Math 311w-001 - Concepts of Discrete Mathematics
Introduction
This is the web page for section 1 of Math 311w taught by Tim Reluga in the autumn of 2024.
This course introduces students to the ideas of formal knowledge, and its central roll in mathematics. Using a theorem-proof framework much like that used by Euclid millenia ago, we will study elementary number theory advances from ancient times to our current technological age. Theories of modular arithmetic, set theory, formal logic, abstract algebra, and other discrete-math topics will be covered, with applications to encryption and digital information encoding. The course will include several writing assignments to help students develop their communications skills.
Course syllabus, including class data, contact information, office hours, and grading policies (subject to change)
Our textbook is Numbers, Groups, and Codes, by Humphreys and Prest, (library link) (publisher link) and partial solutions courtesy of Prof. Gary Mullen.
Quizes
Past quizes, posted with their answers.
- Quiz 1, Friday, September 6rd (answers)
- Quiz 2, Friday, September 13th (download here)
- Quiz 3, Friday, September 20th (answers)
- Exam 1, Friday, October 4th (solutions)
- Quiz 4, Friday, October 11th (functions, and relations)
- Quiz 5, Friday, October 18th
- Quiz 6, Friday, November 1th
- Quiz 7, Friday, November 15th
Homework
- Monday, October 14
- Section 1.4, #1
- Section 1.5, #1
- practice with congruence arithmetic
- Monday, October 7
- Practice homework: Section 2.3, problems 1,2,3,4,6,7,9
- extra practice with relations
- Wednesday, October 2nd
- Read sections 2.2 and 2.3 of H+P
- Problems 2, 5i, 8 from section 2.2 of H+P
- Problems 1, 2, 3 from section 2.2 of H+P
- Wednesday, September 25th
- Monday, September 23th
- Friday, September 20th
- Problems 1-5 here
- Section 3.1, #4
- Section 3.2, #1,2
- Monday, September 16th
- Do 2 problems from here
- Classify all the statements here, with proofs when appropriate
- Friday, September 13th
- Section 1.2, #12
- Do this proof practice
- Read section 3.1 of H+P on propositional logic
- Truth table practice here and here
- Monday, September 9th
- Read section 1.2 of H+P on induction
- Do some practice here and - 1-3 here
- Friday, September 6th
- Read section 1.1 of H+P.
- Do some of the problems 5-19 here to get practice calculating linear combinations and gcd’s.
- Use the gcd duality theorem to prove that gcd (ax, ay) = agcd (x, y).
- How do we know that Euclid’s algorithm will always terminate in a finite number of steps?
- Friday, August 30th
- Read section 1.1 of H+P.
- Do problems 1-4 here
- Wednesday, August 28th
Handouts
These are math-related links fished from the data-torrents as the semester progresses. Feel free to pass on your own.