Looking for a book on Modern Algebra

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For an advanced undergraduate in Physics seeking an engaging introduction to modern algebra, several book recommendations emerged. Fraleigh's book is highlighted as a solid choice, particularly older editions for their clarity. Additionally, Flanders' mathematical physics texts are suggested for those interested in group theory relevant to physics. "A First Course in Abstract Algebra" is praised for its beginner-friendly approach, while Dummit and Foote's "Abstract Algebra" is noted for its comprehensive and well-written content. Mac Lane and Birkhoff's "Algebra" is also recommended for its rigorous treatment of various algebraic structures.
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Hi. I'm an advanced undergrad in Physics but I am interested in reading something about modern algebra and possibly, modern math research, in my free time. I'm looking for something that will be informal enough that I can read it easily and not get bored but also with enough detail to represent the subjects. (A lot of actual math in it would be okay with me, as long as the written text is good enough.) Does anyone have any suggestions of a book like this?

-Thanks!
 
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I would recommend https://www.amazon.com/dp/0201763907/?tag=pfamazon01-20 by Fraleigh. You'll probably be able to find an old edition cheaper, and I think they're probably better than the newer ones. The book has changed quite a bit from the earlier editions. Learning some linear algebra (not just matrix algebra) would be helpful as well.

I'm not for sure of any introductory group theory books aimed at physicists though. You might try some mathematical physics books. Two good books are https://www.amazon.com/dp/9810220340/?tag=pfamazon01-20 by Flanders. Learning this material before graduate school would be very helpful, especially if you plan on going into theoretical physics.
 
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Ok, thanks for the recommendations and links! I will check those out...
 
n!kofeyn said:
I would recommend https://www.amazon.com/dp/0201763907/?tag=pfamazon01-20 by Fraleigh. You'll probably be able to find an old edition cheaper, and I think they're probably better than the newer ones. The book has changed quite a bit from the earlier editions. Learning some linear algebra (not just matrix algebra) would be helpful as well.

I'm not for sure of any introductory group theory books aimed at physicists though. You might try some mathematical physics books. Two good books are https://www.amazon.com/dp/9810220340/?tag=pfamazon01-20 by Flanders. Learning this material before graduate school would be very helpful, especially if you plan on going into theoretical physics.

I've gone through about the first 35 sections of "A First Course in Abstract Algebra" and it is definitely a great book for the beginner. The first few sections are an excellent primer to group theory and if you find you're itching for a bit more, Dummit and Foote's "Abstract Algebra" is not only filled with information (almost encyclopedic) but also very well written.
 
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I'd recommend Mac Lane and Birkhoff's "Algebra". It was my first modern algebra book and it is fantastic; covering categories, lattices, groups, rings, fields, and linear and multilinear algebra in a concise, illuminating, and rigorous way.
 
By looking around, it seems like Dr. Hassani's books are great for studying "mathematical methods for the physicist/engineer." One is for the beginner physicist [Mathematical Methods: For Students of Physics and Related Fields] and the other is [Mathematical Physics: A Modern Introduction to Its Foundations] for the advanced undergraduate / grad student. I'm a sophomore undergrad and I have taken up the standard calculus sequence (~3sems) and ODEs. I want to self study ahead in mathematics...

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