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; graphs and trees; recurrences; 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, and data mining.
Topics covered include: logic and proof; mathematical induction; 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; asymptotic notation and rates of growth; recurrences; basic number theory.
- Lectures: Students are responsible for all material presented in lectures.
- Discussion sessions: Weekly discussion sessions are held on Saturdays. Students are responsible for all material covered at the discussion sessions. Class participation is encouraged.
- Homework: Weekly homework assignments are assigned after class and due the following week at the beginning of class.
- Exams: There are four quizzes (weeks 4, 5, 9, and 10), a midterm exam (week 6), and a final exam (week 11). There will be no make-up exams.
The course grade is based on homework, quizzes, and exams.
- Homework: 5%.
- Quizzes: 20% (5% for each of 4 quizzes).
- Midterm examination: 25%.
- Final examination: 50%.
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 not required. High-school level familiarity with sets, functions, and relations will be assumed.
There are no programming prerequisites.