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: |
Monday, Wednesday, Friday | Section 101: | 10:00am - 10:50am |
| Wehr Chemistry 113 | ||
| Section 102: | 11:00am - 11:50am | |
| Wehr Chemistry 107 | ||
Office Hours: |
Monday, | 2:00pm - 3:00pm |
| Wednesday, | 3:00pm - 4:00pm | |
| Friday, | 8:30am - 9:30am | |
| 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 26 | Classes begin |
| Mon, Sept 2 | Labor Day, no classes |
| Tues, Sept 3 | Last day to add/drop classes or request CR/NC option |
| Thurs, Oct 17 — Fri, Oct 18 | Midterm break, no classes |
| Fri, Nov 18 | Last day to withdraw from classes |
| Wed, Nov 27 — Fri, Nov 29 | Thanksgiving break, no classes |
| Fri, Dec 6 | Last day of classes |
| Monday, Dec 9 1:00pm - 3:00pm |
Final exam for Section 102 (11:00am-11:50am lecture time) |
| Tuesday, Dec 10 8:00am - 10:00am |
Final exam for Section 101 (10:00am-10:50am lecture time) |
| # | Date | Topics | Announcements and Suggested HW |
|---|---|---|---|
| Week 1 | |||
| 1 | Mon, Aug 26 |
Syllabus Section 7.1 - Graph Theory (started) |
No suggested HW |
| 2 | Wed, Aug 28 | Section 7.1 - Graph Theory (continued) | No suggested HW |
| 3 | Fri, Aug 30 |
Section 7.1 - Graph Theory (finished) Section 1.3 - Truth-tellers, Liars, and Proposition Logic (started) |
7.1: # 1abc, 2ab, 3, 8 ("Eulerian" = "has an Eulerian circuit"), 9 ("Eulerian trail" = "Eulerian path"), 10, 11, 15 |
| Week 2 | |||
| Mon, Sept 2 | Labor Day - no class | ||
| 4 | Wed, Sept 4 |
Homework 1 Assigned Section 1.3 - Truth-tellers, Liars, and Proposition Logic (continued) |
1.3: # 1, 3, 4, 5, 6 |
| 5 | Fri, Sept 6 |
Quiz 1 Section 1.3 - Truth-tellers, Liars, and Proposition Logic (continued) |
1.3: # 7, 8, 9, 10, 11 |
| Week 3 | |||
| 6 | Mon, Sept 9 | Section 1.3 - Truth-tellers, Liars, and Proposition Logic (almost finished!) | 1.3: # 12, 13, 17, 21 |
| 7 | Wed, Sept 11 |
Section 1.3 - Truth-tellers, Liars, and Proposition Logic (finished) Section 1.4 - Predicates (started) |
1.3: # 22, 23, 24 1.4: # 1, 2, 5, 7 |
| 8 | Fri, Sept 13 |
pre-recorded lecture https://www.youtube.com/watch?v=3jOtvChA5Us Section 1.4 - Predicates (continued) |
1.4: # 8, 9ab, 10, 11 |
| Week 4 | |||
| 9 | Mon, Sept 16 | Section 1.4 - Predicates (finished) | 1.4: # 12, 14, 15, 17, 18, 19 |
| 10 | Wed, Sept 18 |
Homework 1 Due Homework 2 Assigned Section 1.5 - Implications (started) |
1.5: # 1, 2abcg, 3, 4, 5, 8, 9 |
| 11 | Fri, Sept 20 |
Quiz 2 — covers Sugg. HW from 9/6, 9/9, 9/11, 9/13, 9/16, and 9/18 Section 1.5 - Implications (continued) |
1.5: # 10, 12, 14, 15, 16, 20 |
| Week 5 | |||
| 12 | Mon, Sept 23 |
Section 1.5 - Implications (finished) Section 2.1 - Mathematical Writing (started) |
1.5: # 25, 26, 27, 28 |
| 13 | Wed, Sept 25 | Section 2.1 - Mathematical Writing (continued) | Nothing new. Study for Exam 1! |
| 14 | Fri, Sept 27 | Exam 1 — covers 7.1, 1.3, 1.4, 1.5 | |
| Week 6 | |||
| 15 | Mon, Sept 30 | Section 2.1 - Mathematical Writing (finished) |
2.1: # 1abcdef, 2dfg, 4abcd, 5, 6, 9ab, 13 (don't "Write a letter to the Reader", just write a proof) |
| 16 | Wed, Oct 2 |
Homework 2 Due Homework 3 Assigned Section 2.2 - Proofs About Numbers (started) |
2.2: # 6ab, 7acde, 8, 9, 11, 15 |
| 17 | Fri, Oct 4 |
Quiz 3 Section 2.2 - Proofs About Numbers (continued) |
2.2: # 10, 17, and continue Wednesday's suggested homework! |
| Week 7 | |||
| 18 | Mon, Oct 7 | Section 2.2 - Proofs About Numbers (continued) | 2.2: # 1, 2, 3, 4, 16, 21 |
