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.
Lectures: |
M, W, F | 9:00am - 9:50am |
Cudahy 131 |
Office Hours: |
Tuesday, | 12:30pm - 1:30pm |
Friday, | 8:00am - 9:00am | |
and by appointment |
I recommend using Overleaf (free) to write your assignments in LaTeX.
I'm happy to help troubleshoot your LaTeX in office hours!
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 |
# | 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 |