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 (adjusted for slow grading) but towards the end of term it will be less than 3 weeks.
§ means "section". ¶ means "paragraph".
* denotes a problem that will not be graded. I will record that you submitted it.
| No. | Date | Readings | To do (hand-in date) | Remarks | |
|---|---|---|---|---|---|
| 0. | 1/17-19 | We discuss basic logic and fundamental properties of the integers, from which many others can be proved. | |||
| 1. | 1/22-26 | Notes for Students & Instructors. Chapter 1 | Prove Props. 1.7, 1.10. (W 1/24) | I will return these proofs with feedback on F 1/26. M 1/22: LaTeX tutorial. | |
| 2. | 1/29 | Prove Props. 1.12-14, 1.23-24. (1/29) | |||
| 3. | 1/29-2/2 | Chapter 3 | Prove 1.25(i), 1.27(ii), and do Projects 3.1, 3.2. (F 2/2) | We'll discuss Chapter 3 all week, beginning with Section 3.1. | |
| 4. | 2/2-5 | Chapter 3 | Prove Prop. 1.16-17, 1.22, 1.27(iv), and do Project 3.7(i,ii). (M 2/5) | ||
| 5. | 2/5-7 | §§2.1-2 | Projects 3.3, 3.5, and Extras #1(a-e). (W 2/7) | Read the advice page for important information. Chapter 2 is the topic for Wed.-Fri. | |
| 6. | 2/7-9 | Prove Props. 2.3, 2.5-6, 2.8-10, 2.13. (M 2/12) | |||
| 7. | 2/12-16 | §§2.3-4. | Prove Props. 2.14(ii), 2.18(iii) by induction, and 2.18.1(i,ii). (F 2/16) | Use Prop. 2.3.1 as if it were in §2.1. | |
| 8. | 2/19-21 | §§4.1-3. | Prove Props. 2.18.1(iii,iv), 2.32.1, and do Project 2.31. (W 2/21) | Use Props. 1.28, 1.17.1 as if they were in Ch. 1. | |
| 9. | 2/23-26 | §§4.4-5. | Prove Props. 2.21, 2.23, 2.18.1(v) (this one using induction), and 4.5. Do Project 2.35 for (4,6). (F 2/23) | ||
| 10. | 2/26-2/28 | Prove Prop. 4.7(i). Do Project 2.35 for (7,13). Do Project 4.3. (W 2/28) | Think carefully about 4.3 to find a proof. | ||
| 11. | 3/2-3/11 | §§4.6, 5.1. | Prove Props. 2.34, 4.16, 4.17. Do Projects 4.23, 4.26, and Problem 4.3.1. (M 3/11) | I'm giving a lot of lead time for this because some of it needs exceptional thought. | |
| 12. | 3/11-15 | §§5.1-3 | Do Projects 4.33, 5.5. Do Project 5.3 using def. of set equality. Prove Props. 4.30, 5.14. (F 3/15) | Be sure to read the advice page for additions to the book and advice on solving problems. In Project 5.5, the set Vm is defined in part (ii). For extra study related to Project 5.5, see Problems Sets: 5.5 and Sets: 5.5+. | |
| 13. | 3/15-20 | §5.4 & my Web pages. | Do Projects 5.12(i,ii), 5.16(ii), 5.21(i). Prove Prop. 5.20(ii). (M 3/18) | Wed. 3/20: review and answering questions. I will expand §5.4 very much with material on the announcements and advice pages. Read them! | |
| Fri. 3/22 | Midterm Exam | Covering Ch. 1-5 except §5.4. | The withdrawal date: Mon. 3/25. | ||
| 14. | 3/25-29 | §§5.4, 6.1, my Web pages on functions. | Prove Prop. 6.5. (F 3/29) | ||
| 15. | 3/29-4/3 | §6.1. | Prove Prop. 6.6. Do Projects 6.7, 6.8. (F 4/5) | ||
| 16. | 4/5 | §§6.2-3. | Prove Props. 6.15-16, 6.19. Do Project 6.9. (M 4/8) | In §6.2 focus on the Division Algorithm for integers. Project 6.9 is related to the rational numbers. | |
| 17. | 4/8 | §6.3. | Prove Props. 6.25-26. Do Project 6.27. (F 4/12) | This is one of the more important parts of the book. | |
| 18. | 4/8-10 | §6.4. | Prove Prop. 6.31, 8.6, and Theorem 6.32. (M 4/15) | What's important: 6.29 and proof, 6.31, 6.32. 6.35 is a famous theorem of modular arithmetic. For fun, use it to reduce a googol (10100) modulo 13. | |
| 19. | 4/10-12 | §§8.1-4. | Prove Props. 8.40, 8.43, 8.49. Do Projects 8.44, 9.3(i-iii). (F 4/19) | See Proposition 8.25A; it's useful and you may use it. Most of §§8.1-3 is familiar, but not §8.4. Don't forget to read the advice page. | |
| 20. | 4/15-17 | §9.1. | Prove Props. 8.50, 8.53, 9.7(ii). Do Projects 9.4, 9.6, 9.9. (Th 4/25) | Remember, Th 4/25 is "Monday". In class 4/17, I went over the important aspects of §9.2. | |
| 21. | 4/19 | §9.2-3, bits of Ch. 10, §11.1, part of §11.2. | Prove Props. 9.11, 9.14, 9.15. Do Projects 9.13, 11.11. (M 4/29) | We'll have only one or two exercises on §9.2. Read it so you can see how we put Z and R into a single system. In Ch. 10, read Thm. 10.1 (it means no real number is an upper bound for Z) & the definitions of |x| and of distance from x to y in R. In §11.2 only read Props. 11.10 and 11.20 and Project 11.11. For the optional concept (not on homework or exams) of isomorphism see the advice page. | |
| 22. | 4/25-26 | §§13.1-2. | Prove Props. 13.2, 13.3, 13.8, 13.13, 13.18, Thm. 13.12. (W 5/1) | See the notes on Ch. 13. | |
| 23. | 4/29-5/1 | §§13.3-4. | Prove Prop. 13.23, Thms. 13.25, 13.28, 13.31. (M 5/6) | See correction to 13.25. | |
| M 5/6 | Review session | 2:00-4:00 p.m. in WH 309. | (for our class) | ||
| Tu 5/6, F 5/10 | Office hours | My office, about 2:00-4:00 p.m. | To return and collect homework and answer questions. | ||
| Wed 5/8 | FINAL EXAM | 3:15-5:15 p.m. in CW 106. | The final exam covers all the material of the course. It will emphasize the parts we covered since the midterm, in Ch. 6, 8, 9, 10, 11, 13. | ||
| Fri 5/10 | All homework is due. | Absolute deadline 4:00 p.m. at my office. | You can leave papers in the envelope on my office door at any time. I will accept PDF's if you are out of town; I can print them. | ||