## Galois Theory (Math 5658), Spring 2014
Instructor: Andrew Obus
email: obus [at] virginia.edu
office: Kerchof Hall 208 |

Textbook

*Galois Theory*, 2nd ed.,
by David A. Cox. Available at the bookstore and on amazon.
There is an electronic copy on reserve in the
library. This is a large book, but a lot of that is due to having
very detailed exposition, along with copious historical and
mathematical notes.

- Galois Theory by Emil Artin (the original lecture series on Galois theory from a modern perspective. Takes an approach that emphasizes linear algebra more than Cox's book does. From 1942, but very clear and readable!) Available here.
- Algebra by Michael Artin (Emil's son! The last two chapters give a more concise account of Galois Theory than Cox does.)

- Galois Theory, by Ian Stewart (roughly follows E. Artin's presentation, but includes a great chapter on history.)

- Galois Theory for Beginners, by Jörg Bewersdorff (informal, requires less background, but makes you get your hands dirty with polynomials.)
- Galois Theory, by Steven H. Weintraub (more advanced, goes very quickly through the basic theory, although techinically does not require more background than Cox's book).

In particular, I hope to cover most of Chapters 1-8 of Cox's book in the first 11 or so weeks of class. This is the core material of the course. There are many topics we can discuss for the last couple of weeks (explicit solutions of quartics and quintics, ruler and compass/origami constructions, the inverse Galois problem, Galois theory in characteristic p, transcendental extensions...). I will seek the class's input!

Évariste Galois, the inventor of Galois theory, also had an amazing life story, culminating in his death at age 20 in a duel. I will spend some time discussing the history of Galois himself, as well as the history of his mathematics.

Mondays 1-2, Fridays 12-1. Kerchof Hall 208 (my office). If these times do not work for you, please make an appointment with me.

Homework will be graded in a somewhat non-traditional way. Each problem will get a grade of "Correct" or "Redo." "Correct" means that there are only very minor problems with the argument, which I can point out quickly. "Redo" means that there is a reasonably serious gap in your reasoning, or that the argument does not make sense (I will try to write some comments in this case). Problems marked "Redo" can be handed in within a week of being returned for 80% credit. If a problem handed in a second time gets a "Redo," then it can be handed in a third time for 60% credit, a fourth time for

40% credit, etc. If you elect not to redo a problem, then it earns 0% credit. My feeling is that this allows for better learning than standard homework procedure, and is workable for a small class.

Homework will be assigned more or less weekly, and will be posted on Collab. Grades will be posted there as well.

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