MOOCs for college-level discrete math? Specifically I am looking for short lectures (and quizzes) on specific topics.
(like Khan Academy offers)
Topics I am learning about include;
Intro logic-theory + set-theory

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*Notation, negation, simplification, result of set operations)

*Relations, functions

Intro proofs

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*By contradiction, induction, well-ordering

Intro graph theory

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*Graph coloring (chromatic numbers), Eulerian paths, Eulerian circuit, Hamiltonian paths, Minimal spanning trees (Prim's and Kruskal's algorithms), shortest path computation

Intro combinatorics

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*Permutations, combinations, inclusion-exclusion, binomial theorem

 A: MIT has a portal where they put lots of courses on MANY subjects, and in a less informal way than Kan. Their material is really good, and you will probably find those topics in some of the courses there.
http://ocw.mit.edu/index.htm 
EDIT: As mentioned in the comment by eccstartup coursera is another option, but with only a fraction of what you can find on MIT's opencourseware, but it still might have many different courses.
A: I would suggest you look at coursera. They have a large variety of courses, university level, with $15$ minute lectures (depending on the prof). Generally, these courses are $6-8$ weeks long and have accompaning exercises, quizzes and end of the year exams. I am currently taking a few courses and I have to say that I am quite impressed with the quality of material. 
For Intro to proofs check out: Introduction to Mathematical Thinking by Keith Delvin. It starts Sept. $2^{nd}$. You can also check out Intro to Logic by Michael Genesereth and this starts Sept. $30^{th}$. 
For graph theory you can check out Social and Economic Networks: Models and Analysis. While it may not explicitly teach what you have mentioned, I am sure it will have those aspects as it is dealing with networks. 
For Probability There is a probability course but it is in Mandarin (?). You can check it out here if you can understand it. You can also check out Intro to Probability and Statistics from MIT open courseware. 
As one of the answers has said, the MIT network is quite large. You may also want to look at the Sakai Project but I'm not familiar with it. 
