Assignments are due on Thursday, at the beginning of class. The row that an assignment appears in is the day that it is due.
| Date | Topic | Book | Homework | Practice Problems | Tutorial Topic | ||
|---|---|---|---|---|---|---|---|
| Jan. | 8 | Introduction to the course | |||||
| 10 | Induction | §1.1 | 7, 11, 18 | ||||
| 11 | Division with remainder | §1.2 | 2, 3, 4 | ||||
| 15 | The Greatest Common Divisor | §1.2 | 6, 15 | ||||
| 17 | The extended Euclidean algorithm | §1.2 | H1 | 1, 8 | Induction | ||
| 18 | Unique factorization | §1.2 | A1 | 12, 13, 14 | |||
| 22 | Modular Arithmetic | §1.3 | 5, 8, 9, 11 | ||||
| 24 | More modular arithmetic | §1.3 | H2 | 12, 16, 18 | Gcd | ||
| 25 | Solving equations mod m | §1.3 | A2 | 20 | |||
| 29 | The Chinese remainder theorem | §1.3 | 21, 22, 23 | ||||
| 31 | Euler's theorem | §1.3 | H3 | 19, 30, 32 | Working mod m | ||
| Feb. | 1 | Equivalence relations | A3 | ||||
| 5 | The ring Z/mZ | §1.4 | 1, 2, 3, 5 | ||||
| 7 | Fields | §1.4 | H4 | 13, 14, 16 | T4 | ||
| 8 | Sums of two squares | A4 | |||||
| 12 | Catch-up day | ||||||
| 14 | Polynomial rings in one variable | §3.1 | H5 | 5, 6, 7, 8 | Equivalence classes | ||
| 15 | Division with remainder | §3.1 | A5 | 1, 2 | |||
| 19 | |||||||
| 21 | Reading Week | ||||||
| 22 | |||||||
| 26 | Unique factorization in polynomial rings | §3.2 | |||||
| 28 | Arithmetic mod m(x) | H6 | 6a-c | Midterm answers | |||
| 29 | The Chinese remainder theorem | §3.1 | A6 | 20b-c | |||
| Mar. | 4 | The ring F[x]/m(x)F[x] | |||||
| 6 | Criteria for irreducibility of polynomials | §3.3 | H7 | 2, 10 | roots of polynomials | ||
| 7 | Polynomial rings with more variables | A7 | |||||
| 11 | Commutative rings | §4.1 | 1, 2 | ||||
| 13 | Ring homomorphisms; ideals. | §4.1 | H8 | 4, 5, 6 | T8 | ||
| 14 | Examples of ideals | §4.1 | A8 | 13, 15, 16 | |||
| 18 | Quotient rings | §4.2 | 1, 2, | ||||
| 20 | The homomorphism theorems | §4.2 | H9 | 3, 4, 5, 11 | T9 | ||
| 21 | Good Friday | A9 | |||||
| 25 | More homomorphism theorems | ||||||
| 27 | Fields; maximal ideals | §4.2 | H10 | 13, 16, 17 | T10 | ||
| 28 | The Chinese remainder theorem | A10 | |||||
| Apr. | 1 | The Gaussian integers | §4.3 | 1, 10 | |||
| 3 | Factorization in the Gaussian integers | §4.3 | H11 | 2, 12 | T11 | ||
| 4 | Principal ideal domains | A11 | |||||
| 15 | H12 | ||||||
| 16 | A12 | ||||||