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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.
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Description
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 content
- 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
Instructor
