Symmetries (Springer Undergraduate Mathematics Series) [Paperback]

D.L. Johnson (Author)

Book Description

Publication Date: February 11, 2004 | Series: Springer Undergraduate Mathematics Series

The main  object of study for this book is geometry, with group theory providing an appropriate language in which to express geometrical ideas.  Key features include: An overview of the preliminaries from group theory and geometry Coverage of the discrete subgroups of the Euclidean group A clear and complete derivation and classification of the 17 plane crystallographic groups Tessellations of various spaces (they are constructed, described and classified) A brief introduction to hyperbolic geometry.  Each chapter contains a number of exercises, most with solutions, and suggestions for background, alternative and further reading.  The author's accessible and down-to-earth approach make this an ideal introduction for readers in the second or third year of a mathematics undergraduate course.  It is also recommended for mechanical engineers, architects, physicists and crystallographers needing an understanding of 3-dimensional geometry, symmetry and trigonometry.

Editorial Reviews

Review

From the reviews: MATHEMATICAL REVIEWS "This book is an inviting exposition to basic group theory and geometry and the close relationship between both in the context of studying symmetries. The approach taken by the author as well as the topics included and the many exercises present make it an excellent book for undergraduates, and not only in mathematics…The contents, the style, the accessibility, the examples and exercises and to do’s make this book a highly recommended introductory work for anybody having an interest in understanding geometrical ideas through a group theory language." "The study of symmetry by means of group theory is an especially suited topic for undergraduates. The author treats mainly plane geometry ... . The group theoretical material is developed from scratch and goes finally beyond the usual topics ... . Also the throughout consequent use of group theoretic arguments is not commonplace. All in all a very recommendable book for undergraduates." (G. Kowol, Monatshefte für Mathematik, Vol. 139 (1), 2003) "D. L. Johnson’s Symmetries is based on lecture courses for mathematics students at Nottingham University and at the University of the West Indies, and is written in a friendly style. Some sections will also be of interest to physicists and crystallographers. Prerequisite knowledge is limited to a good understanding of sets and functions ... . Each chapter has a number of exercises." (Nigel Steele, Times Higher Education Supplement, November, 2002) "This book is an inviting exposition to basic group theory and geometry and the close relationship between both in the context of studying symmetries. The approach taken by the author as well as the topics included and the many exercises present make it an excellent book for undergraduates, and not only in mathematics. ... The contents, the style, the accessibility, the examples and the exercises and to do’s make this book a highly recommended introductory work ... ." (Paul Igodt, Mathematical Reviews, Issue 2001 m) "The book studies geometry via group theory to express geometric ideas. ... It offers complete derivation and classification of the 17 plane crystallographic groups and guides suggestion to further reading. Each chapter contains a number of exercises, most with solutions. This book is suitable for all undergraduate geometry courses and for architects, physicists and crystallographers needing an understanding of 3-dimensional geometry, symmetry and trigonometry." (Jozef Fiamcik, Zentralblatt MATH, Vol. 980, 2002) "The main object of study for this book is geometry, with group theory providing an appropriate language in which to express geometrical ideas. Key features include: An overview of the preliminaries from group theory and geometry; ... a clear and complete derivation and classification of the 17 plane crystallographic groups; tessellations of various spaces (they are constructed, described and classified), a brief introduction to hyperbolic geometry. Each chapter contains a number of exercises, most with solutions, and suggestions for background, alternative and further reading." (L’Enseignement Mathematique, Vol. 47 (3-4), 2001)

Product Details

• Paperback: 227 pages
• Publisher: Springer; Corrected edition (February 11, 2004)
• Language: English
• ISBN-10: 1852332700
• ISBN-13: 978-1852332709
• Product Dimensions: 9 x 7.3 x 0.5 inches
• Shipping Weight: 12.8 ounces (View shipping rates and policies)
• Amazon Best Sellers Rank: #1,699,720 in Books (See Top 100 in Books)

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