MPCS 50103 Mathematics for Computer Science: Discrete Mathematics (Autumn 2021)

Section 1
Instructor(s) Brady, Geraldine (gb52)
Location Ryerson 251 (Hybrid)
Meeting Times Wednesday 5:30pm - 7:30pm
Fulfills Immersion Math

Syllabus

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

On completion of the course, students will be practiced in using mathematical concepts and techniques to solve problems, and in expressing 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, and modular arithmetic; counting, including permutations, combinations, binomial theorem, pigeonhole principle, inclusion/exclusion principle; discrete probability, including conditional probability, independence, Bayes's rule, random variables, expected value, variance, Markov and Chebyshev bounds; graphs, including graph isomorphism, Euler and Hamiltonian paths and circuits, trees, and graph coloring; recurrences and asymptotic notation. 
 

Requirements
Students are responsible for all material presented in lectures and on homework assignments.

   Lectures: Students are responsible for all material presented in lectures. 

  Class sessions: Course material from the current week will be presented in lecture format at the class meetings.

  Homework: Weekly homework assignments are assigned after class and due the day before the next class.  Students are required to submit homework electronically.

   Exams: There will be four quizzes, a midterm exam, and a final exam.  There will be no make-up exams.

Course grade
The course grade is based on homework, quizzes, and exams.

    Homework: 5%.

    Quizzes: 20%.

    Midterm examination: 25%.

    Final examination: 50%.


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.

Course Prerequisites

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

Other Prerequisites

MPCS Students only.

This course requires competency in Unix and Linux. Please plan to attend the MPCS Unix Bootcamp (https://masters.cs.uchicago.edu/page/mpcs-unix-bootcamp) or take the online MPCS Unix Bootcamp Course on Canvas.

Overlapping Classes

This class is scheduled at a time that conflicts with these other classes:

  • MPCS 52011-2 -- Introduction to Computer Systems
  • MPCS 53112-1 -- Advanced Data Analytics
  • MPCS 51240-2 -- Product Management
  • MPCS 56520-1 -- Advanced Security Topics
  • MPCS 52555-1 -- Backends for Applications
  • MPCS 56511-1 -- Introduction to Computer Security

Eligible Programs

Masters Program in Computer Science MS in Computational Analysis in Public Policy (Year 2) MA in Computational Social Science (Year 1) MA in Computational Social Science (Year 2) Bx/MS in Computer Science (Option 3: Profesionally-oriented - Non-CS Majors)