Please show me some group theory books

In summary, group theory is a branch of mathematics that studies the algebraic structures called groups. It has a wide range of applications in various fields and provides a powerful framework for understanding symmetry and patterns in nature. Some recommended books for learning group theory include "Abstract Algebra" by David S. Dummit and Richard M. Foote, "Group Theory: A Physicist's Survey" by Pierre Ramond, and "A Course in Group Theory" by John F. Humphreys. The best way to learn group theory is by studying the fundamental concepts and practicing solving problems, and there are also many online resources available for learning, such as Khan Academy, MIT OpenCourseWare, and YouTube channels like MathDoctorBob and Professor Leonard.
  • #1
ndung200790
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Please show me some group theory books that considering the combination of quantum mechanics and relativity theory that leads to the needing of notion of fields.I have heard that the irreducible representation of Poicare group leading to the infinite dimensions representation(meaning field notion).Which books consider that problem?
 
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  • #2
All of them. People get attracted by the second chapter of Weinberg's book, though.
 

1. What is group theory?

Group theory is a branch of mathematics that studies the algebraic structures called groups. A group is a set of elements with a binary operation that satisfies certain properties, such as closure, associativity, identity, and inverse.

2. Why is group theory important?

Group theory has a wide range of applications in various fields, including physics, chemistry, biology, computer science, and cryptography. It provides a powerful framework for understanding symmetry and patterns in nature and has led to many significant discoveries and advancements in these fields.

3. What are some recommended books on group theory?

Some popular books on group theory include "Abstract Algebra" by David S. Dummit and Richard M. Foote, "Group Theory: A Physicist's Survey" by Pierre Ramond, and "A Course in Group Theory" by John F. Humphreys. These books cover different levels of difficulty, so it's essential to choose one that suits your needs and background.

4. How can I learn group theory?

The best way to learn group theory is by studying the fundamental concepts and practicing solving problems. You can start by reading a textbook or taking an online course on group theory. It's also helpful to join a study group or seek guidance from a mentor who is knowledgeable in the subject.

5. Are there any online resources for learning group theory?

Yes, there are several online resources for learning group theory, such as Khan Academy, MIT OpenCourseWare, and YouTube channels like MathDoctorBob and Professor Leonard. You can also find lecture notes, practice problems, and quizzes on websites like Brilliant and Math StackExchange.

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