Any recommendations for group theory books with applications in relativity?

In summary, the individual is looking for introductory books on group theory and algebra, specifically ones that are more in-depth than the one used in their class and have applications in physics. They also mention wanting a book with minimal assumed knowledge and ask for any recommendations. Two suggestions are Tinkham's "Group Theory and Quantum Mechanics" and Cotton's "Chemical Applications of Group Theory," with a third recommendation being Bunker and Jensen's "Molecular Symmetry and Spectroscopy" for its modern applications in molecular physics. The individual also asks for any books on applications of group theory in relativity.
  • #1
lizzie96'
26
5
Hello,

I’m looking for introductory books/notes on group theory and algebra. We are using “Groups” by Jordan and Jordan in class, but I am looking for something a little more in-depth. I wouldn’t mind a book that was entirely focused on the pure maths side but if it had lots of applications to physics that would be even better. Also, this is my first class in the subject so something without too much assumed knowledge of the subject would be good.

Thanks for any ideas!
 
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  • #2
lizzie96' said:
Hello,

I’m looking for introductory books/notes on group theory and algebra. We are using “Groups” by Jordan and Jordan in class, but I am looking for something a little more in-depth. I wouldn’t mind a book that was entirely focused on the pure maths side but if it had lots of applications to physics that would be even better. Also, this is my first class in the subject so something without too much assumed knowledge of the subject would be good.

Thanks for any ideas!

Tinkham "Group Theory and Quantum Mechanics" is a brief book with lots of applications
Cotton: Chemical Applications of Group Theory" is a classic for chemists
Bunker and Jensen "Molecular Symmetry and Spectroscopy" is a very good book with "modern" applications to molecular physics
 
  • #3
Thank you, I will have a look at those. Also, do you know of any books about applications of group theory in relativity?
 

FAQ: Any recommendations for group theory books with applications in relativity?

What is group theory?

Group theory is a branch of mathematics that studies the properties of groups, which are sets of elements that can be combined together using a binary operation (such as multiplication or addition). It is a fundamental concept in algebra and has applications in various fields such as physics, chemistry, and computer science.

What is an introductory group theory course like?

An introductory group theory course typically covers the basic concepts and properties of groups, such as group operations, subgroups, and group isomorphisms. It may also include topics like group actions, cosets, and the structure of finite groups. The course may involve both theoretical and computational exercises to help students understand and apply the concepts.

What are some real-life applications of group theory?

Group theory has applications in many areas of science and technology. In physics, it is used to study the symmetries of physical systems and to describe fundamental particles and their interactions. In chemistry, group theory is used to understand the symmetry of molecules and their electronic structures. It also has applications in cryptography, coding theory, and computer graphics.

How is group theory related to other branches of mathematics?

Group theory is closely related to other branches of mathematics, such as abstract algebra, number theory, and topology. It is also used in the study of other algebraic structures, such as rings, fields, and vector spaces. Many mathematical concepts and structures, such as symmetry, symmetry groups, and group actions, have their foundations in group theory.

Is group theory difficult to learn?

Like any branch of mathematics, group theory can be challenging to learn, but it is also a highly rewarding subject. It requires a solid understanding of algebra and mathematical reasoning, but with dedication and practice, it can be mastered by anyone. A good way to start learning group theory is by familiarizing yourself with the basic concepts and solving problems to strengthen your understanding.

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