Jay Pantone

Math 2100

This course is an introduction to abstract mathematics through the lens of discrete mathematics, a field centered on the study of mathematical objects such as sets, functions, and graphs. We will learn many techniques that allow one to rigorously prove mathematical facts, and we will apply those techniques to the study of discrete mathematics. Emphasis is placed on logical, abstract thinking and clear and precise mathematical writing.

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Course Information

The Revision Cover Sheet must be submitted with every revision.

Homework Assignments

• Assignment 1 — due Wednesday, September 21 by the start of class (tex file (in a zip file with images))
• Assignment 2 — due Wednesday, October 5 by the start of class (tex file)
• Assignment 3 — due Wednesday, October 19 by the start of class (tex file) (updated Oct 17, 10am - does not have to be typed or submitted on D2L)
• Assignment 4 — due Wednesday, November 2 by the start of class (tex file)
• Assignment 5 — due Wednesday, November 16 by the start of class (tex file)
• Assignment 6 — due Wednesday, December 7 by the start of class (tex file)

Announcements

• Aug 29: You should use the Course Grade Matrix to keep track of your progress.

Exams

• Exam 1
• Exam 2
• Exam 3

Textbook

• Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games, by Douglas E. Ensley and J. Winston Crawley. There is only one edition of this book.

LaTeX Resources

I recommend using Overleaf (free) to write your assignments in LaTeX.

Resources

• Tutorial

Outside Tutorials

• DeTexify — you draw a symbol, and it tries to identify it and tell you the command
• Cheat Sheet and list of symbols
• A simple guide to LaTeX
• Overleaf's LaTeX tutorial
• Getting to grips with LaTeX

I'm happy to help troubleshoot your LaTeX in office hours!

Important Dates

Mon, Aug 29	Classes begin
Mon, Sept 5	Labor Day, no classes
Tues, Sept 6	Last day to add/drop classes or request CR/NC option
Thurs, Oct 13 — Wed, Oct 19	Midterm exams
Thurs, Oct 20 — Fri, Oct 21	Midterm Break, no classes
Fri, Nov 18	Last day to withdraw from classes
Fri, Dec 9	Last day of classes
Thurs, Dec 15 1:00pm - 3:00pm	Math 2100 final exam

Daily Calendar

• Topics for future dates are tentative and subject to change.

