Early homework is always accepted. You can leave homework in the collection envelope on my office door at any hour.
Papers for the same assignment must be stapled (bending a corner is not secure); if not, I will not grade the papers. Every different assignment must be written on separate papers; if not, I will only grade one assignment.
Rewrites can be handed in at any time within the time limit. The time limit is normally 3 weeks after the due date (but it's adjusted for slow grading) but towards the end of term it will be less than 3 weeks.
| No. | Date | Readings | To do (hand-in date) | Remarks | |
|---|---|---|---|---|---|
| 0. | 1/22-24 | Notes for Students & Instructors. § 1.1 | We discuss basic logic and fundamental properties of the integers, from which many others can be proved. | ||
| 1. | 1/27-29 | § 1.2 | Prove Props. 1.7, 1.10. (W 1/24) | I will return these proofs with feedback on | |
| 2. | 2/3-5 | Chapter 1, all | Prove Props. 1.12-14, 1.24, 1.25(i), 1.26. (W 2/5) | ||
| 3. | 2/10 | §§2.1-2. | Prove Props. 2.3, 2.5-6, 2.8. (M 2/10) | Inequalities (and positivity). See the advice page for applying < propositions to ≤. | |
| 4. | 2/12 | §2.3. | Prove Prop. 2.18(ii) by induction. (F 2/14) | Mathematical induction. | |
| 5. | 2/17 | §2.4. | Prove Props. 2.10, 2.21, 2.33. Do Project 2.28. Prove Props. 2.18(iii) by induction, and 2.18.1(i,ii), 2.32.1. (F 2/21) | ||
| 6. | 2/23 | Chapter 3 | Do Projects 2.35 for (4,6), 3.3, 3.7, Extras #1(a-e). Prove Props. 2.23, 2.18.1(iii,iv). (F 2/28) | Use Props. 1.28, 1.17.1 as if they had appeared in Ch. 1. | |
| 7. | 2/28, 3/7 | §§5.1-2. | None until after the break. | These sections are related to logic. | |
| Wed. 3/5 | Midterm Exam 1 | Covering Ch. 1-3 (all). | Open book; you must use a physical book. | ||
| 8. | 3/19 | §§5.3-4 & advice for Ch. 5; §4.1. |
Do Project 5.3 using def. of set equality. Do Projects 5.5, 5.12(i,ii), 5.16(ii), 5.21(i), and 5.4A(a). Prove Prop. 5.20(ii). Do Project 4.3. (M 3/24) | In Project 5.5, the set Vm is defined in part (ii). For extra study related to Project 5.5, see Problems on Sets 5.5A and 5.5B. | |
| 9. | 3/26 | Ch. 4 & §6.1. | Prove Props. 4.7(i), 4.13, 4.16(ii), 4.22. Do Projects 4.12, 4.23, 4.26, 6.7(i). (M 3/31) | I won't assign anything from §4.6, but it's worth reading. | |
| Mon. 3/31 | The withdrawal date. | ||||
| 10. | 3/30 | §6.2. | Prove Props. 6.5, 6.6. Do Projects 6.7(ii-vi), 6.8(i-iii). (F 4/4) | Correction to definition of a partition. Fri. class discussion: proof of Theorem 6.13. Can you think of an idea or question for class? | |
| 11. | 3/30 | §§6.3, 8.1-2. | Prove Props. 6.15-16, 6.25, 8.6. Do Projects 6.9, 6.27. (W 4/9) | Project 6.9 is related to the rational numbers. 6.35 is a famous theorem of modular arithmetic. For fun, use it to reduce a googol (10100) modulo 13. | |
| 12. | 4/5,12 | §§8.1-4; §9.1. | Prove Props. 8.40, 8.43, 8.49. Do Projects 8.44, 8.51, 9.3(i-iii), 9.4. (W 4/16) | You may use Proposition 8.25A without proof. Most of §§8.1-3 is familiar, but not §8.4. Don't forget to read the advice page. | |
| 13. | 4/13 | §§9.1-3. | Prove Props. 9.7(ii,iii), | ||
| Mon. 4/28 | Midterm Exam 2 | Covering Ch. 4-6, 8, and §9.1. | Open book; you must use a physical book. | Review on Wed. 4/23. | |
| 14. | 4/26 | Parts of Ch. 10 & 11. All of §§13.1-2. | Do Project 11.11. Prove Props. 13.1, 13.3, 13.6, 13.13. (F 5/2)
Study Thm. 10.1, §10.2 def. of |x|, §10.3 distance from x to y. §11.1: Know def. of rational numbers. §11.2: Study Prop. 11.10. | See the notes on Ch. 13. | |
| 15. | 4/26 | §§13.3-4. | Prove Thm. 13.14, Cors. 13.18, 13.23, Thm. 13.28. (W 5/7) | See correction to 13.25. | |
| F 5/9 | Review session | 4:00-6:00 p.m. in WH 100E. | (for our class) | ||
| Tues. 5/13 | FINAL EXAM | 8:00-10:00 a.m. in CW 107. | The final exam covers all the material of the course. It will emphasize (relatively speaking) the parts we covered after Midterm 2 in §9.2 & Ch. 10, 11, 13. | ||
| Tues. 5/13 | All homework is due by 5:00 p.m. | You can leave papers in the envelope on my office door at any time. |