Department of Mathematical Sciences
Binghamton University

Math 330: Number Systems
Class Schedule and Assignments

Section 7, Zaslavsky · Fall 2018

Rewrites can be handed in any time within the 3-(or 4)-week limit. Early homework is always accepted. You can leave homework in the collection bag 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.

§ means "section".
¶ means "paragraph".

No.	Date due	Readings	To do (hand in)		Remarks
	W 8/22				W-F: We discuss fundamental properties of the integers, from which many others can be proved!.
	F 8/24	Notes for Students & Instructors and §1.1 to Prop. 1.14
1.	M 8/27	P. 7 bottom: Divisibility	Prove Props. 1.8, 1.12.		Quiz 1
2.	F 8/31	Finish Ch. 1.	Prove Props. 1.14, 1.16, 1.27(i).		Quiz 2
3.	W 9/5	§§2.1-2.	Prove Prop. 1.17, Cor. 1.21, Props. 1.27(iv), 2.3.		In §2.2, focus on definition and basic properties of >, ≥. Quiz 3 on §2.1.
4.	W 9/12	§2.3.	Prove Props. 1.24, 2.14(ii).		Class will focus on §2.3.
5.	F 9/14	§2.3 (again).	Prove Prop. 2.5.		Class will focus on §2.4.
	M 9/17	§§2.4, 3.1.			Induction. Logic!
	F 9/21	§§3.1-3.			Logic!
6.	M 9/24	§4.1.	Prove Props. 2.18(ii), 2.33. Do Projects 3.1, 3.7(i,vi).		Induction! Logic!
7.	W 9/26		Prove Props. 2.21, 2.23, 4.5. Do Projects 3.2, 3.7(ii,v).		Induction! Logic! Recursion!
8.	F 9/28	§4.2.	Prove Props. 2.26, 2.34, 4.6(i). Do Project 3.7(vi).		Induction! Logic! Recursion!
9.	M 10/1	§§4.3-6.	Do Project 4.3. Prove Prop. 4.7(i).		Recursion! Induction!!!
10.	F 10/5	Ch. 5.	Do Project 5.3.
11.	M 10/8		Do Project 5-A.		Project 5-A. Among the four sets A, B, F (Project 5.3) and H = {3x−21: x ∈ Z and x > 7}, find all pairs such that (a) X = Y, (b) X ⊆ Y. Advice: Check every pair of sets. Prove all your answers thoroughly, using the set definitions. That includes proving non-subsets.
12.	W 10/10	§6.1.	Prove Props. 5.14, 5.20.
	M 10/15	§6.2.
13.	W 10/17		Prove Thm. 5.15, Props. 6.4, 6.15. Do Projects 5.16, 5.21, 6.7.		Midterm on Friday 10/26. Coverage: Ch. 1-5 and §§6.1-2.
14.	M 10/22	§6.3.	Prove Props. 6.24, 6.25. Do Project 6.27.		Midterm on Friday, Oct. 26. Don't spend much time on Project 6.27 yet.
	W 10/24				Discussion: General review and §6.3.
	F 10/26				Midterm on Ch. 1-5 and §§6.1-2.
15.	M 10/29	§6.4, especially 6.29 and proof.	Do Project 6.8(ii). Prove Proposition 6.31.
	F 11/2	§8.1.			See Proposition 8.25A; it's useful.
16.	M 11/5	§§8.2-4.	Prove Lemma B, Props. 8.6, 8.40.		Most of §§8.1-3 is familiar, but not §8.4!
17.	F 11/9*	Ch. 9.	Do Project 9.3.		*Due W 11/7 if you have a time machine.
18.	M 11/12		Prove Props. 9.11, 9.15.		Study Ch. 9 carefully. It has a lot in few pages.
	F 11/16 M 11/19	§§10.1-4.
19.	M 11/26	§10.5.	Prove Props. 10.10(ii,iv), 10.13(ii), 10.14. Do Project 9.13.
	W 11/28	§§11.1-2.
20.	F 11/30	§11.3.	Prove Props. 9.18, 10.27, 11.2 (completed), 11.4. Do Problem 10.25C.
21.	M 12/3	§§13.1-2.	Prove Theorem 11.8, Props. 11.17, 11.22.		See the notes on Ch. 13.
22.	W 12/5	§13.3.	Prove Props. 13.1, 13.13, 13.18.		Some of these proofs are quite short.
23.	F 12/7	§13.4.	Prove Prop. 13.23, Thm. 13.25.		See correction to 13.25.
	Sun 12/9	Tutor's review session	(for all 330 classes)		2:00-5:00 in LH-11.
	M 12/10	My review session	(for our class)		1:00-2:30 in WH-309.
	Tu 12/11	FINAL EXAM	5:50-7:40 in SW-113.		The final exam covers all the material of the course. It will emphasize Ch. 8-13 and §§ 6.3-4.
	Th 12/15 F 12/16	All homework.	Absolute deadline 5:00 p.m. at my office.		You can leave papers in the envelope on my office door at any time. I will be in on Wednesday and Friday afternoon (and possibly Thursday) to return homework. (Hours to be announced.)