#	Date	Topics	Announcements and Suggested HW
	Week 1
1	Mon, Aug 29	Syllabus
2	Wed, Aug 31	Section 7.1: Graph Theory (started)	No suggested HW.
3	Fri, Sept 2	Section 7.1: Graph Theory (finished) Section 1.3: Truth-tellers, Liars, and Propositional Logic (started)	7.1.{1abc, 7abcd, 10} 1.3.{1a, 2}
	Week 2
	Mon, Sept 5	Labor Day - no class
4	Wed, Sept 7	Homework 1 Assigned Section 1.3: Truth-tellers, Liars, and Propositional Logic (continued)	1.3.{1bc, 3, 4, 5, 6, 7, 8, 10}
5	Fri, Sept 9	Quiz 1 — covers Section 7.1 only Section 1.3: Truth-tellers, Liars, and Propositional Logic (continued)	1.3.{9, 11, 14, 17}
	Week 3
6	Mon, Sept 12	Section 1.3: Truth-tellers, Liars, and Propositional Logic (basically finished)	1.3.{12, 13, 16, 17, 21ac, 23} (Double negative property for #23: \(\neg(\neg p) \equiv p\).)
7	Wed, Sept 14	Section 1.4: Predicates (started)	1.4.{4, 5, 7, 9}
8	Fri, Sept 16	Quiz 2 — covers ALL suggested HW from 1.3 and the 1.4 questions from Sept. 14 Section 1.4: Predicates (continued)	1.4.{10, 11, 13, 16, 17}
	Week 4
9	Mon, Sept 19	Section 1.4: Predicates (finished)	1.4.{14, 15, 18, 19, 20}
10	Wed, Sept 21	Homework 1 Due Homework 2 Assigned Section 1.5: Implications (started)	1.5.{1, 2ac, 4, 5, 8, 10, 12, 22ab}
11	Fri, Sept 23	Quiz 3 — covers ALL suggested HW from 1.4 and the 1.5 questions from Sept. 21 Section 1.5: Implications (finished)	1.5.{13, 14, 15, 16, 17, 25, 26, 27}
	Week 5
12	Mon, Sept 26	Section 2.1: Mathematical Writing (started)	Read the handout from class today.
13	Wed, Sept 28	Section 2.1: Mathematical Writing (finished)	2.1.{1, 2adfgh, 4abcd, 5, 9ab, 13} (don't "write a letter" like they say, just write a proof)
14	Fri, Sept 30	Exam 1 — covers all material up to and including Sept. 28
	Week 6
15	Mon, Oct 3	Section 2.2: Proofs about Numbers (started)	2.2.{7abcde, 9, 11}
16	Wed, Oct 5	Homework 2 Due Homework 3 Assigned Section 2.2: Proofs about Numbers (continued)	No new suggested homework, keep practicing your proofs!
17	Fri, Oct 7	Quiz 4 — covers 2.1 and 2.2 suggested homework Section 2.2: Proofs about Numbers (continued)	2.2.{1, 2, 3, 4ab}
	Week 7
18	Mon, Oct 10	Section 2.2: Proofs about Numbers (finished) Section 2.3: Induction, Part 1 (started)	2.2.{14, 15, 16, 19}
19	Wed, Oct 12	Section 2.3: Induction, Part 1 (continued)	2.3.{1abcd, 8a}
20	Fri, Oct 14	Quiz 5 — covers suggested homework from last Friday, this Monday, and this Wednesday Section 2.3: Induction, Part 1 (finished)	2.3.{8,9}
	Week 8
21	Mon, Oct 17	Section 2.4: Induction, Part 2	2.4.{4a, 5, 8a, 13, 15} NOTE: There are two "#3s" in my book. When I say "4a", I mean the second #3.
22	Wed, Oct 19	Homework 3 Due Homework 4 Assigned Section 2.5: Contradiction and the Pigeonhole Principle (started the pigeonhole principle part)	2.5.{33, 34a, 35b}
	Fri, Oct 21	Midterm Break - no class
	Week 9
23	Mon, Oct 24	Section 2.5: Contradiction and the Pigeonhole Principle (finished the pigeonhole principle part)	2.5.{32a, 36}
24	Wed, Oct 26	Section 2.5: Contradiction and the Pigeonhole Principle (got most of the way through the contradiction part)	2.5.{1,2,3,4,5,7}
25	Fri, Oct 28	Exam 2
	Week 10
26	Mon, Oct 31	Section 2.5: Contradiction and the Pigeonhole Principle (finished) Section 3.1: Set Definitions and Operations	2.5.{11, 22} 3.1.{} (none yet!)
27	Wed, Nov 2	Homework 4 Due Homework 5 Assigned Section 3.1: Set Definitions and Operations (continued)	3.1.{3, 4, 6, 7, 8, 9, 10, 11, 12abcd}
28	Fri, Nov 4	Quiz 6 — covers proofs by contradiction and Section 3.1 Section 3.1: Set Definitions and Operations (continued)	3.1.{1, 2, 5}
	Week 11
29	Mon, Nov 7	Section 3.1: Set Definitions and Operations (finished)	3.1.{13, 15a, 17abc, 32}
30	Wed, Nov 9	Section 3.2: More Operations on Sets (started)	3.2.{1ab, 2, 10abd, 11, 18, 21}
31	Fri, Nov 11	Quiz 7 — covers suggested homework from last Friday, this Monday, and this Wednesday Section 3.2: More Operations on Sets (finished) Section 3.3: Proving Set Properties (started)	3.2.{1cde, 3, 4, 10c, 12, 13, 14} 3.3.{2, 3, 5}
	Week 12
32	Mon, Nov 14	Section 3.3: Proving Set Properties (finished)	3.3.{6ab, 7, 8ab, 9a, 10d, 11, 20, 21, 22, 23}
33	Wed, Nov 16	Homework 5 Due Homework 6 Assigned Section 4.1: Definitions, Diagrams, and Inverses (started)	4.1.{1, 2, 3, 6, 14ab}
34	Fri, Nov 18	Quiz 8 — covers suggested homework from last Friday, this Monday, and this Wednesday Section 4.1: Definitions, Diagrams, and Inverses (continued)	4.1.{4, 5, 12, 13}
	Week 13
35	Mon, Nov 21	Section 4.1: Definitions, Diagrams, and Inverses (finish) Section 4.2: The Composition Operations (start)	4.1.{14, 15, 16, 17, 20} 4.2.{1, 2, 3}
	Wed, Nov 23	Thanksgiving Break - no class
	Fri, Nov 25	Thanksgiving Break - no class
	Week 14
36	Mon, Nov 28	Section 4.2: The Composition Operation (finished)	4.2.{5, 6, 7}
37	Wed, Nov 30	Section 4.3: Properties of Functions and Set Cardinality (started)	4.3.{1, 2, 3ab, 4 ("invertible" = "bijective")}
38	Fri, Dec 2	Exam 3
	Week 15
39	Mon, Dec 5	Section 4.3: Properties of Functions and Set Cardinality (finished)	4.3.{5, 6, 9, 12, 14}
40	Wed, Dec 7	Homework 6 Due Section 4.4: Properties of Relations (started)	4.1.{23 (arrow diagrams as we did in class, ignore \(R^{-1}\))} 4.4.{1, 2, 3, 4, 6, 9, 13}
41	Fri, Dec 9	Section 4.4: Properties of Relations (finish) Section 4.5: Equivalence Relations — did very briefly, the only thing to know is that an equivalence relation is a realtion that is (1) reflexive, (2) symmetric, (3) transitive	4.4.{15} 4.5.{2, 3, 8 (ignore the "partition part"), 10abc}
	Finals Week
	Thurs, Dec 15	Final Exam, 1pm - 3pm