**Course Description**
This course is an introduction to ideas and techniques in 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 have been 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.
**Course Contents**
Topics covered include: methods of proof; mathematical induction; basic number theory; basic counting (permutations, combinations, binomial theorem, pigeonhole principle, inclusion/exclusion); discrete probability theory (conditional probability, independence, Bayes's theorem, random variables, expected value, variance); recurrences; graphs and trees; asymptotic notation.
**Requirements**
• Lectures: Students are responsible for the material presented in lectures.
• Problem sessions: Weekly problem-solving sessions are held on Saturdays. Homework, quiz, and exam problems are reviewed and discussed at problem sessions. Attendance at problem sessions is strongly recommended for all students.
• Homework: Students are responsible for the material covered in homework assignments. Homework is assigned after class each week and is due the day before class the following week. 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.
**Course grade**
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%.
**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 not required. High-school level familiarity with sets and functions will be assumed. |