Department of Mathematical Sciences
Binghamton University

Math 330: Number Systems
Class Schedule and Assignments

Section 3, Zaslavsky

Main class page | Schedule and homework | Announcements | Term Project | Syllabus

Schedule

Index:     | Ch. 1 || Ch. 2 || Ch. 3 || Ch. 4 || Ch. 5 || Ch. 6 || Ch. 8 || Ch. 9 || Ch. 10 || Ch. 11 || Ch. 13 |

No.DateReadingsTo do (hand in)     Remarks
—W 8/31Notes for Students;
Sect. 1.1,
start Sect. 1.2		None yet.M 8/29: We discuss fundamental properties of the integers, from which many others can be proved! (but not all; more about it in Ch. 2).
W - F: We find out what we were talking about on Monday.
1.Th 9/1Chapter 1Prove Props. 1.8 & 1.11(i).
2.F 9/2Finish Ch. 1Prove Props. 1.17 & 1.22.
3.W 9/7Sect. 2.1Prove Props. 1.11(v), 1.25(i,ii), & 1.27(ii).This week we begin work on Ch. 2, where we get to the essence of the integers.
Th-F 9/8-9 No classes. Really bad weather.
4. Th 9/8
M 9/12 		Sect. 2.2 Rewrites.
Prove Props. 2.3. 2.6.
5. F 9/9
W 9/14		Sect. 2.3 Prove Props. 2.5, 2.7(ii), 2.8.
6. Th 9/15 Prove Props. 2.10, 2.12(iii).
7. F 9/16 Sect. 2.4 Prove Props. 2.18(iii), 2.20, 2.23.
8. M 9/19 Prove Props. 2.27 2.27½, 2.33.
Do Project 2.35: gcd(4,6).		Replace Prop. 2.27 by Proposition 2.27½. For all integers k ≥ 2, k3 > k2+k+1.

In Project 2.35 use the book's definition of gcd.
T 9/20 Rewrites.
W 9/21 Rewrites
Th 9/22 Sects. 3.1 & 3.2. Rewrites. See the announcements page for the difference between "if and only if" and "is logically equivalent to".
F 9/23 Rewrites.
9. M 9/26 Sects. 3.3 & 3.4. Project 3.1(iv).
Project 3.2(iii,iv). 		See the announcements page for a write-up of what I said in class about the structure of quantified statements, and for details about unique quantification.
10. W 9/28 Sects. 4.1 & 4.2. Project 3.7(ii, v, vi, vii).
M 10/3 Rewrites. Discussed recursive definitions in class.
Did I make a little mistake in class today? The book defines (n+1)! := n!(n+1), and I defined it as (n+1)n!. Of course, we know these are equal by Ax. 1.1, so it doesn't matter.
11. W 10/5 Props. 4.5 & 4.7(i).
12. Th 10/6 Sects. 4.3 & 4.4. Props. 4.13, 4.15(iii), 4.16(ii).
13. F 10/7 Prop. 4.17 & Cor. 4.22.
14. M 10/10 Sects. 4.5, 4.6, & 5.1. Prop. 4.30.
15. W 10/12 Sect. 5.2 & 5.3. Projects 5.3 & 5.5(iii).
Prop. Thm. 5.15. 		AWTTW: In 5.5, what does (iii) say about the value of m?
16. Th 10/13 Sects. 5.3, 5.4, & 6.1. Project 5.21.
17. F 10/14 Sect. 6.2. Prop. 6.5,
Project 6.7. 		See corrections on the announcements page.
M 10/17 Rewrites.
18. W 10/19 Sect. 6.2. Props. 6.15 & 6.20. If you do these by Wed., hand them in, either in my mailbox at the Math Dep't (any time up to 5:00) or at my office (any time up to 6:00). Then I'll return the papers on Thursday.
Otherwise, do them for Thurs. so I can return them Fri., before the midterm. On Thursday you can turn in your papers up till 5:00 in my mailbox.
Th 10/20 Rewrites.
18½. F 10/21 Sect. 6.3. Rewrites. Study Project 4.10 for discussion in class. Can you see how to do it?
Midterm M 10/24 Midterm examination. The midterm covers Chapter 1 through Section 6.2.
19. W 10/26 Sects. 6.3 & 6.4. Prop. 6.25.
Project 6.27.
20. F 10/28 Prop. 6.32.
21. M 10/31 Sect. 8.1. Thm. 6.35.
22. W 11/2 Sect. 8.2. Props. 8.6 & 8.40(ii).
23. Th 11/3 Thm. 8.43.
F 11/4 Rewrites. The last day to submit homework from Chapters 1 to 4.
24. M 11/7 Sect. 9.1. Props. 8.47 & 8.50. See correction to Prop. 8.50.
25. W 11/9 Sect. 9.2. Projs. 8.51½ & 9.3(ii, iii). Project 8.51½. For each set A find two or more upper and lower bounds (if any exist). Find the set U of all upper bounds and the set L of all lower bounds. Find sup(A) and inf(A). Also find max(A) and min(A).
A1 = {1/n : n ∈ N}.
A2 = {n, 1/n : n ∈ N}.
A3 = {n, −1/n : n ∈ N}.
26. F 11/11 Prop. 9.7(ii). The last day to submit homework from Chapter 5 (Homework Sets 15 - 16).
27. M 11/14 Sects. 10.1-3. Props. 9.11 & 9.15.
28. W 11/16 Sect. 10.4. Props. 9.18, 10.7, 10.9.
Th 11/17 Sect. 10.4. Rewrites.
29. F 11/18 Sect. 10.4. Prop. 10.11.
M 11/21 The last day to submit homework from Chapter 6 (Homework Sets 17 - 21).
30. W 11/23 Sect. 10.5. Props. 10.17, 10.21(i), & 10.23(iii).
M 11/28 Sect. 10.5. The last day to submit Homework Sets 22 - 23 (Ch. 8).
31. W 11/30 M 11/28 Props. 10.27 & 10.28. The last day to submit Homework Sets 24 - 27 (Chs. 8 & 9).
Th 12/1 Sects. 11.1-2.
32. F 12/2 Sect. 11.3. Props. 11.2 & 11.6.
33. M 12/5 Sect. 13.1. Thm. 11.12, Props. 11.17 & 11.25.
W 12/7 Sect. 13.2.
34. H 12/8 Sect. 13.3. Props. 13.2 & 13.6.
35. F 12/9 Sect. 13.4. Props. 13.10, 13.18, & 13.25. Suggested reading for computer or logic or philosophy people: Sect. 13.5.
Sun 12/11 Review Session. Time: 2:00-4:00. Room: LN-2205.
The last day to submit all homework and the Term Project.
T 12/13 Final Examination. The final exam covers all the material of the course.
Main class page | Schedule and homework | Announcements | Term Project | Syllabus