Course 02: Discrete Mathematics (Arsdigita University)
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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.
01 What kinds of problems are solved in discrete math?
02 Boolean Algebra and formal logic
03 More logic: quantifiers and predicates
04 Sets
05 Diagonalization, functions and sums review
06 Basic arithmetic and geometric sums, closed forms.
07 Chinese rings puzzle
08 Solving recurrence equations
09 Solving recurrence equations (cont.)
10 Mathematical induction
11 Combinations and permutations
12 Counting Problems
13 Counting problems
14 Counting problems using combinations, distributions
15 Counting problems using combinations, distributions
16 The pigeonhole principle and examples. The inclusion/exclusion theorem and advanced examples. A combinatorial card trick.
17 Equivalence Relations and Partial Orders
18 Euclid's Algorithm
19 Recitation -- a combinatorial card trick
20 Cryptography
More information about this course: http://www.archive.org/details/arsdigita_02_discrete_math http://www.aduni.org/courses/discrete
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