Getting started with symmetry groups

In summary, the conversation is about the person's interest in learning about group theory in relation to quantum mechanics and their search for beginner-level resources or someone to explain the major concepts to them. A recommended resource is the book "A First Course In Abstract Algebra" by John Fraleigh, which covers important topics such as groups, subgroups, homomorphisms, and group actions.
  • #1
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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  • #2
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).
 

1. What are symmetry groups?

Symmetry groups are mathematical structures that describe the symmetries of an object or system. They are groups of transformations that leave the object or system unchanged, such as rotations, reflections, and translations.

2. How do I identify the symmetry group of an object?

To identify the symmetry group of an object, you need to examine its symmetries and determine which transformations leave the object unchanged. Then, you can use mathematical tools such as group theory to classify the symmetries and determine the symmetry group.

3. What is the importance of symmetry groups in science?

Symmetry groups have many practical applications in science, including in physics, chemistry, and biology. They help us understand the underlying structure and properties of objects and systems, and can be used to predict and analyze various phenomena.

4. How do symmetry groups relate to crystal structures?

Symmetry groups play a crucial role in describing and classifying the different types of crystal structures. Each crystal structure has a specific symmetry group that determines its physical and chemical properties.

5. Can symmetry groups be applied to other fields besides science?

Yes, symmetry groups have applications in various fields such as art, architecture, and music. They can be used to create aesthetically pleasing designs, analyze patterns, and understand the underlying structure of artistic works.

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