This course in an introduction to discrete mathematics oriented toward computer science. The course emphasizes mathematical proof and problem solving, employed on a variety of useful topics: logic; proof by induction; counting, factorials, and binomial coefficients; discrete probability; random variables, expected value, and variance; recurrences; graphs and trees; basic number theory.
On completion of the course, students will have been trained to think about and absorb mathematical concepts, to solve problems requiring more than standard recipes, and 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, data mining, and machine learning.
Topics covered include: logic and proof; mathematical induction; modular arithmetic; basic counting, permutations, combinations, binomial theorem, pigeonhole principle, inclusion/exclusion; discrete probability spaces, conditional probability, independence, Bernoulli trials, Bayes's theorem, random variables, expected value, variance, geometric and binomial distributions; graphs and trees; recurrences and methods of solving simple recurrences.
- Lectures: Students are responsible for all material presented in lectures.
- Problem sessions: Weekly problem sessions are held on Saturdays. Students are responsible for all material covered at the problem sessions.
- Homework: Weekly homework assignments are assigned after class and due the following week at the beginning of class. Homework must be submitted electronically using LaTeX.
- Exams: There are four quizzes (weeks 4, 5, 8, and 9), a midterm exam (week 6), and a final exam (week 10). There will be no make-up exams.
The course grade is based on homework, quizzes, and exams.
- Homework: 20%.
- Quizzes: 20% (5% for each of 4 quizzes).
- Midterm examination: 20%.
- Final examination: 40%.
Discrete Mathematics and its Applications (7th edition) (McGraw-Hill) by Kenneth H. Rosen (ISBN 978-0073383095).
Course information, announcements, assignments, and supplemental material can be found on the course web page:
First class: Tuesday June 20
Lectures: Tuesdays 5:30–8:30 pm in Ryerson 251
* No lecture July 4; make-up lecture Thursday, July 6 5:30–8:30 pm
Last Class will meet Tuesday, August 22th, 5:30–8:30 pm
Final Exam — Thursday August 24th, 5:30–8:30 pm
Problem-solving sessions: Saturdays 12:00 noon–2:00 pm in Ryerson 251