Good books for a high schooler self-studying Abstract Algebra?

Does anyone have any suggestions for abstract algebra books particularly suited to self-study?


Here is some background and motivation, if it’s helpful.

I’m currently a junior in high school, but I have some familiarity with groups, rings, polynomials and fields, as I went through Fraleigh’s book. I liked its writing style, but many of the problems were not helpful. I would like to get better at algebra with some other book, particularly one that’s aimed at someone who already has a little familiarity with the objects, but is by no means completely comfortable.

One of my longer-term goals is to learn a bit of algebraic number theory, as I’ve only been studying elementary number theory. That’s why I feel it good to learn more algebra first. (I’d also be interested in suggestions of other good subjects to learn prior to tackling algebraic number theory.)

I was considering using one of Lang’s books, since they seem pretty universal, but I’ve heard rumors that they are very terse and not good for self-learning.

Answer

For Algebra you can look at these books:

  • Topics in Algebra by I.N. Herstein

  • Abstract Algebra by Dummit and Foote

  • Algebra by Michael Artin

  • Algebra by T.Hungerford (Springer)

  • Lectures in Abstract Algebra by N.Jacobson (Has 3 volumes!)

  • Algebra by Anthony Knapp. (2 Volumes.)

My feeling of Herstein is it has lot of problems which are challenging. For theory part i would like to use Dummit and Foote. Artin’s Algebra is very well written and contains a lot of Linear Algebra. Anthony Knapps treatment of Algebra is very comprehensive, and contains a lot of Algebra. Since your aim is to read Algebraic Number Theory you might want to learn some Galois theory also for which there many good books like:

  • Lectures in Galois theory by Emil Artin

  • Field theory and its Classical problems by Charles Hadlock.

  • Galois theory by J.Rotman (Springer.)

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