| Day | Topics | Preparation |
|---|---|---|
| Mon. 8/27 | Introduction. The Division Theorem. |
Sec. 1.1 |
| Wed. 8/29 | Uniqueness in the division theorem. | Sec. 1.1-2 |
| Fri. 8/31 | Divisibility and the
Euclidean algorithm. More on the gcd. | Sec. 1.2-3 |
| Wed. 9/5 | Primes and unique factorization. | Sec. 1.3 |
| Fri. 9/7 | Congruence modulo m in the integers. | Sec. 2.1-2 |
| Mon. 9/10 | Congruence class arithmetic, Z_m. | Sec. 2.2-3 |
| Wed. 9/12 | More congruence class arithmetic. | Sec. 2.2-3 |
| Fri. 9/14 | General rings and fields. | 3.1 |
| Mon. 9/17 | EXAMCh 1-2 | |
| Wed. | Product of rings. Matrix rings | 3.1 |
| Fri. 9/21 | Properties of rings. | 3.2 |
| Mon. 9/24 | Idempotents, and some exercises.Ch 3.1-2 | |
| Wed. 9/26 | Homomorphism. Homomorphisms Z_n to Z_d |
Sec. 3.3 |
| Fri. 9/28 | Homomorphisms and isomorphisms. | Sec. 3.3 |
| Mon. 10/1 | Miscellaneous problems. | Ch. 3 |
| Wed. 10/3 | Polynomial arithmetic over rings. | Sec. 4.1 |
| Fri. 10/5 | The division theorem | Sec. 4.1 |
| Mon. 10/8 | Divisibility , the gcd, and the Euclidean algorithm. |
Sec. 4.2 |
| Wed. 10/10 | Unique factorization. | Sec. 4.3 |
| Fri. 10/12 | Unique factorization. | Sec. 4.3 |
| Mon. 10/15 | Roots and factors. | Sec. 4.4 |
| Wed. 10/17 | Questions on Ch. 3,4? Congruence in F[x]. |
Sec. 5.1 |
| Fri. 10/19 | Congruence class arithmetic, F[x]/p(x). | Sec. 5.2 |
| Mon. 10/22 | EXAM postponed! Congruence in polynomial rings. |
Sec. 5.1 |
| Wed. 10/24 | Classes cancelled due to fire. | . |
| Fr. 10/26 | Classes cancelled due to fire. | . |
| Mon. 10/29 | EXAM. | Ch. 3, 4 |
| Wed. 10/31 | Arithmetic of F[x]/p(x) | Sec. 5.2-3 |
| Fri. 11/2 | Discussion of exam. Arithmetic of F[x]/p(x) |
Sec. 5.2-3 |
| Mon. 11/5 | Ideals in rings. Examples. | Sec. 6.1 |
| Wed. 11/7 | Retake EXAM. | Ch. 3, 4 |
| Fri. 11/9 | Rings with only principal ideals. | Sec. 6.1 |
| Wed. 11/14 | New ideals from old: intersection, sum of ideals. | Sec. 6.1 |
| Fri. 11/16 | A ring modulo an ideal. | Sec. 6.2 |
| Mon. 11/19 | Homomorphisms and some exercises. | Sec. 6.2 |
| Wed. 11/21 | Groups. Groups from rings. | Sec. 7.1 |
| Mon. 11/26 | Groups. Permutation and symmetry groups. | Sec. 7.1-2 |
| Wed. 11/28 | Permutation groups. The order of an element. | Sec. 7.2 |
| Fri. 11/30 | EXAM. | Ch. 5, 6 |
| Mon. 12/3 | Subgroups. | Sec. 7.3 |
| Wed. 12/3 | Homomorphisms and isomorphisms. | Sec. 7.4 |