Discrete Math by Shai Simonson (Arsdigita University)

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source: Jaap Weel     2012年8月19日
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.
More information about this course: http://www.archive.org/details/arsdig...http://www.aduni.org/courses/discrete
Licensed under Creative Commons Attribution ShareAlike 2.0: http://www.aduni.org/FAQ/#redist1http://creativecommons.org/licenses/b...

Lecture 1/20 1:19:02 What kinds of problems are solved in discrete math?

Lecture 2/20 1:33:38 Boolean Algebra and formal logic

Lecture 3/20 1:09:04 More logic: quantifiers and predicates

Lecture 4/20 1:04:48 Sets

Lecture 5/20 [video is missing] Diagonalization, functions and sums review
Lecture 6/20 1:28:03 Basic arithmetic and geometric sums, closed forms.
Lecture 7/20 1:22:05 Chinese rings puzzle
Lecture 8/20 1:10:22 Solving recurrence equations
Lecture 9/20 1:26:29 Solving recurrence equations (cont.)
Lecture 10/20 1:19:48 Mathematical induction
Lecture 11/20 1:24:35 Combinations and permutations
Lecture 12/20 5:33 Counting Problems
Lecture 13/20 1:09:14 Counting problems
Lecture 14/20 1:30:56 Counting problems using combinations, distributions
Lecture 15/20 1:19:46 Counting problems using combinations, distributions
Lecture 16/20 1:37:20 The pigeonhole principle and examples. The inclusion/exclusion theorem and advanced examples. A combinatorial card trick.
Lecture 17/20 1:05:57 Equivalence Relations and Partial Orders
Lecture 18/20 1:18:25 Euclid's Algorithm
Lecture 19/20 59:30 Recitation -- a combinatorial card trick

Lecture 20/20 1:16:52 Cryptography

Discrete Mathematics (IIT Roorkee)

# playlist of the 41 videos (click the up-left corner of the video)

source: nptelhrd    2015年5月7日
Mathematics - Discrete Mathematics by Dr. Tanuja Srivastava, Dr. Sugata Gangopadhyay & Dr. Aditi Gangopadhyay, Department of Mathematics, IIT Roorkee. For more details on NPTEL visit http://nptel.ac.in

Mod-01 Lec-01 Introduction to the theory of sets 56:09
Mod-01 Lec-02 Set operation and laws of set operation 49:08
Mod-01 Lec-03 The principle of inclusion and exclusion 47:29
Mod-01 Lec-04 Application of the principle of inclusion and exclusion 55:28
Mod-02 Lec-01 Fundamentals of logic 46:03
Mod-02 Lec-02 Logical Inferences 43:06
Mod-02 Lec-03 Methods of proof of an implication 50:27
Mod-02 Lec-04 First order logic(1) 42:34
Mod-02 Lec-05 First order logic(2) 43:17
Mod-02 Lec-06 Rules of influence for quantified propositions 38:22
Mod-03 Lec-01 Mathematical Induction(1) 43:21
Mod-03 Lec-02 Mathematical Induction(2) 52:38
Mod-04 Lec-01 Sample space, events 57:57
Mod-04 Lec-02 Probability, conditional probability 57:57
Mod-04 Lec-03 Independent events, Bayes theorem 42:48
Mod-04 Lec-04 Information and mutual information 53:46
Mod-05 Lec-01 Basic definition 41:36
Mod-05 Lec-02 Isomorphism and sub graphs 44:01
Mod-05 Lec-03 Walks, paths and circuits operations on graphs 54:48
Mod-05 Lec-04 Euler graphs, Hamiltonian circuits 42:09
Mod-05 Lec-05 Shortest path problem 45:42
Mod-05 Lec-06 Planar graphs 41:34
Mod-06 Lec-01 Basic definition. 1:05:09
Mod-06 Lec-02 Properties of relations 47:30
Mod-06 Lec-03 Graph of relations 49:33
Mod-06 Lec-04 Matrix of relation 51:34
Mod-06 Lec-05 Closure of relaton (1) 57:54
Mod-06 Lec-06 Closure of relaton(2) 56:52
Mod-06 Lec-07 Warshall's algorithm 1:03:17
Mod-07 Lec-01 Partially ordered relation 49:21
Mod-07 Lec-02 Partially ordered sets 55:06
Mod-07 Lec-03 Lattices 53:57
Mod-08 Lec-01 Boolean algebra 58:42
Mod-08 Lec-02 Boolean function(1) 1:02:51
Mod-08 Lec-03 Boolean function(2) 57:36
Mod-09 Lec-01 Discrete numeric function 1:00:36
Mod-09 Lec-02 Generating function 59:26
Mod-10 Lec-01 Introduction to recurrence relations 49:07
Mod-10 Lec-02 Second order recurrence relation with constant coefficients(1) 50:58
Mod-10 Lec-03 Second order recurrence relation with constant coefficients(2) 59:35
Mod-10 Lec-04 Application of recurrence relation 55:59