Other What are some good books for learning Galois Theory?

[Math100]

May anyone/someone please suggest/recommend some books on learning Galois Theory? Before learning this pure mathematics subject, is the knowledge of group theory required in order to study Galois Theory? I have the e-textbook of Galois Theory by Ian Stewart, 4th edition but was wondering if there are other Galois Theory books for practice.

 

[jedishrfu]

Galois theory sits at the intersection of group theory, field theory, and linear algebra. Learning more about groups, rings, and fields will prepare you for Galois theory. Linear Algebra concepts are good to have under your belt as well.

Some folks recommend:

- Introduction to Galois Theory by Hernandez & Laszlo -- a modern and concise undergrad text

or

- Galois Theory by David Cox — many students and self-learners like how Cox presents multiple perspectives and emphasizes clarity.

In any event, you need to remember that self-study means you'll be using many books to develop your understanding of Galois theory.

 

[Math100]

Galois theory sits at the intersection of group theory, field theory, and linear algebra. Learning more about groups, rings, and fields will prepare you for Galois theory. Linear Algebra concepts are good to have under your belt as well.

Some folks recommend:

- Introduction to Galois Theory by Hernandez & Laszlo -- a modern and concise undergrad text

or

- Galois Theory by David Cox — many students and self-learners like how Cox presents multiple perspectives and emphasizes clarity.

In any event, you need to remember that self-study means you'll be using many books to develop your understanding of Galois theory.

I've taken Linear Algebra before but haven't taken classes/courses for group theory nor field theory. I think I have to buy/purchase these books then. Thank you for the suggestion/recommendation.

 

[martinbn]

You need to know some group theory and field theory first. Why do you want to study galois theory? I think that most books on the subject are fine, as long as the style of presentation suits you. You can take a look at jmilne.org in the course notes section. He has galois theory notes as well as group/field theory.

 

[pines-demon]

I do not think group or field theory is essential in the sense that most books on Galois theory will introduce the important concepts. I think I used Postnikov back in the time.

 

[wrobel]

Van der Waerden Modern Algebra

 

[Math100]

Thank you very much for the suggestion/recommendation, guys!

 

[WWGD]

I liked the one by Ian Stewart. It was pretty much self-contained.

 

[MidgetDwarf]

I may be wrong. Its been a while since I learned the basics.

I believe a member on this forum, Mathwonk, wrote some notes explaining Galois Theory first and filling in the blanks.

I can be wrong.

In anycase, check out his algebra notes.

If you want something easier but well written, to get into group/rings. Have a look at Galian: Contompary Algebra. Artin Algebra can also be a good book, but it requires more mathematical maturity.

In any case,

Not knowing what a group/field is may make understanding something simple like a Galois Group imposible imo.

 

[WWGD]

@mathwonk

 

[WWGD]

@fresh_42 may also know.

 

[martinbn]

I believe a member on this forum, Mathwonk, wrote some notes explaining Galois Theory first and filling in the blanks.

May be you mean these?
https://www.math.uga.edu/sites/default/files/inline-files/844-1.pdf
https://www.math.uga.edu/sites/default/files/inline-files/844-2.pdf

 

[fresh_42]

I have learned it from van der Waerden's Algebra book
https://www.amazon.de/Algebra-German-B-van-Waerden/dp/3642855288/
and I also read Artin's book specifically about Galois Theory
https://www.amazon.de/Galois-Theory-Delivered-University-Mathematical/dp/0486623424/

Both are rather old-fashioned and written in a pre-Bourbaki style. Hence, it is more of a question about the style of representation than it is a question about sources. Here is a more modern treatment by Milne
https://www.jmilne.org/math/CourseNotes/FT.pdf

I found Milne while searching for "galois theory pdf".

 

[mathwonk]

Those notes 844-1, 844-2, of mine linked in post #12, have as prerecquisite the earlier notes 843-1, 843-2, on the same webpage:
https://www.math.uga.edu/directory/people/roy-smith

The notes 843-1 are on groups, the notes 843-2 use groups and specifically Galois groups to give a necessary condition for solvability of equations, and to identify some polynomials which do not have solution formulas in terms of radicals. Then the notes 844-1 discuss rings and fields, and the notes 844-2 use all of this to give a sufficient condition for solvability, and to actually give solution formulas.

I have recently expanded the notes 843-1, hopefully making them more readable, but have not posted them anywhere.

I think Milne's writing is excellent.

Tomorrow I will try to post a summary of Galois theory.