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.
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.
Students are responsible for all material presented in lectures and problem sessions.
• Lectures: Students are responsible for all material presented in lectures.
• Problem sessions: Weekly problem-solving sessions are held on Saturdays. Students are responsible for all material covered at the problem sessions. Class participation is encouraged.
• 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 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 recommended but not required. High-school level familiarity with sets, functions, relations, and mathematical notation will be assumed.