ArsDigita University - Discrete Mathematics

ArsDigita University - Discrete Mathematics. This consists of 20 video lectures given by Professor Shai Simonson, covering the mathematical topics most directly related to computer science. Topics covered this course included: 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 will be placed on providing a context for the application of the mathematics within computer science. The analysis of algorithms requires the ability to count the number of operations in an algorithm. Recursive algorithms in particular depend on the solution to a recurrence equation, and a proof of correctness by mathematical induction. The design of a digital circuit requires the knowledge of Boolean algebra. Software engineering uses sets, graphs, trees and other data structures. Number theory is at the heart of secure messaging systems and cryptography. Logic is used in AI research in theorem proving and in database query systems. Proofs by induction and the more general notions of mathematical proof are ubiquitous in theory of computation, compiler design and formal grammars. Probabilistic notions crop up in architectural trade-offs in hardware design. (from ADUni.org)

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 Lecture 01 - What kind of problems are solved in discrete math? Lecture 02 - Boolean algebra and formal logic Lecture 03 - More logic: quantifiers and predicates Lecture 04 - Sets Lecture 05 - Diagonalization, functions and sums review Lecture 06 - Basic arithmetic and geometric sums, closed forms Lecture 07 - Chinese rings puzzle Lecture 08 - Solving recurrence equations Lecture 09 - Solving recurrence equations (cont.) Lecture 10 - Mathematical induction Lecture 11 - Combinations and permutations Lecture 12 - Counting Problems Lecture 13 - Counting Problems (cont.) Lecture 14 - Counting problems using combinations, distributions Lecture 15 - Counting problems using combinations, distributions Lecture 16 - The pigeonhole principle and examples Lecture 17 - Equivalence Relations and Partial Orders Lecture 18 - Euclid's Algorithm Lecture 19 - Recitation - a combinatorial card trick Lecture 20 - Cryptography

 Web.. Discrete Mathematics Instructor: Shai Simonson. Course Description. Lecture and Course Files. Student Evaluations. This course covered the mathematical topics most directly related to computer science. aduni.org/courses/discrete/ Web Course 02: Discrete Mathematics (Arsdigita University) Instructor: Shai Simonson. Readings. Video Files. Other Files. This educational material is part of the collection: ArsDigita Computer Science University. www.archive.org/details/arsdigita_02_discrete_math