Mathematics for Computer Science

This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

Table of Contents

• What is a Proof?
• Induction I
• Induction II
• Number Theory I
• Number Theory II
• Graph Theory
• Graph Theory II
• Communication Networks
• Relations
• Sums, Approximations, and Asymptotics
• Sums, Approximations, and Asymptotics II
• Recurrences I
• Recurrences II
• Counting I
• Counting II
• Counting III
• Generating Functions
• Introduction to Probability
• Conditional Probability
• Independence
• Random Variables
• Expected Value I
• Expected Value II
• Weird Happenings
• Random Walks