Arsdigita 02 (Discrete Mathematics) Lecture 3/20

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Course 02: 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: Licensed under Creative Commons Attribution ShareAlike 2.0: ArsDigita

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