Discrete Math Lecture 3/20

Discrete Mathematics (Arsdigita University)

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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