Symmetry: A Very Short Introduction (Very Short Introductions) 1st Edition by Ian Stewart (PDF)

Description

In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics isgoverned by symmetries in the laws of nature.It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book deserves five stars for its broad coverage of a very interesting subject, and one star for its dense mathematical presentation of that topic. Reading it is like drifting into a graduate-level seminar on group theory that first enticed you in with its catchy title. Every chapter starts with an interesting presentation of a fascinating aspect of symmetry, from Islamic art to the regular gaits of animals, from Rubik’s cube to the symmetry of the laws of nature. Soon enough, though, you start running into the sentences such as “A cycle is a permutation of distinct numbers X1,…,Xm that sends Xj to Xj+1 if 1 <= j <= m-1, and sends Xm to X1." Or from the Rubik's cube section discussing the permutations of the cube: "These invariants correspond to three homomorphisms from the potential symmetry group G to Z2,Z2 and Z3 respectively. They therefore correspond to three normal subgroups N1, N2 and N3, whose orders are respectively |G|/2, |G|/2, and |G|/3. As already observed, in different language, N1 and N2 are different. The same goes for N3 because 3 is prime to 2. Basic group theory now tells us that the intersection N = N1 ^ N2 ^ N3 is a normal subgroup of G and |N| = |G|/12. (Here 12 = 2.2.3.)"If you're nodding your head in agreement with that last quote, you will find this book to be a great 5-star broad-brush exploration of the mathematical foundations of symmetry and its applications to the real world. On the other hand, if you're not conversant in the terminology and symbology of group theory (as I'm not) you're scratching your head thinking 'WTF?' This book primarily investigates symmetry in its mathematical sense, and for its important role in developing group theory. Like many math professors, the author treats the actual physical world and its various manifestations of symmetry as a corner-case starting point from which a more pure conceptual view can be derived. If that's what you're looking for, great. Otherwise, be prepared for a tough slog. ⭐This is the second very short introduction I read written by Ian Stewart, and my third "very short introduction". My first VSI was on Wittgenstein, and this was a great book for someone who enjoyed (but did not major in) philosophy in college. This was great in helping me get past Wittgenstein, at least with a finite lifetime and spare time availalble.The second VSI was Stewart's "Infinity", which I received as a gift. I expected to be somewhat bored, but I should have known better given Steward as an author. I did know a great deal of it, but there was a lot I learned - I thoroughly enjoyed the experience.This book was in a subject (group theory) that I'm still expanding my knowledge of, and it is fantastic. As a warning, it is a gateway to Stewart's other books (Galois theory - which I'm also enjoying). I have always like Dr. Stewart's writing (starting from Scientific American, way back). ⭐A+ ⭐Physics concepts were OK. ⭐Ian Stewart is the greatest teacher of Math today. In this very too short introduction to one of the most aesthetic, most usefuland most fruitful concepts of Human Thought, he succeeds to completely describing and explaining it, more simply than possible, sothat more people may enjoy the beauty and complexity of Symmetry. Very well done! ⭐Dr. Steward does what he always does, clear and complete exposition even in a 'very short' format. Worth every penny. ⭐A very disappointing book. Very misleading Title. There was nothing introductory about this book. It was intended for advanced physicists and mathematicians. ⭐Book is as described. Prompt delivery. ⭐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! ⭐Not quite the 'symmetry' that I thought it was, more a simplified mathematical text to shape functions, but useful though. ⭐Fabulous book Professor Ian Stewart.One comment though, shouldn't there be two of them? 😉 ⭐possibly too intense for an introduction ⭐A ready reference book in a short time.

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