MAT 241: Discrete Mathematics
Fall 2022
Exam 3 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.
- In terms of counting:
- Leave answers such as $3\cdot7\cdot2+2^3-6$ as is; do not simplify.
- Do not leave answers in terms of $P(-,-)$ or $C(-,-)$; simplify to factorials or binomial coefficients.
- Simplify $\binom7r$ for $r=0,1,7$; these do not require calculators.
- Leave answers such as $7!$ or $\binom73$ as is; do not simplify.
- In terms of solving LHRRwCCs:
- You may need to solve quadratics using factoring or the quadratic formula (memorized).
- You may need to use the Rational Roots Theorem to find rational roots for higher-degree polynomials.
- Once a rational root is found as above, you may need to use long division (or factoring) to proceed.
- You may need to solve a system of linear equations.
- I will carefully engineer the questions so the arithmetic you have to do by hand is reasonable.
- In terms of counting:
- Since this class is scheduled within the 70-minute B4 block, you may use the entire 70 minutes.
2. How to study
Please see tips from first exam.
3. Exam content
The exam covers everything we have done, up to and including Section 10.3 (Section 10.5 will be on the next exam.) While the exam is cumulative, we will focus on what was not already tested. Here are some topics we emphasized since the last exam:- counting
- counting principles: Pigeonhole, Inclusion–Exclusion.
- recurrence relations: various types, back substitution.
- LHRRwCCs: characteristic polynomials, with or without repeated roots, found using factoring, quadratic formula, or the Rational Roots Theorem.
- graph theory
- lots of terminology.
- handshake theorem.
- connectivity: walks, paths, cycles, etc.
- adjacency matrix, matrix multiplication, counting walks.
- Euler circuits, trails; Hamilton cycles, paths.
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.