6.042J/18.062J Mathematics for Computer Science (Fall 2010, MIT OCW). Instructors: Prof. Tom Leighton and Dr. Marten van Dijk.
694 years, 4 months
25
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)
Course Currilcum
- Lecture 01 – Introduction to Proofs Unlimited
- Lecture 02 – Induction Unlimited
- Lecture 03 – Strong Induction Unlimited
- Lecture 04 – Number Theory I Unlimited
- Lecture 05 – Number Theory II Unlimited
- Lecture 06 – Graph Theory and Coloring Unlimited
- Lecture 07 – Matching Problems Unlimited
- Lecture 08 – Graph Theory II: Minimum Spanning Trees Unlimited
- Lecture 09 – Communication Networks Unlimited
- Lecture 10 – Graph Theory III Unlimited
- Lecture 11 – Relations, Partial Orders, and Scheduling Unlimited
- Lecture 12 – Sums Unlimited
- Lecture 13 – Sums and Asymptotics Unlimited
- Lecture 14 – Divide and Conquer Recurrences Unlimited
- Lecture 15 – Linear Recurrences Unlimited
- Lecture 16 – Counting Rules I Unlimited
- Lecture 17 – Counting Rules II Unlimited
- Lecture 18 – Probability Introduction Unlimited
- Lecture 19 – Conditional Probability Unlimited
- Lecture 20 – Independence Unlimited
- Lecture 21 – Random Variables Unlimited
- Lecture 22 – Expectation I Unlimited
- Lecture 23 – Expectation II Unlimited
- Lecture 24 – Large Deviations Unlimited
- Lecture 25 – Random Walks Unlimited
