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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. 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.
Instructor: Shai Simonson
Text: Discrete Mathematics and its Applications, Rosen.
Reference: Concrete Mathematics, Graham, Knuth and Patashnik
Requirements: Four exams, seven problem sets, one research problem set.
This educational material is part of the collection: ArsDigita Computer Science University
| Date: | 2000 |
![[4.0 out of 5 stars]](/images/star.png "[4.0 out of 5 stars]")
Reviewer: liuzhi - - May 29, 2009
Subject: thanks
thanks
Reviewer: Mano Priya - - May 5, 2009
Subject: Help me to dwonload materials
How can i download materials. Please help me out
Reviewer: group_sub - - October 24, 2008
Subject: Course 02: Discrete Mathematics (Arsdigita University)
Kindly tell how to download this lecture...
Reviewer: waacoc0 - - October 13, 2008
Subject: .
how can i download this?
Reviewer: bellrus - - August 6, 2008
Subject: A good material
Funny lecturer.
Thank you so much.
Reviewer: vse - - December 13, 2007
Subject: Very Good Course
Shai is a good intructor and teaches the material in a fun way.
I found a truth table tester that may help you train the concepts from lecture 1. It is in German but that shouldnt matter for that topic.
Here is the url http://www.uni-due.de/~gph120/wahrheitstafeln/ .
Reviewer: sivam.iitm - - August 23, 2007
Subject: its a greeeeeeeeeeeeet work
thanks for giving a valuable informaaaaaaaaaaaation
Reviewer: wackyStudent - - August 19, 2007
Subject: Great refresher
Wish I had knew this site before I took this class, but I downloaded it since my professor didn't cover half this stuff.
Reviewer: ramboisme - - May 16, 2007
Subject: video lectures are really good
video lectures are really good. I am so glad to find them here.
Reviewer: Vaasu - - February 12, 2007
Subject: GooD
Good Book