Akshay Venkatesh, MWF 11-11:50pm.

Office hours: MWF before class, 10--10:50. The CA is Jeremy Booher. His office hours will be Wednesday 4-5:30 and Thursday 2-3:30.

References: The course text is Lang's Algebra. We will supplement it with other references.

Grading and homework The grade is based entirely on homework. Homeworks will be posted on Wednesday and due the Friday of the next week, except for the first homework, which will be posted on the first day of class and due Monday of the second week.

1. Homework 1, posted January 7, due Monday January 14. We'll cover splitting fields by Friday in class; for other unexplained notions (Gauss' lemma, Eisenstein polynomial) refer to Lang.
2. Homework 2, posted January 10, due Friday January 18. WARNING: the polynomial x^3-3x-2 in question 1 was reducible, and has been replced by x^3-3x-3. Also, the roots of f in question 1 should have been assumed to be distinct.
3. Homework 3, due Friday January 25. Note for question 1: S_5 acts on the six subgroups of order 5; thus the normalizer of a subgroup of order 5 has index 6.
4. There will be no homework 4, i.e. there will be no homework due Friday February 1.
5. Homework 5, due Friday February 8.
6. Homework 6, due Friday February 15.

Lecture summaries

1. Week 1. Algebraic elements in field extensions. Field extensions generated by one element, primitive element theorem.Galois field extensions and the Galois correspondence in characteristic zero, using primitive element theorem. Splitting fields: existence and uniqueness. Splitting fields in characteristic zero are Galos.
2. Week 2. Applications of splitting fields: primitive element theorem, theorem of symmetric functions. Existence (sketch) and uniqueness of algebraic closure. The galois group as a permutation group on roots. Examples: cubic equations, discriminant to differentiate between A_3 and S_3. Quartic equations: cubic resolvent and how to see if the Galois group is dihedral. How to solve quartic given solution to cubic resolvent. How to solve cubic (very rapidly and badly explained by me).
3. Week 3: no class
4. Week 4 (anticipated): normality and separability.