Good introductory textbooks for group theory

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Discussion Overview

The discussion revolves around recommendations for introductory textbooks on group theory, with a particular focus on representation theory, suitable for an undergraduate studying theoretical physics. Participants share their experiences with various texts and express their needs for both conceptual understanding and formal exposition.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks recommendations for a formal textbook to accompany "Visual Group Theory" by Carter, emphasizing the need for a solid understanding of representation theory.
  • The same participant expresses dissatisfaction with previous texts, including Hammermesh and Raymond, citing their difficulty in understanding representation theory and finding some explanations odd or too advanced.
  • Another participant suggests "Ramond" as a good option and mentions "Ehrlich" as a potential preliminary text, although it lacks representation theory.
  • A different participant recommends "Smirnov, Higher Mathematics vol. III/1" for its coverage of linear algebra and group-representation theory, although they are uncertain about its availability in English.
  • One participant lists several recommended texts for theoretical physics, including "Lie Algebras in Particle Physics" by Georgi, "Group Theory" by Ramond, and "Lie Groups, Physics and Geometry" by Gilmore, along with a concise recommendation for "Symmetries and Conservation Laws in Particle Physics" by Haywood.
  • There is a suggestion that if financial constraints exist, "Haywood" and "Georgi" should be prioritized.

Areas of Agreement / Disagreement

Participants present multiple competing views on which textbooks are most suitable, and there is no consensus on a single recommended text. The discussion remains unresolved regarding the best approach to learning group theory in the context of theoretical physics.

Contextual Notes

Some participants express specific needs based on their background in theoretical physics, which may influence their textbook recommendations. There are also varying levels of familiarity with the texts mentioned, leading to differing opinions on their appropriateness for undergraduates.

steve0606
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Hi there. Can anybody recommend a good textbook for an undergraduate wanting to study group theory (especially representation theory). I'm thinking of reading "visual group theory" by Carter for conceptual understanding but I also need a book to study alongside this that gives a more formal exposition.

I took a class at university that involved group theory but I bombed it! (Ended up with a D) Mostly because I struggled to understand representation theory (especially irreps) in detail.

Im now taking a class in Lie algebras and Lie groups (at graduate level) next year but of course I want/need to gain a solid understanding of the basics! I tried hammermesh but I found it quite strange (the explanation he gives for representations is very odd I found!) and also Raymond which I found too advanced, given I was an undergrad at the time.

Many thanks!
 
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Sorry, I should also mention that I'm studying theoretical physics (not mathematics).
 
Ramond looks really good to me. Are you also considering getting a book to use before Ramond? This one by Ehrlich looks really nice (no representation theory though).
 
I don't know, whether it is available in English, but I like Smirnov, Higher Mathematics vol. III/1 very much, of which I know the German edition. It covers linear algebra and group-representation theory for the physically important groups (rotation group, Lorentz group).
 
I would suggest the following 3 books are very good for theoretical physics;

1: Lie Algebras in Particle physics--Georgi
2: Group Theory--Ramond
3: Lie Groups, Physics and geometry --Gilmore

a concise and very good book for Lie Algebras is
Symmetries and Conservation Laws in particle Physics--Haywood.

If finance is the problem then get the Haywood and Georgi in anycase.
 

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