Weeks

Topics

Sections

1

Basic results on groups

2.1

2

Examples of groups

3.1, 5.3

3

Subgroups

4.1-4.2

4

Lagrange's theorem, quotient groups

4.3-4.4

5

Homomorphisms and isomorphisms

5.1-5.2

6

Actions, direct products

5.4-6.1

7

Conjugacy classes

7.1-7.2

8

Sylow Theorems

7.3-7.4

9

Finite abelian groups

9.1

10

Basic results on rings

10.1-11.1

11

Ideals, homomorphisms

11.2-11.3

12

Embeddings and sums

12.1-13.1

13

Polynomial rings, Euclidean domains

14.1-15.3

14

Unique factorization domains

16.1-16.3

15

Zorn's lemma, maximal and prime ideals

17.1