Looking for a book on Modern Algebra

[Winter Flower]

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!

 

[n!kofeyn]

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.

 

[Winter Flower]

Ok, thanks for the recommendations and links! I will check those out...

 

[Newtime]

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.

 

[Reedeegi]

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.