9
$\begingroup$

All:

I had studied abstract algebra long time ago. Now, I would like to review some material, particularly about Galois theory (and its application).

Can anyone recommend an abstract algebra book which cover Galois theory (and its applications)?

I have been a software engineer for past many years. Ideally, I would like an algebra book with programming assignments or exercise (help me to understand concept.) For example, homework assignments to write a program to verify Galois theory, or to construct 'solvable Group", or anything like that. (Of course, I can think some random questions, but I prefer a text book with well designed, and meaningful home works).

I felt that I was not good at deriving formula anymore, I would like to use my programming skills to help me to understand subject, do more hand-on exercise and calculations.

$\endgroup$
  • 1
    $\begingroup$ Interesting question. Abstract algebra seems like a subject that could lend itself well to work involving computer software. Here's an exercise for you. Suppose you know that $a$ and $b$ are roots of two given polynomials whose coefficients are integers. Write a program to find the minimal polynomial of $a+b$. $\endgroup$ – Michael Hardy Aug 10 '14 at 21:18
  • $\begingroup$ That's not a well-posed problem, Michael. :) Ask for some polynomial with root $a+b$. $\endgroup$ – darij grinberg Aug 10 '14 at 21:19
  • 1
    $\begingroup$ While it doesn't cover Galois theory, Ideals, Varieties, and Algorithms by Cox, Little, and O'Shea (springer.com/mathematics/algebra/book/978-0-387-35650-1) is an accessible intro to commutative algebra and algebraic geometry with an emphasis on writing programs for problem-solving. $\endgroup$ – Gyu Eun Lee Aug 10 '14 at 22:03
  • 1
    $\begingroup$ In addition to Ideals, Varieties and Algorithms, I came here to suggest Abstract Algebra with GAP. Sadly, it concludes with Galois theory. college.cengage.com/mathematics/gallian/abstract_algebra/6e/… $\endgroup$ – dls Aug 10 '14 at 22:42
  • 1
    $\begingroup$ Two more links: math.colostate.edu/~hulpke/CGT/howtogap.pdf gap-system.org/Doc/Teaching/teaching.html $\endgroup$ – dls Aug 10 '14 at 22:46
3
$\begingroup$

All books listed in the comments above are listed in my answer to the question Novel approaches to elementary number theory and abstract algebra, so I am placing a CW-answer here to remove this question from the unanswered queue.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.