Math 31, Summer 2021
Topics in Algebra

Fri Jun 25

1: Why Abstract Algebra?

Sat Jun 26

2: Operations (and A: Set Theory)

Mon Jun 28

3: The Definition of Groups

Wed Jun 30

4: Elementary Properties of Groups

Thu Jul 1

Proofs

Fri Jul 2

5: Subgroups

Wed Jul 7

6: Functions

Fri Jul 9

7: Groups of Permutations

Mon Jul 12

8: Permutations of a Finite Set

Wed Jul 14

9: Isomorphism

Fri Jul 16

10: Order of Group Elements

Mon Jul 19

11: Cyclic Groups (and B: Integers)

Wed Jul 21

12: Partitions and Equivalence Relations

Fri Jul 23

13: Counting Cosets

Mon Jul 26

14: Homomorphisms

Wed Jul 28

15: Quotient Groups

Fri Jul 30

16: The Fundamental Homomorphism Theorem

Mon Aug 2

17: Rings

Wed Aug 4

18: Ideals and Homomorphisms

Fri Aug 6

19: Quotient Rings

Mon Aug 9

20: Integral Domains

Wed Aug 11

21: The Integers, C: Induction

Fri Aug 13

22: Factoring into Primes

Mon Aug 16

24: Rings of Polynomials

Wed Aug 18

25: Factoring Polynomials

Fri Aug 20

26: Substitution in Polynomials

Mon Aug 23

27: Extensions of Fields

Wed Aug 25

Wrap-up