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" ... many eminent scholars, endowed with great geometric talent, make a point of never disclosing the simple and direct ideas that guided them, subordinating their elegant results to abstract general theories which often have no application outside the particular case in question. Geometry was becoming a study of algebraic, differential or partial differential equations, thus losing all the charm that comes from its being an art." H. Lebesgue, Ler;ons sur les Constructions Geometriques, Gauthier� Villars, Paris, 1949. This book is based on lecture courses given to final-year students at the Uni� versity of Nottingham and to M.Sc. students at the University of the West Indies in an attempt to reverse the process of expurgation of the geometry component from the mathematics curricula of universities. This erosion is in sharp contrast to the situation in research mathematics, where the ideas and methods of geometry enjoy ever-increasing influence and importance. In the other direction, more modern ideas have made a forceful and beneficial impact on the geometry of the ancients in many areas. Thus trigonometry has vastly clarified our concept of angle, calculus has revolutionised the study of plane curves, and group theory has become the language of symmetry.
- Sales Rank: #4558729 in Books
- Brand: Brand: Springer
- Published on: 2013-10-04
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .49" w x 6.10" l, .68 pounds
- Binding: Paperback
- 198 pages
Features
- Used Book in Good Condition
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 f�r 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)
Most helpful customer reviews
1 of 1 people found the following review helpful.
Has the proofs, Lacks thorough explanation
By Skeptic
This book has its good and bad together. First the good:
It is correctly titled. That is not meant as a back handed complement, but sincerely. Too many books have a misleading title,
and it will lure you into buying a book you really didn't want. (We've all been there).
By that, I also mean that it delivers what it promises. You get a mathematical treatise on symmetry and enough information in there to use it, provided you already know group theory. As an added benefit the author also uses some humor along the way in what is usually considered a very dry subject matter, so that's another plus in favor of the book. Also, there's a very nice index of mathematical notation at the end of the book which I used frequently.
Where the book fails is on a few accounts: It just isn't beefy enough. It's too sketchy due to the lack of explanation. So, you'll get the information you want on mathematical symmetry, but the highly concentrated version, proof after proof after proof.
So, the prime complain is the light explanations. The book could easily have double the pages to make everything more concrete in the reader's mind. Other books on this subject matter have a "walk-through" style of writing. They take a known geometrical object, and analyze it using group theory. This book keeps it mostly abstract. Even the Wikipedia page gives you a walk-through on the symmetry of the square, and I found myself repeatedly referring to Wikipedia for more in-depth explanations of material the book was lacking. When I was reading about isomorphisms in a different book, that writer provided side-by-side tables of two different isomorphic groups, and the idea of an isomorphism was something very easy. That's the kind of writing that should have been in this book, but wasn't.
My other complaint is that no where does it say that you need to already know abstract algebra in order to understand this symmetry book. Well it does on the back cover in an off-hand way, when it says its for people that are in their second or third years of a mathematics undergraduate course. I'd rather that they spell it out: You must already know group theory for this book to be useful (despite the crash course in this book). Also, another problem is that the drawings could be better. You get a few drawings, but they don't spell out what's going on. Like figure 4.1. Where are the arrows showing where the point P gets mapped to? Then in the coverage of Platonic solids, why not show an icosahedron or a dodecahedron? Not everyone knows what they look like already.
So, overall, I have to give the book 3 stars. It somewhat succeeds in what it sets out to do, but lacks all the explanatory prose you'd expect out of a book (a textbook no less). If you're doing self-study then Symmetry by Roy McWeeny (kind of old, but still good), or maybe the Armstrong book would be good choices. They cover the material with a lot of prose, pictures, walk-through examples. Unfortunately, the DL Johnson book comes across as a lecture put to paper.
1 of 1 people found the following review helpful.
Five Stars
By Vitaly Zaderman
good
See all 2 customer reviews...
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