| 9/12 |
0.1-0.3 |
Equivalence relations, partitions, $\mathbb Z/n\mathbb Z$ |
| 9/13 (x) |
0.1-0.3 |
Equivalence relations, partitions, $\mathbb Z/n\mathbb Z$ |
| 9/14 |
1.1 |
Definition of groups; examples; begin dihedral group |
| 9/17 |
1.2 - 1.3 |
Dihedral and Symmetric groups |
| 9/19 |
1.4 - 1.5, start 1.6 |
Matrix Groups, Quaternions, Isomorphism |
| 9/21 |
1.6, 2.1 |
Homomorphisms and subgroups |
| 9/24 |
2.3 |
Cyclic groups |
| 9/26 |
2.3, 2.4 |
Subgroups generated by a set; cosets |
| 9/27 (x) |
3.1 |
Cosets and homomorphisms; quotient groups |
| 9/28 |
3.2 |
More on cosets; Lagrange's theorem |
| 10/1 |
No class |
|
| 10/3 |
First Midterm |
In-class part; take-home part due in class on Friday |
| 10/4 (x) |
3.3 |
First isomorphism theorem |
| 10/5 |
3.3 |
Other isomorphism theorems |
| 10/8 |
3.5, 1.7, 4.1, 4.2 |
The alternating group; Groups actions and Cayley's theorem |
| 10/10 |
4.2 |
Group actions continued |
| 10/12 |
4.3 |
Groups acting by conjugation; the class equation |
| 10/15 |
3.4, 4.5 |
Holder program; Sylow theorems |
| 10/17 |
5.2, 5.4 |
Fundamental theorem of finite
abelian groups; recognizing direct products; applications of the Sylow theorems |
| 10/19 |
7.1, 7.2 |
Rings (basic definitions and examples); Polynomial rings |
| 10/22 |
7.3 |
Homomorphisms and quotient rings |
| 10/24 |
Second midterm |
In-class part; take-home part due in class on Friday |
| 10/25 (x) |
7.4 |
Quotient rings and properties of ideals |
| 10/26 |
8.1, 9.1 |
Euclidean domains; Polynomial rings |
| 10/29 |
8.2, 9.2 |
PIDs |
| 10/31 |
8.3 |
gcds; irreducibles; primes |
| 11/2 |
8.3 |
UFDs |
| 11/5 |
9.3 |
Gauss's lemma and consequences |
| 11/7 |
9.4 |
Irreducibility criteria |
| 11/9 |
9.4 |
Extension fields |
| 11/12 |
|
Wrap it up |
| 11/16 |
Final Exam |
8am - 11am |