University of Chicago MPCS 50103—General Information

MPCS 50103: Discrete Mathematics for Computer Science
Summer 2022
General Information

Goal

This course is an introduction to ideas and techniques from discrete mathematics that are widely used in computer science. Topics include: proof methods (direct proof, proof by contradiction, mathematical induction), basic number theory (divisibility and modular arithmetic, Euclid's algorithm, prime numbers, Chinese remainder theorem, Fermat's little theorem), counting (permutations, combinations, binomial theorem, pigeonhole principle), discrete probability (conditional probability and independence, random variables, expected value, variance, Markov's and Chebyshev's inequalities), recurrences and methods of solving linear recurrences, graph theory (graph isomorphism, connectedness, trees, graph coloring, planar graphs). This course is prerequisite for courses in Algorithms, Data Analysis, Machine Learning, Networks, and Numerical Methods.

Prerequisites

Precalculus, especially logarithms and exponentials, is a prerequisite; calculus is recommended. High-school level familiarity with sets, functions, and relations will be assumed. There are no programming prerequisites.

Textbook

The required textbooks for the course are:
Discrete Mathematics and its Applications. 7th ed. (McGraw-Hill) by Kenneth H. Rosen (ISBN 978-0073383095)
Course notes of MIT's Mathematics for Computer Science

Syllabus

week topics
1 logic and methods of proof (ch 1)
mathematical induction, strong induction (ch 5)
2 number theory (ch 4):
divisibility, primes, and greatest common divisor; modular arithmetic; applications to cryptography
3 counting (ch 6):
permutations and combinations; pigeonhole principle; binomial theorem; combinatorial proofs
4/5 discrete probability (ch 7):
conditional probability, independence
random variables, expected value, variance
6 Midterm: online closed-book closed-note closed-internet midterm exam
7/8/9 graphs and trees (ch 10, ch 11):
basic properties of graphs; graph isomorphism; connectivity
Euler and Hamilton paths; graph coloring; trees; planar graphs
10Final exam: online closed-book closed-note closed-internet final exam

Note: Details of the syllabus may change, depending on class progress.

brady at cs dot uchicago dot edu