| Day | Topics | Preparation |
|---|---|---|
| Mon. 8/30 | Introduction. | Sec. 1.1 |
| Wed. 9/1 | The Division Theorem. Properties of divisibility. |
Sec. 1.1-2 |
| Fri. 9/3 | The Euclidean algorithm. The greatest common divisor theorem. | Sec. 1.2 |
| Wed. 9/8 | Primes and irreducibles. Unique Factorization. |
Sec. 1.3 |
| Fri. 9/10 | GCD and unique factorization exercises. Congruence modulo n |
Sec. 1.1-3 |
| Mon. 9/13 | Congruence modulo m in the integers. Congruence class arithmetic, Z_m. |
Sec. 2.1-2 |
| Wed. 9/15 | Sage: meet in 425. Z_n in Sage. |
Sec. 2.2 |
| Fri. 9/17 | Units and zero divisors in Z_n. | Sec. 2.2-3 |
| Mon. 9/20 | Solving equations in Z_n. Using the Euclidean algorithm to compute the GCD. |
Sec. 2.2-3 |
| Wed. 9/22 | General rings and fields. Subrings. Properties of rings. |
Sec. 3.1-2 |
| Fri. 9/24 | Matrix ringsSec. 3.1-2 | |
| Mon. 9/27 | EXAM | Ch 1-2 |
| Wed. 9/29 | Sage: meet in 425. Euclidean algorithm, etc. |
Sec. 1.1, 3.1-3 |
| Fri. 10/1 | Subrings of Z and Z_n. | Sec.3.1-2 |
| Mon. 10/4 | Subrings of matrix rings.Sec.3.1-2 | |
| Wed. 10/6 | Integral domains and fields.Sec 3.1-2 | |
| Fri. 10/8 | Homomorphisms.Sec. 3.3 | |
| Mon. 10/11 | Homomorphisms and isomorphisms. | Sec. 3.3 |
| Wed. 10/13 | Isomorphisms and onon-isomorphic rings Polynomial arithmetic over rings. |
Sec 3.3 Sec. 4.1 |
| Fri. 10/15 | Polynomial rings over a field. The division theorem. Divisibility |
Sec. 4.1-2 |
| Mon. 10/18 | The gcd theorem Irreducible and prime polynomials. |
Sec. 4.2-3 |
| Wed. 10/20 | Sage: meet in the lab.Sage code. The Euclidean algorithm. |
Sec. 4.2-3 |
| Fri. 10/22 | Unique factorization. | Sec. 4.3 |
| Mon. 10/25 | Roots and factors. | Sec. 4.4 |
| Wed. 10/27 | Roots and factors. | Sec. 4.5 |
| Fri. 10/29 | Congruence in F[x]. | Sec. 5.1 |
| Mon. 11/1 | Congruence class arithmetic. | Sec. 5.1-2 |
| Wed. 11/3 | Sage: meet in lab. | Ch. 5 |
| Fri. 11/5 | Problems. | Ch. 3, 4 |
| Mon. 11/8 | EXAM. | Ch. 3, 4 |
| Wed. 11/10 | F[x]/m(x) for m(x) reducible and irreducible. | Sec. 5.2-3 |
| Fri. 11/12 | Ideals in rings. Examples. | Sec. 6.1 |
| Mon. 11/15 | Rings with only principal ideals.
New ideals from old: intersection, sum, product, radical. |
Sec. 6.1 |
| Wed. 11/17 | Two rings with non-principal ideals A ring modulo an ideal. |
Sec. 6.2 |
| Fri. 11/19 | Quotient rings and homomorphisms. | Sec. 6.2-3 |
| Mon. 11/22 | Some exercises: the examples from Friday, and 5.3 #9, 6.2 #25. |
Sec. 6.2 |
| Wed. 11/24 | Prime and maximal ideals. | Sec. 6.3 |
| Mon. 11/29 | Groups. Groups from rings. | Sec. 7.1 |
| Wed. 12/1 | First properties of groups. The order of an element. Matrix groups |
Sec. 7.1-2 |
| Fri. 12/3 | EXAM. | Ch. 5, 6. |
| Mon 12/6 | Permutation and symmetry groups. | Sec. 7.1-2 |
| Wed. 12/8 | Subgroups. | Sec. 7.3 |
| Fri. 12/10 | Homomorphisms and isomorphisms of groups. | Sec. 7.4 |