## Mathematics for Computer Science: Discrete Mathematics (Immersion Math)

Title Mathematics for Computer Science: Discrete Mathematics (Immersion Math) (50103)
Quarter Winter 2021
Instructor Timothy Ng (timng@cs.uchicago.edu)
Website

Syllabus

*This course will be conducted remotely and will be online only for Winter 2021*

#### Course Description

This course is an introduction to ideas and techniques from discrete mathematics that are widely used in computer science.  The course emphasizes mathematical proof and problem solving, employed on a variety of useful topics in counting, discrete probability, graphs, and basic number theory.

On completion of the course, students will be trained to think about and use mathematical concepts and techniques to solve problems, and to express mathematical notions precisely. They will be able to use ideas and techniques from discrete mathematics in subsequent courses in computer science, in particular courses in the design and analysis of algorithms, networks, numerical methods, software engineering, data analysis, and machine learning.

#### Course Contents

Topics covered include: methods of proof, including mathematical induction; number theory, incuding divisibility, prime numbers, greatest common divisors, modular arithmetic, Chinese remainder theorem, Fermat's little theorem; counting, including permutations, combinations, binomial theorem, pigeonhole principle, inclusion/exclusion principle; discrete probability, including conditional probability, independence, Bayes's theorem, random variables, expected value, variance, covariance; graphs, including graph isomorphism, graph coloring, trees, planar graphs; recurrences and asymptotic notation.

#### Textbook

Discrete Mathematics and its Applications (7th edition) (McGraw-Hill) by Kenneth H. Rosen (ISBN 978-0073383095).

#### Prerequisites

Precalculus, especially logarithms and exponentials, is a prerequisite; calculus is recommended but not required.  High-school level familiarity with sets, functions, relations, and mathematical notation will be assumed.

Prerequisites (Courses)

MPCS 50101 Concepts of Programming (completed or concurrently taking) OR successfully passing the Programming Placement exam.

Prerequisites (Other)

MPCS Students only.

Satisfies

Immersion Math

Time

Wednesday 5:20pm - 8:20pm

Location

Online Only