May 19

Topics you can expect on the final:

Set stuff: partitions, equivalence relations, 1:1, onto

Automorphism groups of graphs

Permutations: even/oddness, cycle decomposition, order, conjugacy

Group homomorphisms, kernels

Cyclic groups

Homomorphisms from cyclic groups to other groups

Every subgroup of a cyclic group is cyclic, because of the Euclidean algorithm

Subgroups correspond 1:1 to divisors of |G|

Lagrange's theorem, coset spaces

Normal subgroups, direct products, quotient groups, First Iso Theorem

Groups acting on sets

Sizes of orbits

G a p-group

Fermat's Little Theorem

Stabilizers

Sylow's theorems

Semidirect products

Rings

Ideals, prime ideals, maximal ideals, principal ideals

Quotient rings, First Iso Theorem

Fields, field extensions, multiplicativity

Here are some more problems that you should consider easy.

5.1 #1,4,7,12,14,18

5.4 #1,2,3,6,8,10,18,19

5.5 #11,18

7.1 #1-14,19,21,25,28,29

7.2 #1,3

7.3 #3,6,8,10,11,16,18,19,25,28,29,32,37

7.4 #4,6,8,9,10,11,16,27,31

8.1 #1,2,3,11

8.2 #3,5

9.1 #4,5,6

13.2 #3,12,13,16