| No. | Date | Readings | To do (hand in) | Remarks |
|---|---|---|---|---|
| 0. | M 1/26 | Notes for Students & Sect. 1.1 to p. 7 | None yet. | M-Tu: We discuss fundamental properties of the integers, from which many others can be proved! (but not all; more about it in Ch. 2). |
| 1. | Tu 1/27 | W 1/28: Notes for Instructors & Sects. 1.1-2 F 1/30: Sect. 1.3 | (a) W 1/28: Prove Prop. 1.8. (b) F 1/30: Prove Props. 1.9 & 1.11(i). | Tu-F: We find out what we were talking about on Monday. |
| 2. | M 2/2 | Finish Ch. 1 | Prove Props. 1.17, 1.19 & 1.22. | |
| 3. | Tu 2/3 | Sect. 2.1 | Prove Props. 1.25(i,ii) & 1.27(ii). | This week we begin work on Ch. 2, where we get to the essence of the integers. |
| 4. | Tu 2/10 | Sects. 2.2-3 | Rewrites. Prove Props. 1.11(v), 2.3. 2.6. | This week we reach the final essential property of the integers. |
| 5. | F 2/13 | Sect. 2.4 | Prove Props. 2.5, 2.7(ii), 2.8, 2.10, 2.1½. | Prop. 2.1½. For integers m and n, m−n is the unique solution of the equation x+n=m. |
| 6. | M 2/23 | Ch. 3 | Prove Props. 2.12(iii), 2.18(iii), 2.20, 2.23. Projects 3.1(iv), 3.2(iii,iv). |
Read the additions and corrections. Read the difference between "if and only if" and "is logically equivalent to". |
| 7. | W 2/25 | Sect. 4.1 | Prove Props. 2.27½, 2.33. | Proposition 2.27½. For all integers k ≥ 2, k3 > k2+k+1. |
| 8. | F 2/27 | Sects. 4.2-3 | Project 3.7(ii, v, vi, vii). Project 2.35 for gcd(4,6). |
Reminder: In Project 2.35 use the book's definition of gcd (as is our policy). |
| 9. | F 3/6 | Sects. 4.4-6 & 5.1 | Prove Prop. 4.6(iii). Project 3.2(i,ii). | |
| 3/16-20 | Ch. 5 Sects. 6.1-3 |
Rewrites. | Always check the Additions and Corrections for each chapter – e.g,, regarding the definition of a partition. |
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| 10. | M 3/23 | Ch. 6 (all) | Projects 5.3, 5.5(i, iii), 6.7. Prove Props. 5.14, 6.6. |
Note that Vm is defined in (ii).
In 5.5, what does (iii) say about the value of m? |
| Tu 3/24 | Sect. 8.1 | Rewrites. | ||
| 11. | W 3/25 | Sect. 8.2 | Project 6.8. Prove Props. 6.15, 6.25(multiplication), 6.26, 8.6. |
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| F 3/27 | Sects. 8.3-4 | Rewrites. | ||
| 12. | M 3/30 | Sect. 9.1 | Project 6.27.
Props. 4.7(i), 4.15(iii); Thm. 8.43. |
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| 13. | W 4/1 | Sects. 9.2-3 | Project 5.21.
Props. 6.20, 8.40(ii), 8.45; Thm. 6.35. |
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| Tu 4/14 | Midterm | The midterm covers Chapters 1 - 6. | ||
| 14. | M 4/20 | Sects. 10.1-3 | Props. 8.50, 9.15. Projs. 8.51½ & 9.3(ii, iii). |
See correction to Prop. 8.50.
Project 8.51½. Three sets: A1 = {1/n : n ∈ N}. A2 = {n, 1/n : n ∈ N}. A3 = {n, −1/n : n ∈ N}. For each set A: (i) Find two or more upper and lower bounds (if any exist). (ii) Find the set U of all upper bounds and the set L of all lower bounds. (iii) Find sup(A) and inf(A). Also find max(A) and min(A). |
| 15. | F 4/24 | Sect. 10.4 | Props. 9.11, 10.9, 10.11, 10.13(ii). | N.B. There may be a quiz any day on definitions in Sects. 10.1-4. |
| 16. | M 4/27 | Sect. 10.5. | Props. 9.18, 10.7, 10.16. | |
| 17. | Tu 5/5 | Ch. 11-12 | Props. 10.27, 11.6, 12.4. Proj. 11.11. | Revised project due date: 6:00 p.m. on Friday of finals week. |
| 18. | W 5/6 | Sect. 13.1. | Prop. 11.22 & Thms. 10.26, 11.12. | |
| F 5/8 | Sects. 13.2-4. | Suggested reading for computer, logic, or philosophy people: Sect. 13.5. |
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| 19. | F 5/8 (officially) | Finish all readings. | Props. 11.17, 13.6, 13.10, 13.18, 13.25, 13.28, 13.29, & 13.32. |
Turn in initial submissions of HW 17-19 by M 5/11 if you want them back at the review session for rewriting. |
| Finals week Tu 5/12 | Review session | 12:50 - 2:50 Room WH-100B = OW-100B | ||
| Finals week F 5/15 | Final Examination | 12:50-2:50 in AA-G019 | The final exam covers all the material of the course. |
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| Finals week F 5/15 | Absolute deadline | 6:00 p.m. at my office. | Last moment to submit all homework and the project. |
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