MAT 241: Discrete Mathematics
Spring 2023
Exam 2 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.
3. Exam content
The exam covers everything we have done, up to and including Section 3.6. (Section 5.1 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:- predicate logic: predicates and quantifiers, negating quantified statements, proofs.
- proofs
- axiomatic mathematics: entities that do or do not require proofs.
- elementary number theory: lots of definitions, the Well-Ordering Principle, understand the proof of the Quotient-Remainder Theorem, proofs.
- proofs: strategies (I may or may not tell you which one to use); pay attention to example proofs in the text, some are quite famous: Quotient-Remainder Theorem, irrationality of $\sqrt2$, infinitude of primes, prime divisibility property, Fundamental Theorem of Arithmetic (uniqueness).
- induction: including complete induction.
- applications* in number theory (3.4)
- *in this section, the emphasis is on using—not proving—these famous and useful theorems.
- (extended) Euclidean Algorithm to calculate GCD and inverse modulo $m$ (3.4.1).
- linear congruence, Chinese Remainder Theorem (3.4.4).
- Fermat's Little Theorem (3.4.5).
- RSA encryption (3.4.6).
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.