh
ISBN : 9780486796680
Genre : Mathematics
File Size : 67. 23 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.

Topology

Author : John G. Hocking
ISBN : 9780486141091
Genre : Mathematics
File Size : 50. 69 MB
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Superb one-year course in classical topology. Topological spaces and functions, point-set topology, much more. Examples and problems. Bibliography. Index.

The Green Book Of Mathematical Problems

Author : Kenneth Hardy
ISBN : 9780486169453
Genre : Mathematics
File Size : 22. 72 MB
Format : PDF
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Rich selection of 100 practice problems — with hints and solutions — for students preparing for the William Lowell Putnam and other undergraduate-level mathematical competitions. Features real numbers, differential equations, integrals, polynomials, sets, other topics. Hours of stimulating challenge for math buffs at varying degrees of proficiency. References.

Linear Algebra

Author : Georgi? Evgen?evich Shilov
ISBN : 048663518X
Genre : Mathematics
File Size : 50. 57 MB
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Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

Journey Into Mathematics

Author : Joseph J. Rotman
ISBN : 9780486151687
Genre : Mathematics
File Size : 21. 75 MB
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This treatment covers the mechanics of writing proofs, the area and circumference of circles, and complex numbers and their application to real numbers. 1998 edition.

Foundations Of Hyperbolic Manifolds

Author : John Ratcliffe
ISBN : 9781475740134
Genre : Mathematics
File Size : 57. 92 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.

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