Groups and Symmetry

Abstract

These notes were designed to fit the syllabus of the course "Groups and Symmetries", taught at Nanyang Technological University in autumn 2012, and 2013. Many thanks to Dr. Nadya Markin and Fuchun Lin for reading these notes, finding things to be fixed, proposing improvements and extra exercises. Many thanks as well to Yiwei Huang who got the thankless job of providing a first latex version of these notes. These notes went through several stages: handwritten lecture notes (later on typed by Yiwei), slides, and finally the current version that incorporates both slides and a cleaned version of the lecture notes. Though the current version should be pretty stable, it might still contain (hopefully rare) typos and inaccuracies. Relevant references for this class are the notes of K. Conrad on planar isometries [3, 4], the books by D. Farmer [5] and M. Armstrong [2] on groups and symmetries, the book by J. Gallian [6] on abstract algebra. More on solitaire games and palindromes may be found respectively in [1] and [7]. The images used were properly referenced in the slides given to the students , though not all the references are appearing here. These images were used uniquely for pedagogical purposes.