MATH 213-X1 - Introduction to Discrete Mathematics (Fall 2024)
| General Information |
Homework |
Lecture Notes |
Other Resources |
This course provides an introduction to basic discrete mathematics with an emphasis on algorithms. Topics include sets and functions, algorithms, induction, enumeration, probability, relations, graphs, and trees.
| Lecture | MWF 12:00pm-12:50pm
Engineering Hall 106B1 |
| Textbook | Kenneth H. Rosen.
Discrete Mathematics and Its Applications, 7th edition |
| Instructor | Andrew Hardt
Office: CAB 69B
Email: ahardt@illinois.edu
Office Hours: MF 1:00pm-1:50pm, CAB 69B |
| More Details | Syllabus | Gradescope | If you can't access the Gradescope course, email me |
Homework assignments are weekly, due at 11:59pm on Sundays via Gradescope. Using LaTeX for your homework is encouraged, and you will receive 1 bonus point for each homework you typeset using LaTeX.
Here is a short LaTeX tutorial video.
- Lecture 1 (8/26): Syllabus, course overview
- Lecture 2 (8/28): Subset, power set, Cartesian product, etc. (Video, LaTeX tutorial)
- Lecture 3 (8/30): Set operations, proof techniques
- Lecture 4 (9/4): Functions
- Lecture 5 (9/6): Injectivity, surjectivty, inverse functions; Introduction to algorithms
- Lecture 6 (9/9): Searching and sorting algorithms
- Lecture 7 (9/11): Big-O notation (Extra Video)
- Lecture 8 (9/13): Mathematical Induction
- Lecture 9 (9/16): Strong Induction
- Lecture 10 (9/18): Counting Basics
- Lecture 11 (9/20): More Counting, and the Pigeonhole Principle
- Lecture 12 (9/23): Midterm 1 Review
- Lecture 13 (9/27): Permutations and Combinations
- Lecture 14 (9/30): Binomial coefficients and identities
- Lecture 15 (10/2): Generalized permutations and combinations (Last example)
- Lecture 16 (10/4): Introduction to probability
- Lecture 17 (10/7): Conditional probability, independence, Bernoulli trials
- Lecture 18 (10/9): Bayes' Theorem
- Lecture 19 (10/11): Recurrence relations
- Lecture 20 (10/14): Solving linear recurrence relations (Video)
- Lecture 21 (10/16): Inclusion-exclusion
- Lecture 22 (10/18): Applications of inclusion-exclusion
- Lecture 23 (10/21): Relations
- Lecture 24 (10/23): Midterm 2 Review
- Lecture 25 (10/28): Representing relations
- Lecture 26 (10/30): Equivalence relations
- Lecture 27 (11/1): Equivalence relations (cont.)
- Lecture 28 (11/4): Introduction to graphs
- Lecture 29 (11/6): More on graphs
- Lecture 30 (11/8): Adjacency/incidence matrices, and graph isomorphism
- Lecture 31 (11/11): Paths and connectivity
- Lecture 32 (11/13): Eulerian and Hamiltonian paths/circuits
- Lecture 33 (11/15): Shortest-path problems
- Lecture 34 (11/18): Midterm 3 Review
- Lecture 35 (12/2): Planar graphs
- Lecture 36 (12/4): Graph coloring
- Lecture 37 (12/6): Introduction to trees
- Lecture 38 (12/9): Applications of rooted trees
- Lecture 39 (12/11): Final Exam Review
Important Course Events
Midterm Exam 1: Wednesday, 9/25 in class (Solutions)
Midterm Exam 2: Friday, 10/25 in class (Solutions)
Midterm Exam 3: Wednesday, 11/20 in class (Solutions)
Final Exam: Thursday, 12/19 -- 1:30pm-4:30pm, 4025 Campus Instructional Facility (Solutions)
Problem Sessions: Thursdays, 10:00am-11:30am, Everitt Laboratory 2101 (through 10/17, then virtual)
Links