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 412 |
Office Hours: |
Monday, | 9:00am - 10:00am |
| Cudahy 307 | Tuesday, | 3:00pm - 4:30pm |
| Friday, | 2:30pm - 4:00pm | |
| 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!
| Jan 14 | Classes begin |
| Jan 21 | Martin Luther King, Jr. Day, no classes |
| Jan 22 | Last day to add/drop classes or request CR/NC option |
| March 4-8 | Midterm exams |
| March 10-17 | Spring break, no classes |
| April 12 | Last day to withdraw from classes |
| April 18-22 | Easter break, no classes |
| May 4 | Last day of classes |
| TBD | Math 2100/2105/2350 final exam |
| # | Date | Topics | Suggested HW & Announcements |
|---|---|---|---|
| 1 | Mon, Jan 14 |
Syllabus 7.1: Graph Theory |
There will be no office hours on Tuesday, Jan 15 or Friday, Jan 18. Office hours will resume the following week. |
| 2 | Wed, Jan 16 | 1.3: Truth-tellers, Liars, and Propositional Logic | |
| Mon, Jan 21 | Martin Luther King, Jr. Day — no class | ||
| 3 | Wed, Jan 23 |
Homework 1 assigned Finish 7.1 Dijkstra's Algorithm Finish 1.3 |
1.3.{5,6,11b,16,21ace, 23cd} |
| 4 | Mon, Jan 28 |
1.4: Predicates Snow Day! — Read lecture notes on your own. |
1.4.{4,5,7,9,10,11,13,16,17} |
| 5 | Wed, Jan 30 |
Snow Day! — Continue to read 1.4 lecture notes. |
|
| 6 | Mon, Feb 4 |
Review 1.4 1.5: Implications |
1.5.{4,5,8,10,12,13,14,15,16,17,22,25,26,27} Optional Quiz 0 |
| 7 | Wed, Feb 6 |
Homework 1 due Homework 2 assigned Finish 1.5 3.1: Set Definitions and Operations |
3.1.{1,2,4,5,7,10} |
| 8 | Mon, Feb 11 |
Finish 3.1 |
3.1.{1,2,4,5,7,10,14,16} |
| 9 | Wed, Feb 13 |
Quiz 1 (1.5 and 3.1) 3.2: More Operations on Sets |
3.2.{1,2,3,4,10,11,12} |
| 10 | Mon, Feb 18 | Catchup / Review | |
| 11 | Wed, Feb 20 |
Homework 2 due Exam 1 (covers 7.1, 1.3, 1.4, 1.5, 3.1, 3.2) |
|
| 12 | Mon, Feb 25 |
Homework 3 assigned 2.1: Mathematical Writing |
2.1.{2,3,4,9,10,13} When the book asks you to write "letters", write formal proofs instead. |
| 13 | Wed, Feb 27 |
Quiz 2 2.2: Proofs About Numbers |
2.2.{7,11,14,15,16,17,18,27} |
| 14 | Mon, Mar 4 | Finish 2.2 | 2.2.{7,11,14,15,16,17,18,27} |
| 15 | Wed, Mar 6 |
Homework 3 due Homework 4 assigned 2.3: Mathematical Induction |
2.3.{8} |
| Mon, Mar 11 | Spring Break — no class | ||
| Wed, Mar 13 | Spring Break — no class | ||
| 16 | Mon, Mar 18 |
Finish 2.3 2.4: More about Induction |
2.4.{3, 6 (hint: prove \(7\) divides \(2^{3n}-1\) for all \(n \geq 1\)), 8, 12, 13, 15, 16} |
| 17 | Wed, Mar 20 |
Quiz 3 2.5: Contradiction and The Pigeonhole Principle |
2.5.{3,4,5,11,17,22} |
| 18 | Mon, Mar 25 | Finish 2.5 | 2.5.{32,33,34,35,36} |
| 19 | Wed, Mar 27 |
Homework 4 due Homework 5 assigned 3.3: Proving Set Properties |
|
| 20 | Mon, Apr 1 | Finish 3.3 | 3.3.{2,3abc,5,6,11,13,20,21,22,23} |
| 21 | Wed, Apr 3 |
Quiz 4 4.1: Definitions, Diagrams, and Inverses |
4.1.{1, 3, 6, 7, 12, 13, 14, 15, 20} |
| 22 | Mon, Apr 8 | Catchup / Review | |
| 23 | Wed, Apr 10 |
Homework 5 due Homework 6 assigned Exam 2 |
|
| 24 | Mon, Apr 15 |
Finish 4.1 4.3: Functions and Set Cardinality |
4.3.{1,2,3,4,5,11,14,16,19,21} |
| 25 | Wed, Apr 17 |
Quiz 5 4.2: The Composition Operation |
4.2.{1,3,5,10} 4.3.{6,7,8} |
| Mon, Apr 22 | Easter Break — no class | ||
| 26 | Wed, Apr 24 | 4.4: Properties of Relations | 4.4.{1,3,4,9,10,15,21a} |
| 27 | Mon, Apr 29 |
Finish 4.4 4.5: Equivalence Relatios |
4.5.{group work from class} |
| 28 | Wed, May 1 |
Homework 6 due Quiz 6 |
Read Theorem 4.3.10 Read Example 4.3.10 4.3.{28, 29, 30} |