Groups Around Us
by Pavel Etingof
Publisher: Massachusetts Institute of Technology 2018
Number of pages: 25
These are notes of a mini-course of group theory for high school students that I gave in the Summer of 2009. This mini-course covers the most basic parts of group theory with many examples and applications. The notes contain many exercises, which are necessary for understanding the main text.
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by F. J. Yndurain - arXiv
The following notes are the basis for a graduate course. They are oriented towards the application of group theory to particle physics, although some of it can be used for general quantum mechanics. They have no pretense of mathematical rigor.
by E. Lee Lady - University of Hawaii
Contents: Modules Over Commutative Rings; Fundamentals; Rank-one Modules and Types; Quasi-Homomorphisms; The t-Socle and t-Radical; Butler Modules; Splitting Rings and Splitting Fields; Torsion Free Rings; Quotient Divisible Modules; etc.
by Michael Ruzhansky, Ville Turunen - Aalto TKK
Contents: Groups (Groups without topology, Group actions and representations); Topological groups (Compact groups, Haar measure, Fourier transforms on compact groups..); Linear Lie groups (Exponential map, Lie groups and Lie algebras); Hopf algebras.
by Frank W. K. Firk - Orange Grove Texts Plus
This is an introduction to group theory, with an emphasis on Lie groups and their application to the study of symmetries of the fundamental constituents of matter. The text was written for seniors and advanced juniors, majoring in the physical sciences.