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on 12 September 2016
I have a degree in Maths - and can confirm some of this book is at the final year of an undergraduate degree level, so not for the faint hearted. I thought some of it was very hard going but as usual with Ian Stewart it's a lovely, fluent read nonetheless. If you want to understand, or try to understand, the wonders of abstract algebra (i.e. Group Theory and similar topics) buy it. But don't expect to understand everything!
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on 30 August 2014
Not quite the 'symmetry' that I thought it was, more a simplified mathematical text to shape functions, but useful though.
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on 22 May 2016
possibly too intense for an introduction
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on 8 August 2014
Fabulous book Professor Ian Stewart.

One comment though, shouldn't there be two of them? ;)
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on 29 January 2017
A good book for those mathematically equipped to follow the text - but it's not written for a general reader looking for an introduction to symmetry. You have to wonder if the author understood the intended audience and general purpose of the oup"s short introductions . Buy it as a novice to the subject, only if youre prepared to work hard and supplement the text with other reading (to make up for the lack of care and consideration of the mathematically uninitiated) - But then again if youre game for an introduction that takes you into some maths then you might be better off with something like Hermann Weyl's Symmetry - very well written with everthing from sea creatures to space-time and even packing problems (if youre into that sort of thing) - with lots and lots of photos and diagrams of symmetry - if you dont get the maths first time - you can still flick through and enjoy the pics...
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VINE VOICEon 7 January 2014
Format: Paperback|Vine Customer Review of Free Product( What's this? )
I would have liked books like this when I was studying at university nearly forty years ago. This one provides a useful commentary on the concept of symmetry. However, the brevity of the book's coverage is both a strength and a weakness. You don't purchase a book in thie excellent OUP series expecting to read a comprehensive and revelatory discussion on the concept. What these books do provide is an excellent summary. The clue is in the strap line: 'very short introductions'. So I would argue any volume in the series should be reviewed with this caveat in mind - hence my five stars. The book provides an insightful summary of the concept of symmetry, and it is more than evident that Ian Stewart knows about this subject. So if you're not studying for a degree or even revising for an exam but want a starting point for finding out more about this subject then this slim volume provides an excellent starting point. It is well written, erudite and engaging.
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VINE VOICEon 1 July 2013
Format: Paperback|Vine Customer Review of Free Product( What's this? )
You may be under the misapprehension that this book is an introduction to symmetry for laymen with no knowledge of mathematics. That is wrong! Pretty early on, it is clear that you will at least have to Google what a catenary is (the shape of a hanging chain held at two ends) and know what a sine wave is (a basic periodic curve, with period 2π radians). This is pretty elementary stuff, but if you aren't prepared for it you will get lost almost immediately.

Having said that, Stewart lost me temporarily on page 9 with his rainbow explanation. The problem is a lack of diagrams at this point, and I think he should either expand or drop this example. This is true for a lot of other examples: if you don't know what a catenary is, it is introduced in a joking way and is not essential to what follows. (Square wheels on inverted catenary rutted roads!)

Chapter 2 introduces the reader to the idea of a mathematical Group. Symmetries form groups, groups are all permutation groups, and can all be represented by matrices, at least in the finite case, but can be treated in the abstract, with any general properties then saying something fundamentally useful about permutations and symmetries.

In Chapter 3, probably the most accessible chapter, we see the fundamental frieze and wallpaper patterns, as well as the regular solids like the icosahedron. Frieze patterns are perhaps old-fashioned now, but people used to stick things called borders on their walls. These were thin strips with a repeating pattern. There are only 7 types. At this point, there is a blip in the book, where these 7 are illustrated, and due to the way they are compressed onto one page, with no indication where one ends and another starts, there appear only to be 6. Dividers should have been inserted. However, those horizontal lines that appear to be dividers are in fact part of the friezes, so to get 7 patterns, take the following rows: 1, 2+3, 4+5, 6, 7, 8+9, 10.

