Geometry and Symmetry

Nonfiction, Science & Nature, Mathematics, Combinatorics, Geometry
Cover of the book Geometry and Symmetry by Paul B. Yale, Dover Publications
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Author: Paul B. Yale ISBN: 9780486169323
Publisher: Dover Publications Publication: May 5, 2014
Imprint: Dover Publications Language: English
Author: Paul B. Yale
ISBN: 9780486169323
Publisher: Dover Publications
Publication: May 5, 2014
Imprint: Dover Publications
Language: English

This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.
Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on "practical geometry," emphasizing topics and techniques of maximal use in all areas of mathematics. These topics include:
Algebraic and Combinatoric Preliminaries
Isometries and Similarities
An Introduction to Crystallography
Fields and Vector Spaces
Affine Spaces
Projective Spaces
Special features include a spiral approach to symmetry; a review of the algebraic prerequisites; proofs which do not appear in other texts, such as the Polya-Burnside theorem; an extensive bibliography; and a large collection of exercises together with suggestions for term-paper topics. In addition, special emphasis is placed on the geometric significance of cosets and conjugates in a group.

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This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.
Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on "practical geometry," emphasizing topics and techniques of maximal use in all areas of mathematics. These topics include:
Algebraic and Combinatoric Preliminaries
Isometries and Similarities
An Introduction to Crystallography
Fields and Vector Spaces
Affine Spaces
Projective Spaces
Special features include a spiral approach to symmetry; a review of the algebraic prerequisites; proofs which do not appear in other texts, such as the Polya-Burnside theorem; an extensive bibliography; and a large collection of exercises together with suggestions for term-paper topics. In addition, special emphasis is placed on the geometric significance of cosets and conjugates in a group.

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