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 | 11:00am - 12:15pm |
| Cudahy 401 |
Office Hours: |
Monday, | 3:45pm - 5:00pm |
| Cudahy 307 | Tuesday, | 2:00pm - 3:30pm |
| Friday, | 11:00am - 12:00pm | |
| and by appointment | ||
I recommend using Overleaf (free) to write your assignments in LaTeX. You can use this document as a basic template by cloning it to your own account.
I'm happy to help troubleshoot your LaTeX in office hours!
| Aug 26 | Classes begin |
| Sept 2 | Labor Day, no classes |
| Sept 3 | Last day to add/drop classes or request CR/NC option |
| Oct 10-16 | Midterm exams |
| Oct 17-20 | Midterm break, no classes |
| Nov 15 | Last day to withdraw from classes |
| Nov 27 - Dec 1 | Thanksgiving break, no classes |
| Dec 7 | Last day of classes |
| Dec 9 | Math 2100/2350 final exam |
| # | Date | Topics | Suggested HW & Announcements |
|---|---|---|---|
| 1 | Mon, Aug 26 |
Syllabus 7.1: Graph Theory |
7.1.{9,10,11} There will be no office hours on Monday, September 2 for Labor Day. |
| 2 | Wed, Aug 28 | 1.3: Truth-tellers, Liars, and Propositional Logic | 1.3.{1,3,4,7,8,9,11} |
| Mon, Sept 2 | Labor Day — no class | ||
| 3 | Wed, Sept 4 |
Homework 1 Assigned Finish 1.3 |
1.3.{14,17,21ace,23} |
| 4 | Mon, Sept 9 | 1.4: Predicates | 1.4.{5,7,8,9,10,11,12,13,16,17} |
| 5 | Wed, Sept 11 |
Quiz 1 1.5: Implications |
|
| 6 | Mon, Sept 16 |
Finish 1.5 3.1: Set Definitions and Operations |
1.5.{4,5,8,10,12,13,14,15,16,17,22,25,26,27} |
| 7 | Wed, Sept 18 |
Homework 1 Due Homework 2 Assigned Continue 3.1 |
3.1.{1,2,4,5,7,9,10} |
| 8 | Mon, Sept 23 |
Finish 3.1 3.2: More Operations on Set |
3.1.{14,16} 3.2.{1,2,3,4,10,11,12} |
| 9 | Wed, Sept 25 |
Quiz 2 Reviewing 3.1 and 3.2. |
Work on Homework 2 and form a study group for the exam! |
| 10 | Mon, Sept 30 | Exam Review | |
| 11 | Wed, Oct 2 |
Exam 1 Homework 2 Due |
|
| 12 | Mon, Oct 7 |
Homework 3 Assigned 2.1: Mathematical Writing |
2.1.{2,3,4,9,10,13} |
| 13 | Wed, Oct 9 |
Quiz 3 2.2: Proofs About Numbers |
2.2.{7,11,14,16,17,27} |
| 14 | Mon, Oct 14 |
Finish 2.2 SGID |
2.2.{as above} |
| 15 | Wed, Oct 16 |
Homework 3 Due Homework 4 Assigned 2.3: Mathematical Induction |
2.3.{8,9} |
| 16 | Mon, Oct 21 | 2.4: More About Induction | 2.4.{3,8a,12,13,15} |
| 17 | Wed, Oct 23 |
Quiz 4 2.5: Contradiction and the Pigeonhole Principle |
2.5.{32,33,34,35,36} |
| 18 | Mon, Oct 28 | Finish 2.5 | 2.5.{3,4,5,11,17,22} |
| 19 | Wed, Oct 30 |
Homework 4 Due Homework 5 Assigned 3.3: Proving Set Properties |
3.3.{3abc,5,6ab,7,8ab,11,20,21,22,23} |
| 20 | Mon, Nov 4 | 4.1: Functions — Definitions, Diagrams, Inverses | 4.1.{1,3,4,5,6,7,18} |
| 21 | Wed, Nov 6 |
Quiz 5 4.2: The Composition Operation |
4.2.{2,4,5,10,15} |
| 22 | Mon, Nov 11 | Exam Review | |
| 23 | Wed, Nov 13 |
Exam 2 Homework 5 Due |
|
| 24 | Mon, Nov 18 | 4.3: Properties of Functions and Set Cardinality | 4.3.{11,14,15,19,21} |
| 25 | Wed, Nov 20 |
Homework 6 Assigned Quiz 6 (covers 4.2 and 4.3) 4.4: Relations and their Properties |
4.4.{1,3,4,9,10,15,21} |
| 26 | Mon, Nov 25 |
Finish 4.4 4.5: Equivalence Relations |
4.5.{2,3,8(no partitions),9,10(a-c)} |
| Wed, Nov 27 | Thanksgiving Break — no class | ||
| 27 | Mon, Dec 2 | Different Sizes of Infinity and the Hilbert Hotel | 4.3.{28,29,30} |
| 28 | Wed, Dec 4 |
Homework 6 Due Finish Sizes of Infinity |
|
| Mon, Dec 9 | Final Exam |