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: |
Tu, Th | 11:00am - 12:15pm |
| Cudahy 120 |
Office Hours: |
Monday, | 10:00am - 11:00am |
| Cudahy 307 | Wednesday, | 3:00pm - 5:00pm |
| 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!
| August 27 | Classes begin |
| September 3 | Labor Day, no classes |
| September 4 | Last day to add/drop classes or request CR/NC option |
| October 18-19 | Midterm break, no classes |
| November 16 | Last day to withdraw from classes |
| November 21-23 | Thanksgiving, no classes |
| December 7 | Last day of classes |
| December 14 | Math 2100/2105/2350 final exam |
| # | Date | Topics | Suggested HW & Announcements |
|---|---|---|---|
| 1 | Tues, Aug 28 | 3.1: Set Definitions and Operations | |
| 2 | Thurs, Aug 30 |
More 3.1 Quiz 0 (ungraded) Homework 1 assigned |
Suggested Homework: 3.1.{1,2,4,5,7,14,16} |
| 3 | Tues, Sept 4 |
Finish 3.1 3.2: More Operations on Sets |
Suggested Homework: 3.2.{1,2,3,4,10,11,12,14} |
| 4 | Thurs, Sept 6 |
5.1: Introduction to Combinatorics 5.2: Basic Rules for Counting Quiz 1 Homework 1 due Homework 2 assigned |
Suggested Homework: 5.2.{1,2,4,6,7,8,10,14} |
| 5 | Tues, Sept 11 |
5.3: Combinations and the Binomial Theorem |
Suggested Homework: 5.3.{5,6,8,10,11,13,15,16,22,25,26} |
| 6 | Thurs, Sept 13 |
Finish 5.3 Quiz 2 Homework 2 due Homework 3 assigned |
Suggested Homework: 5.3.{31,32} |
| 7 | Tues, Sept 18 | 1.3: Truth-tellers, Liars, and Propositional Logic |
Suggested Homework: 1.3.{1,3,4,7,8,9,11,16,17} |
| 8 | Thurs, Sept 20 |
Finish 1.3 Quiz 3 Homework 3 due Homework 4 assigned |
Suggested Homework: 1.3.{10,14,16,17,18,20,21,23} |
| 9 | Tues, Sept 25 | 1.4: Predicates |
Suggested Homework: 1.4.{4,7,9,10,11,13,16,17} |
| 10 | Thurs, Sept 27 |
Exam 1 Homework 4 due Homework 5 assigned |
|
| 11 | Tues, Oct 2 |
1.5: Implications |
Suggested Homework: 1.5.{4,5,8,10,12,13,14,15,17,22} |
| 12 | Thurs, Oct 4 |
Finish 1.5 2.1: Mathematical Writing Quiz 4 Homework 5 due Homework 6 assigned |
Suggested Homework: 1.5.{16,25,26,27} |
| 13 | Tues, Oct 9 | Finish 2.1 |
Suggested Homework: 2.1.{2,3,4,9,10,13} |
| 14 | Thurs, Oct 11 |
2.2: Proofs about Numbers Quiz 5 Homework 6 due Homework 7 assigned |
Suggested Homework: 2.2.{3,7,14,15,16,17,18,27} |
| 15 | Tues, Oct 16 | Finish 2.2 |
Suggested Homework: 2.2.{3,7,14,15,16,17,18,27} |
| Thurs, Oct 18 | Midterm Break, no class | ||
| 16 | Tues, Oct 23 |
2.3: Mathematical Induction |
Suggested Homework: 2.3.{8,9} |
| 17 | Thurs, Oct 25 |
Finish 2.3 Quiz 6 Homework 7 due Homework 8 assigned |
Suggested Homework: 2.3.{8,9}, plus the in-class group work |
| 18 | Tues, Oct 30 | 2.5: Contradiction and the Pigeonhole Principle |
Suggested Homework: 2.5.{3,4,5,11,17,22} |
| 19 | Thurs, Nov 1 |
Finish 2.5 Quiz 7 Homework 8 due Homework 9+10 assigned |
Suggested Homework: 2.5.{32,33,34,35,36,39} |
| 20 | Tues, Nov 6 | 3.3: Proving Set Properties | |
| 21 | Thurs, Nov 8 | Finish 3.3 |
Suggested Homework: 3.3.{2, 3, 5, 6, 11, 13, 20, 21, 22, 23} |
| 22 | Tues, Nov 13 |
Exam Review Quiz 8 |
|
| 23 | Thurs, Nov 15 |
Exam 2 Homework 9+10 due Homework 11 assigned |
|
| 24 | Tues, Nov 20 | 4.1: Definitions, Diagrams, and Inverses |
Suggested Homework: 4.1.{1,12,15,16,17,20} 4.3.{1,2,3,4} |
| Thurs, Nov 22 | Thanksgiving Break, no class | ||
| 25 | Tues, Nov 27 | 4.3: Properties of Functions and Set Cardinality |
Suggested Homework: 4.3.{11,14,16,19,21} |
| 26 | Thurs, Nov 29 |
4.4: Properties of Relations Quiz 9 Homework 11 due Homework 12 assigned |
Suggested Homework: 4.4.{1,3,4,9,10,15,21} |
| 27 | Tues, Dec 4 | 4.5: Equivalence Relations |
Suggested Homework: 4.5.{2,3,9,10a-c,11a-c,14} |
| 28 | Thurs, Dec 6 |
Sizes of Infinity Quiz 10 Homework 12 due |
watch this video |
| Fri, Dec 14 | Final Exam, 3:30pm - 5:30pm |