MPCS 50103 Mathematics for Computer Science: Discrete Mathematics (Autumn 2020)

Section 1
Instructor(s) Brady, Geraldine (gb52)
Location Online Only
Meeting Times Thursday 5:30pm - 7pm
Fulfills Immersion Math


*This course will be conducted remotely and will be online only for Autumn 2020*

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 theorem, random variables, expected value, variance; graphs, including graph isomorphism, Euler and Hamiltonian paths and circuits, trees, and graph coloring; recurrences and asymptotic notation. 

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

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

  Class sessions: Course material from the current week and homework problems from the previous week will be discussed 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 a midterm exam (week 5), and a final exam the last day of class.  There will be no make-up exams.

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

    Homework: 25%.

    Midterm examination: 35%.

    Final examination: 40%.

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

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 successfully passing the Programming Placement exam.

Other Prerequisites

MPCS Students only.

Overlapping Classes

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

  • MPCS 53001-1 -- Databases
  • MPCS 51400-1 -- Functional Programming
  • MPCS 51240-1 -- Product Management
  • MPCS 53014-1 -- Big Data Application Architecture