## 2017-07-18

### Discrete Math by Shai Simonson (Arsdigita University)

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source: Jaap Weel     2012年8月19日
This course covers the mathematical topics most directly related to computer science. Topics include: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, discrete probability, recursion, recurrence relations, and number theory. Emphasis is placed on providing a context for the application of the mathematics within computer science.
Instructor: Shai Simonson
Text: Discrete Mathematics and its Applications, Rosen.

Lecture 1/20 1:19:02 What kinds of problems are solved in discrete math?
Lecture 2/20 1:33:38 Boolean Algebra and formal logic
Lecture 3/20 1:09:04 More logic: quantifiers and predicates
Lecture 4/20 1:04:48 Sets
Lecture 5/20 [video is missing] Diagonalization, functions and sums review
Lecture 6/20 1:28:03 Basic arithmetic and geometric sums, closed forms.
Lecture 7/20 1:22:05 Chinese rings puzzle
Lecture 8/20 1:10:22 Solving recurrence equations
Lecture 9/20 1:26:29 Solving recurrence equations (cont.)
Lecture 10/20 1:19:48 Mathematical induction
Lecture 11/20 1:24:35 Combinations and permutations
Lecture 12/20 5:33 Counting Problems
Lecture 13/20 1:09:14 Counting problems
Lecture 14/20 1:30:56 Counting problems using combinations, distributions
Lecture 15/20 1:19:46 Counting problems using combinations, distributions
Lecture 16/20 1:37:20 The pigeonhole principle and examples. The inclusion/exclusion theorem and advanced examples. A combinatorial card trick.
Lecture 17/20 1:05:57 Equivalence Relations and Partial Orders
Lecture 18/20 1:18:25 Euclid's Algorithm
Lecture 19/20 59:30 Recitation -- a combinatorial card trick
Lecture 20/20 1:16:52 Cryptography