| Wednesday, 1/4 | Intro to the course. Propositional logic. |
| Friday, 1/6 | More propositional logic. Sets. Reading: Skim Chapter 1, so that you can go back to it later when you get stuck on a problem. Read Sections 2.1 and Section 2.2 up to the part on the real numbers. |
| Monday, 1/9 | Sets. Predicates and Quantifiers. Reading: Section 2.3 Homework 1 due: Section 2.1, #1ae, 6a, 11, 12, 14, 16, 19. Section 2.2, #4abe, 5, 9. |
| Wednesday, 1/11 | More Predicates and Quantifiers. Direct Proof. Read: Section 3.1. |
| Friday, 1/13 | Direct and Indirect proofs. Re-read Section 3.1, and read section 3.2. Homework 2 due: Section 2.2 (p.45), #12a, 16. Section 2.3 (p. 51), #2, 6, 7, 11, 13, 14, 16, 18, 21, 27bcg. Section 3.1 (p. 61), 10, 12, 13, 18. |
| Monday, 1/16 | Mathematical Induction. Read: Section 3.3 |
| Wednesday, 1/18 | More on induction, including strong induction. Read: Section 3.4. Homework 3 due: Section 3.2, #1, 5a, 7, 9, 10, 13, 14. Section 3.3, #2, 5, 12, 14, 16, 18b. |
| Friday, 1/20 | Case analysis and proof strategy. Sets revisited. Read through Sections 3.5 and 3.6. Some nice proofs are discussed. |
| Monday, 1/23 | Power sets. Read: Section 4.1. Homework 4 due: Section 3.3 (pp. 76-77) #19, 20 and the problems on this sheet. Section 3.4 (pp. 82-83) #4, 8, 10. |
| Wednesday, 1/25 | Cartesian products. Relations. Read: pages 109-114, 117-123. |
| Friday, 1/27 | More on relations. Read: pages 123-130. Homework 5 due: Section 4.1 (pp. 114-116), #3f, 4ce, 7ab, 8a, 9, 11abc, 12, 19, 22bcd. Section 4.2 (pp. 130-132), #3abcde, #4ab |
| Monday, 1/30 | Relations and Functions (Section 4.3) Read: pages 132-147. Homework 6 due: Section 4.2 (pp. 130-132), #6ab, 8c, 12bcef. Section 4.3 (pp. 150-153), #1bcef. |
| Wednesday, 2/1 | Functions (Section 4.3) |
| Friday, 2/3 | In-class exam |
| Monday, 2/6 | No class -- mid-term break. |
| Wednesday, 2/8 | More on Functions (4.3) |
| Friday, 2/10 | Still more on functions (4.3) HW 7 due (group assignment): Section 4.2 (pp. 130-132), #15bcg, 19abc, 21, 24a, 29. Section 4.3 (pp. 150-153), #2abcde, 4bd, 5, 8, 12b, 13, 14, 16, 17, 25, 27, 31. |
| Monday, 2/13 | Equivalence relations (4.4) Read: Section 4.4 |
| Wednesday, 2/15 | More on equivalence relations (4.4) HW 8 due: Section 4.3 (pp. 150-153), #14, 17a(iv), 19, 20, 24, 31. Section 4.4 (pp. 166-168), #6 (give justifications), 7, 8 |
| Friday, 2/17 | Wrap up equivalence relations (4.4). Take-home midterm handed out. HW 9 due: Section 4.4 (pp. 166-168), #11ab, 13, 16, 32, and the problems on this sheet. |
| Monday, 2/20 | Equinumerous Sets (5.1) |
| Wednesday, 2/22 | More equinumerous sets (5.1) |
| Friday, 2/24 | Finite sets and the pigeonhole principle (5.2) Take-home midterm due |
| Monday, 2/27 | Finite sets and the pigeonhole principle 5(.2) Read: Section 5.2 |
| Wednesday, 3/1 | Denumerable Sets (5.3) Read: pages 209-212. HW 10 due: Section 4.4 (pp. 166-168), #23, 29ab, 36. Section 5.1 (pp. 200-201), #2ad, 3ab, 7, 15 (Hint: one method for part a) is to use Theorem 2). Section 5.2 (pp. 207-208), #2, 9, 13, 16. |
| Friday, 3/3 | Uncountable Sets (5.4) Read: Section 5.4. |
| Monday, 3/6 | The transcendental numbers are uncountable (5.4) HW 11 due (group assignment): Section 5.2 (pp. 207-208), #10, 11, 14. Section 5.3 (pp. 215-216), #2, 4c, 8, 12. Section 5.4 (p. 222), #3c, 4, 7, 10, 11. |
| Wednesday, 3/8 | More on uncountable sets. Take-home final handed out. HW 12 due: Section 5.4 (p. 222), #12, 13, 14 (Hint: you can do #14 without explicitly constructing the subsets. One method is to use #12.) |
| Friday, 3/10 | |
| Wednesday, 3/15 | Final exam due, 5 pm |