Symmetry: A Very Short Introduction

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 is governed 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.

Author description

Ian Stewart is Emeritus Professor of Mathematics at Warwick University. He is the author of over 80 books, including Does God Play Dice?: The New Mathematics of Chaos, Flatterland, From Here to Infinity, and several collections of his highly popular math columns from Scientific American. He won the Michael Faraday Prize in 1995 and was elected as a Fellow of the Royal Society in 2001.

Table of contents

Introduction ; 1. What is symmetry? ; 2. Origins of symmetry ; 3. Types of symmetry ; 4. Structure of groups ; 5. Groups and games ; 6. Nature's patterns ; 7. Nature's laws ; 8. Atoms of symmetry ; Further reading ; References