# Any abstract algebra book with programming (homework) assignment?

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.

• 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 $a+b$. – Michael Hardy Aug 10 '14 at 21:18
• That's not a well-posed problem, Michael. :) Ask for some polynomial with root $a+b$. – darij grinberg Aug 10 '14 at 21:19
• 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. – Gyu Eun Lee Aug 10 '14 at 22:03
• 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/… – dls Aug 10 '14 at 22:42
• – dls Aug 10 '14 at 22:46