Getting started with symmetry groups

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    Groups Symmetry
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SUMMARY

The discussion centers on the foundational concepts of symmetry groups, particularly Lie groups and SU groups, essential for understanding quantum mechanics. A recommended resource is "A First Course In Abstract Algebra" by John Fraleigh, which serves as an introductory text for group theory. Key topics covered in the book include Groups & Subgroups, Permutations, Cosets, Direct Products, Homomorphisms, Factor Groups, Sylow Theorems, and Group Actions. These concepts are crucial for anyone delving into the mathematical framework of physics.

PREREQUISITES
  • Basic understanding of group theory concepts
  • Familiarity with algebraic structures
  • Knowledge of quantum mechanics fundamentals
  • Ability to interpret mathematical texts
NEXT STEPS
  • Study "A First Course In Abstract Algebra" by John Fraleigh for foundational group theory
  • Explore online tutorials on Lie groups and their applications in physics
  • Research the Fundamental Theorem for Finitely Generated Abelian Groups
  • Learn about the Sylow Theorems and their significance in group theory
USEFUL FOR

This discussion is beneficial for physics students, mathematicians, and anyone interested in the mathematical foundations of quantum mechanics, particularly those seeking to understand symmetry groups and their applications.

trini
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Hey guys, I've been doing a lot of reading on quantum mechanics lately and realized immediately that i am not going to get far without first understanding the meanings of lie groups, SU groups etc. Now I've loked at wiki but unfortunately wiki is not a very good tool for learning math, it's more so for ppl who were taught and need to brush up on rules. my question is, do you have any good links where i can find simple descriptions of group theory(or at least a beginner level tutorial). or maybe some kind soul will feel bored enough to explain the major concepts to me(i'm mostly interested in physics related matter).

anyways guys cheers!
 
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A First Course In Abstract Algebra by John Fraleigh is a good introduction to groups and is used as a text for many first courses in group theory. It's best suited if you haven't heard of things like the Fundamental Theorem for Finitely Generated Abelian groups and similar things. Even if you can't find it, you can use the table of contents as an indicator of what a beginner should know for group theory (the important sections are: Groups & Subgroups, Permutations, Cosets, & Direct Products, Homomorphisms & Factor Groups, Sylow Theorems, and Group Actions).
 

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