What is the prerequisite knowledge for learning Galois theory?

What is the prerequisite knowledge for learning Galois theory? I don't know what a ring is.


Solution 1:

If you don't know a great deal of abstract algebra so far, maybe "A First Course in Abstract Algebra" by Fraleigh might be a good place to start, as it includes all the prerequisites (groups, rings, fields, linear algebra) as well as a very readable treatment of Galois Theory itself.

Solution 2:

Try also these excellent books:

  • Field theory and its classical problems by Hadlock.

  • Galois Theory for Beginners: A Historical Perspective by Bewersdorff.

  • Galois' Theory of Algebraic Equations by Tignol.

and also

  • Galois Theory for Beginners by John Stillwell, The American Mathematical Monthly, Vol. 101, No. 1 (Jan., 1994), pp. 22-27.