infocobuild

6.042J Mathematics for Computer Science

6.042J/18.062J Mathematics for Computer Science (Fall 2010, MIT OCW). Instructors: Prof. Tom Leighton and Dr. Marten van Dijk. 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)

Introduction to Proofs


Lecture 01 - Introduction to Proofs
Lecture 02 - Induction
Lecture 03 - Strong Induction
Lecture 04 - Number Theory I
Lecture 05 - Number Theory II
Lecture 06 - Graph Theory and Coloring
Lecture 07 - Matching Problems
Lecture 08 - Graph Theory II: Minimum Spanning Trees
Lecture 09 - Communication Networks
Lecture 10 - Graph Theory III
Lecture 11 - Relations, Partial Orders, and Scheduling
Lecture 12 - Sums
Lecture 13 - Sums and Asymptotics
Lecture 14 - Divide and Conquer Recurrences
Lecture 15 - Linear Recurrences
Lecture 16 - Counting Rules I
Lecture 17 - Counting Rules II
Lecture 18 - Probability Introduction
Lecture 19 - Conditional Probability
Lecture 20 - Independence
Lecture 21 - Random Variables
Lecture 22 - Expectation I
Lecture 23 - Expectation II
Lecture 24 - Large Deviations
Lecture 25 - Random Walks

References
Mathematics for Computer Science (Fall 2010)
Instructors: Prof. Tom Leighton and Dr. Marten van Dijk. Exams and Solutions. Readings. This course covers elementary discrete mathematics for computer science and engineering.