Discrete Mathematics

ArsDigita University - Discrete Mathematics. Taught by Professor Shai Simonson, this course covers 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)

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

References
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.