When it comes to wallpapers, with repeating patterns, there are just 17 of them. Yes, I know, the catalogues show far more but in terms of regular repetition, ignoring the actual pattern that is repeated, there are just 17. There are just 5 regular solids, and when it comes to crystal structures, just 14. These are fascinating bits of trivia to bore your friends with!

Chapter 4 looks at the abstract structure of groups and an important idea, conjugacy. You may not know this, but if you have learned how to solve a Rubik cube, you already know about conjugacy. This is in fact covered in Chapter 5, which also looks at Sudoku grids and their number. Don't believe any App that says it gives unlimited numbers of grids!

Chapter 6 covers natural symmetries, and the layman will have no trouble with understanding it. Unfortunately, there follow Chapters 7 and 8 that again become too technical, introducing the symmetries of particles and the classification of so-called simple groups.

So, a mathematician will understand everything in this book apart from that wretched rainbow explanation. For the layman, read it, but skip over anything you don't understand, as it is unlikely to come back and haunt you later. (The opposite is generally true for formal mathematical textbooks!)

Stewart touches briefly on some of his own research interests, including gaits, in the area of catastrophe theory.

It's cheap, it's funny, sometimes frustrating, but well worth buying, reading and leaving on the coffee table before inviting friends round.

[Oh, and for the record, I have three degrees in mathematics and found this mostly very easy reading. It is about 135 pages long but they are only A6 pages.]
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HALL OF FAMETOP 500 REVIEWERon 17 October 2013
Format: Paperback|Vine Customer Review of Free Product( What's this? )
I received this free through the Amazon Vine review programme.

I'm not by any means a Mathematician, however I did 'A' Level Maths, and occasionally have had recourse to statistics in producing a Linguistics-based PhD, I've also bought several titles from the 'Very Short Introduction' series in the past... so I didn't expect to find this entry quite as challenging as it proved.

This is far from a brief work. The 160 pages to this work are densely crammed with theory that goes far beyond 'A' level standard. The book is written in a really small, dense font face - it could easily and quite respectably have been produced in a much larger format. The topic is interesting, but quickly becomes quite complex. An introduction it might be, but perhaps only if this is being assessed at the academic level.

For the retail/Amazon price this can be an extremely good value work. But it most assuredly is NOT an accessible introductory title.
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TOP 500 REVIEWERVINE VOICEon 30 December 2013
Format: Paperback|Vine Customer Review of Free Product( What's this? )
Professor Ian Stewart is noted for his books popularising mathematics, and is one of the authors of the acclaimed 'Science of Discworld' series.
Here he tackles symmetry, leading on from the basic concepts of symmetries through group theory and its theorems, including the leisure uses of group theory, such as the Rubik Cube and Sudoku.

There is a fascinating section on Nature and symmetry - worth the purchase price alone - leading on to Nature's laws, with an introduction to Noether's theorem and continuous symmetry (Lie Theory). Stewart shows how these link to the more relatively recent developments in mathematical theory, such as classification theorems, expander families and Cayley graphs, which are briefly outlined. Computer science students who need to know the basics of expander families for coding will find them neatly summarised here.
A neat pocket guide for students of advanced mathematics; particularly valuable is the further reading section.
Whilst the list relies extensively on Wikipedia for further reading online, there is also a quite extensive list of offline reading covering both populist approaches such as (Notes on Rubik's 'Magic Cube', (along with several of Stewart's own books) and the purer mathematical approach.
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VINE VOICEon 2 January 2014
Format: Paperback|Vine Customer Review of Free Product( What's this? )
I like the very short introduction series - I've read a few. They're not beginners' guides but rather dense and complete overviews.

I found this one to be below par. The beginning, discussing rainbows, relied heavily on a particular model of light (wave theory, rather than particle and let's not forget QED) and to be honest I wasn't sure it was a good way in nor clearly about symmetry. If one knew anything of the topic there was no need for such a soft intro, if a soft intro was considered necessary then the Open University got it right in M336 groups and geometry when using tesellations from Roman and Greek friezes (and, bizarrely, Heathrow)

From then on the book didn't create a journey I could follow. Which is not to say it was content free.
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