MAT 241: Discrete Mathematics

Spring 2023

Final exam information

1. Logistics

• Notes and textbooks are not allowed on exams.
• tables1.pdf will be provided for you.
• Electronic devices (calculator, laptop, smart phone) are not allowed on exams.
• You have 70 minutes.

2. How to study

Please see tips from first exam.

Get enough rest during finals week and the weekend before. Create a list and schedule of what you will do each day, including enough sleep in your schedule. Start studying early enough so you can take breaks; reward yourself after working hard.

Practicing by solving problems is much more effective than reading over solutions. There are plenty of review questions in the textbook. Going over homework/exams and correcting mistakes is also a good idea.

3. Exam content

The exam covers everything we have done. While the exam is cumulative, we will focus on what was not already tested. Here are some topics we emphasized since the last exam:

• graph theory
  • lots of terminology.
  • handshake theorem.
  • connectivity: walks, paths, cycles, etc.
  • adjacency matrix, matrix multiplication, counting walks.
  • Euler circuits, trails; Hamilton cycles, paths.
  • planarity: Kuratowski's theorem, elementary subdivisions, isomorphisms.
  • Euler's formula.
  • regular polyhedra.
  • chromatic number: proper colourings, duals, 4-colour theorem.
  • trees: terminology, characterization.

As usual, please note that this document is not a contract. I may have inadvertently left something off that ends up on an exam question. Moreover, I will not be able to test all of this material given the time limitations of the exam. I will have to pick and choose some subset of it.