Topics list:

• Group basics - definitions, examples, homomorphisms, isomorphisms
  Ch. 1.1-1.3, 1.6, 1.7
• Subgroups - cyclic, generated by subsets, stabilizers, centralizers, normalizers, kernels, images, subgroup lattices
  Ch. 2.1-2.5
• Normal subgroups and quotient groups - cosets, Lagrange's theorem, the isomorphism theorems, the alternating group
  Ch. 3.1-3.3, 3.5
• Group actions - groups acting on themselves by left multiplication and conjugation, the class equation, the Sylow theorems, automorphisms
  Ch. 4.1-4.5
• Direct products and classification of finite abelian groups
  Ch. 5.1, 5.2
  (in 5.2 just finite groups, not finitely generated, and only the primary decomposition, not the invariant factor decomposition)
• Ring basics - definitions, examples, homomorphisms, ideals and quotient rings, properties of ideals (principal, prime, maximal), rings of fractions
  Ch. 7.1-7.5
• Euclidean domains, PIDs and UFDs - definitions, examples and counterexamples, EDs are PIDs are UFDs
  Ch 8.1-8.3
  (in 8.1, skip universal side divisors, in 8.2 skip Dedekind-Hasse norms, in 8.3 skip Factorization in Gaussian Integers.)
• Polynomial rings - basics, polynomials over a field form Euclidean domains, polynomial UFDs, irreducibility criteria
  Ch 9.1-9.4
• Field theory - field extensions, characteristic subfields, finite simple algebraic extensions.
  Ch 13.1, 13.2
  (in 13.2, only simple extensions, and just up through Corollary 13)

Office hours schedule for reading period is as follows:

• Mon May 6, 12-2pm
• Wed May 8 10am-12pm
• Fri May 10 12-2pm
• Mon May 13 12-2pm

Topics: Groups: Left/adjoint actions of a group on itself, automorphisms, class equation, Sylow theorem, classification of finite abelian groups.
Rings: definitions (including integral domains, fields, ideals), quotient rings, properties of ideals (principal, maximal, prime), rings of fractions.

I am making chapter 8.1, #8.a extra credit since it has turned out to be more difficult than I intended.

Until recently there was a typo in the assignment. It should be Chapter 7.3, not 7.4.

No office hours today.

No office hours on Wednesday this week; instead I will hold office hours this afternoon at 3 and on Friday at 11:15am and 3pm. Professor Viray will teach lecture on Wednesday.

It was pointed out that 4.3 #2 a) is done in the book and in class. b) is also done in the book. You should do parts b) and c), checking your answer for b) with the book if you want.

Solutions for HW5.

Exam I will cover material up through today's lecture.

Office hours will be at 3pm instead of 11am today.

In problems 4 and 5 you may assume that N is the kernel of some homomorphism.