MPCS 50103: Discrete Mathematics for Computer Science
Winter 2024

Coursework

• (20%) Homework assignments: Students must submit homework each week to pass the course. Each homework assignment contributes 2.5% to your course grade.
• (30%) Midterm examination: Thursday February 1 5:30–7:30 pm in Eckhart 312
• (50%) Final examination: Thursday March 7 5:30–8:30 pm in Eckhart 312

Course Policies:

• Policy on collaboration: Study groups are strongly encouraged. Collaboration with other students in the class is permitted, except in the writing stage. Collaboration is strictly forbidden in the writing stage. If you collaborate on a problem, you must acknowledge it at the beginning of your solution: give the name(s) of your collaborator(s), and state the nature of the collaboration. Giving or receiving a hint from another student counts as collaboration.
  • All homework problem solutions must be your own work.
  • Collaboration or assistance on homework from other MPCS or CS students prior to the submission deadline is forbidden.
  • Tutors are not permitted to solve or write homework problems for submission.
• Internet, LLM, and written source use: Any sources used on homework, including textbooks other than course textbooks, and ideas from other people, must be explicitly acknowledged and should never be copied or paraphrased.
  • Copied or paraphrased solutions obtained from the internet, LLMs, or other sources will result in a ZERO score for the entire homework assignment and will be flagged to the attention of the instructor for possible academic honesty violations.
• 10% dockage for late homework submissions by Thursday at 11:59 am, 12 hours after submission deadline.
• Handwritten homework submissions will not be graded.

Syllabus and Schedule of class meetings

Week 1: January 4

Logic and methods of proof; mathematical induction and strong induction
Class meeting 5:30–8:30 pm in Eckhart 312

Reading assignment: Rosen chapter 1, sections 1.1; 1.6–1.8; chapter 5, sections 5.1–5.3
Recommended reading: MIT chapter 1; chapter 3, sections 3.1–3.3, 3.6; chapter 5, sections 5.1–5.2; chapter 6, section 6.3

Week 2: January 11

Counting: permutations, combinations, complementary counting, inclusion-exclusion; bijective counting, combinatorial proof; Pascal's triangle and the binomial theorem; pigeonhole principle

Class meeting 5:30–8:30 pm in Eckhart 312

Reading assignment: Rosen chapter 6, sections 6.1–6.5; BH chapter 1, sections 1.1–1.5
Recommended reading: MIT chapter 14

Week 3: January 18

Discrete probability: events & probability spaces; conditional probability & independence; Bernoulli trials, binomial distributionx
Class meeting 5:30–8:30 pm in Eckhart 312

Reading assignment: Rosen chapter 7, sections 7.1–7.3; BH chapter 1, section 1.6, chapter 2, sections 2.1–2.5
Recommended reading: MIT chapter 16, sections 16.4–16.5, chapter 17, sections 17.5–17.8

Week 4: January 25

Discrete probability: random variables, expected value, linearity of expectation, binomial & geometric random variables, variance, Markov's and Chebyshev's inequalities
Class meeting 5:30–8:30 pm in Eckhart 312

Reading assignment: Rosen chapter 7, section 7.4; BH, chapter 3, sections 3.1–3.3, chapter 4, sections 4.1–4.2, 4.4–4.6
Recommended reading: MIT chapter 18, chapter 19, sections 19.1–19.6

Week 5: February 1

Midterm examination: closed-book closed-note closed-internet examination
5:30–7:30 pm in Eckhart 312

Week 6: February 8

Graph theory: degree sequence; graph isomorphism; paths, cycles, and connectivity; trees and spanning trees
Class meeting 5:30–8:30 pm in Eckhart 312

Reading assignment: Rosen chapter 10, sections 10.2–10.4, chapter 11, sections 11.1 & 11.4
Recommended reading: MIT chapter 11, section 11.1, sections 11.3–11.4, 11.8–11.10

Week 7: February 15

Graph Theory: Eulerian and Hamiltonian paths; graph coloring; matchings
Class meeting 5:30–7:30 pm

Reading assignment: Rosen chapter 10, sections 10.2, 10.5, 10.8
Recommended reading: MIT chapter 8, sections 8.1–8.4, 8.6–8.7, 8.9–8.10

Week 8: February 22

Number theory: divisibility, Euclidean algorithm, Bezout's theorem, modular arithmetic, Fermat's little theorem, Chinese remainder theorem
Class meeting 5:30–8:30 pm in Eckhart 312

Reading assignment: Rosen chapter 4, sections 4.1, 4.3–4.4, 4.6
Recommended reading: MIT chapter 14, chapter 8, sections 8.1–8.4, 8.6–8.7, 8.9–8.10

Week 9: February 29

Number theory and cryptography: RSA
Class meeting 5:30–8:30 pm in Eckhart 312

Reading assignment: Rosen chapter 4, section 4.6 MIT chapter 8, sections 8.1–8.4, 8.6–8.7, 8.9–8.10

Week 10: March 7

Final Exam: closed-book closed-note closed-internet examination

5:30 pm to 8:30 pm
Final examination 5:30–8:30 pm in E312