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MIT OpenCourseWare

Mathematics for Computer Science

This course 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. (from ocw.mit.edu )

Instructor

Prof. Tom Leighton and Dr. Marten van Dijk.

Computer science

2012

Lecture 02 - Induction

Lecture 03 - Strong Induction

Lecture 06 - Graph Theory and Coloring

Lecture 07 - Matching Problems

Lecture 08 - Graph Theory II: Minimum Spanning Trees

Lecture 10 - Graph Theory III

Lecture 12 - Sums

Lecture 14 - Divide and Conquer Recurrences

Lecture 16 - Counting Rules I

Lecture 19 - Conditional Probability

Lecture 20 - Independence

Lecture 21 - Random Variables

Lecture 22 - Expectation I

Lecture 24 - Large Deviations

Lecture 25 - Random Walks

Lecture 01 - Introduction to Proofs

Lecture 04 - Number Theory I

Lecture 05 - Number Theory II

Lecture 09 - Communication Networks

Lecture 11 - Relations, Partial Orders, and Scheduling

Lecture 13 - Sums and Asymptotics

Lecture 15 - Linear Recurrences

Lecture 17 - Counting Rules II

Lecture 18 - Probability Introduction

Lecture 23 - Expectation II