| 19 | Wed, Oct 9 |
Section 2.2 - Proofs About Numbers (finished) Section 2.3 - Induction, part 1 (started) |
2.2: # 19, 22 2.3: # 1abd |
| 20 | Fri, Oct 11 |
Quiz 4 Section 2.3 - Induction, part 1 (continued) |
Nothing new, work on Homework 3! |
| Week 8 | |||
| 21 | Mon, Oct 14 | Section 2.3 - Induction, part 1 (mostly finished) | 2.3: # 8abcdefg, 9a |
| 22 | Wed, Oct 16 |
Homework 3 Due Homework 4 Assigned Section 2.3 - Induction, part 1 (finished) |
No new questions, see Monday. |
| Fri, Oct 18 | Midterm Break - no class | ||
| Week 9 | |||
| 23 | Mon, Oct 21 | Section 2.4 - Induction, part 2 (started and finished) | 2.4: # 4ab, 5, 6, 12, 13a |
| 24 | Wed, Oct 23 | Section 2.5, part 1 - Pigeonhole Principle (started and finished) | 2.5: # 32a, 33, 34a, 35ab, and read the Examples! |
| 25 | Fri, Oct 25 | Exam 2 | |
| Week 10 | |||
| 26 | Mon, Oct 28 | Section 2.5, part 2 - Proofs by Contradiction (started and finished) | 2.5: # 1, 2, 3, 7, 11, 15, 22, 27 |
| 27 | Wed, Oct 30 |
Homework 4 Due Homework 5 Assigned Section 3.1 - Set Definitions and Operations (started) |
3.1: # 3, 4, 6, 7, 9, 10, 11, 13 |
| 28 | Fri, Nov 1 |
Quiz 5 — covers section 2.5 (both parts) Section 3.1 - Set Definitions and Operations (continued) |
3.1: # 1, 2, 5, 18 |
| Week 11 | |||
| 29 | Mon, Nov 4 |
Section 3.1 - Set Definitions and Operations (finished) Section 3.2 - More Operations on Sets (started) |
3.1: # 15, 16 17 |
| 30 | Wed, Nov 6 | Section 3.2 - More Operations on Sets (finished) | 3.2: # 1, 3, 4, 10, 11, 12, 13 |
| 31 | Fri, Nov 8 |
Quiz 6 Section 3.3 - Proving Set Properties (started) |
3.3: # 1 (no letters, just proofs), 2, 3ab, 5, 6ab, 7, 8ab |
| Week 12 | |||
| 32 | Mon, Nov 11 | Section 3.3 - Proving Set Properties (finished) | 3.3: # 11, 12ab, 13bc, 21, 22 |
| 33 | Wed, Nov 13 |
Homework 5 Due Homework 6 Assigned Section 4.1 - Functions - Definitions, Diagrams, and Inverses (started) |
4.1: # 1, 2, 3, 6 |
| 34 | Fri, Nov 15 |
Quiz 7 — covers Section 3.3 only Section 4.1 - Functions - Definitions, Diagrams, and Inverses (almost finished) |
4.1: # 12, 13, 14ab |
| Week 13 | |||
| 35 | Mon, Nov 18 |
Section 4.1 - Functions - Definitions, Diagrams, and Inverses (finished) Section 4.2 - The Composition Operation (started) |
4.1: # 14c, 17, 18 4.2: # 1, 2, 3 |
| 36 | Wed, Nov 20 | Section 4.2 - The Composition Operation (finished) | 4.2: # 5, 6, 7, 10 |
| 37 | Fri, Nov 22 | Exam 3 | |
| Week 14 | |||
| 38 | Mon, Nov 25 | Section 4.3 - Properties of Functions and Set Cardinality (started) | 4.3: # 1, 2, 3, 4, 7, 8 |
| Wed, Nov 27 | Thanksgiving Break - no class | ||
| Fri, Nov 29 | Thanksgiving Break - no class | ||
| Week 15 | |||
| 39 | Mon, Dec 2 |
Section 4.3 - Properties of Functions and Set Cardinality (finished) Section 4.4 - Properties of Relations (started) |
4.3: # 11, 16 4.4: none yet |
| 40 | Wed, Dec 4 |
Homework 6 Due Section 4.4 - Properties of Relations (mostly finished) |
4.4: # 1, 2, 3, 4, 6, 13, 14 |
| 41 | Fri, Dec 6 |
Quiz 8 Section 4.4 - Properties of Relations (finished) |
Same as Wednesday. |
| Finals Week | |||
| Mon, Dec 9 |
Final Exam, 1pm - 3pm ONLY for Section 102 (11:00am - 11:50am lecture time) |
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| Tues, Dec 10 |
Final Exam, 8am - 10am ONLY for Section 101 (10:00am - 10:50am lecture time) |
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