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 |
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Mar. | 4 | The ring F[x]/m(x)F[x] |
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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 |