Discrete Mathematics

Course Content:
Topics include set algebra, mappings, relations, semigroups, groups, directed and undirected graphs, Boolean algebra, and propositional logic, with examples and applications of these to various areas of computer science. Emphasis placed on developing an intuitive understanding of basic structures rather than formal theories and influence of these topics on theory and practice of computing.

Site Content:
This site is meant to serve as a course summary as well as a Discrete Mathematics continuing education as I relate the course material to computer science code, methods, concepts or other material.
Bonus paper for the topic, 'Coding and Decoding for The Universal Product Code'

(01-13-03)   Sets and Subsets
(01-15-03)   Power Set of a Set
(01-17-03)   Operations on Sets
(01-20-03)   Examples of Set Operations
(01-22-03)   Computer Representation of Subsets
(01-24-03)   Divisions in the Integer
(01-27-03)   Euclidean Algorithm
(01-29-03)   Application of the Division Algorithm-Computing the GCD and LCM & Matrices
(01-31-03)   Mathematical Structures (Sets of objects with operations)
(02-03-03)   What is Closure?
(02-05-03)   Induction Example
(02-07-03)   Induction Examples
(02-14-03)   Product Sets and Partitions
(02-16-03)   Relations and Digraphs
(02-19-03)   The Digraph of a Relation
(02-21-03)   Properties of Relations
(02-26-03)   Groups
(03-10-03)   Subgroups
(03-12-03)   Subgroups-Basic Results
(03-19-03)   Groups and Subgroups
(03-21-03)   Groups and Coding
(03-24-03)   Coding
(03-26-03)   Group Codes
(03-31-03)   Boolean Matrices
(04-02-03)   Parity Check Matrix
(04-07-03)   Decoding
(04-09-03)   Maximum Likelihood Decoding
(04-14-03)   Encoding
(04-16-03)   Cosets
Sets and Subsets
Power Set of a Set
Operation on Sets
Examples of Set Operations
Computer Representation of Subsets
Divisions in the Integer
Euclidean Algorithm
Application of the Division Algorithm-Computing the GCD and LCM & Matrices
Mathematical Structures (Sets of objects with operations)
What is Closure?
Induction Example
Induction Examples
Product Sets and Partitions
Relations and Digraphs
The Digraph of a Relation
Properties of Relations
Groups
Subgroups
Subgroups and Basic Results
Groups and Subgroups
Groups and Coding
Coding
Group Codes
Boolean Matrices
Parity Check Matrix
Decoding
Maximum Likelihood Decoding
Encoding
Cosets
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