CS381 Discrete Structures/Discrete Mathematics Web Course Material
Last update August 2, 2009
Note: Reasonable efforts have been made to test
interactive exercises and tools that have been developed here. However, they
might still contain some errors. Please use them keeping that in mind.
Table of Contents
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INTRODUCTION to DISCRETE STRUCTURES
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PROBLEM SOLVING
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Problem Solving
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Extrapolation
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LOGIC
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Introduction to Logic
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Propositional Logic
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Introduction to Propositional Logic
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Proposition
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From English to Proposition
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Reasoning with Propositions
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Interactive Exercises ---Has been
repaired -- 8-2-09
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Predicate Logic
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Why Predicate Logic ?
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Well Formed Formula (Wff) of Predicate Logic
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From Wff to Proposition
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English to Logic Translation
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Exercises
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Reasoning with Predicate Logic
SET THEORY
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Basics
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Introduction to Set Theory
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Representation of Set
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Equality, Subset, Etc
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Exercises
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Mathematical Reasoning
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Set Operations
RECURSION
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Recursive Definition
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Recursive Definition
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Generalized Set Operations
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Exercises
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More Examples on Recursive Definition
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--- Optional
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Recursive Definition of Function
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Recursive Algorithm
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Exercises
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Proof by Induction
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First Principle of Mathematical Induction
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Exercises
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Example of Use of Mathematical Induction --- Program Correctness
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Second Principle of Mathematical Induction
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Exercises
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RELATION
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Introduction to Relation
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Definitions
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Binary Relation
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Definition of Relation (general relation)
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Equality of Relations
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Recursive Definition of Relation
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Exercises
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Properties of Binary Relation, and Operations
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Digraph
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Digraph Representation of Binary Relation
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Properties of Binary Relation
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Exercises
Click here
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Operations on Binary Relations
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Special Relations
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Closures of Binary Relation
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Exercises
Click here
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Equivalence Relation
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Exercises
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Order Relation
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Exercises
Click here
FUNCTION
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Definitions
click here
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Exercises
Click here
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Growth of Function
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Exercises
Click here
INDEX
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Links to Related Web Sites
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This material was originallhy given in Fall 1999 as an Internet
course.
People who contributed to this project (alphabetical order)
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Minyi He
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Li Li
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Anjlica Malla
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Guillaume Nerzic
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Mohamed Owis
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Lan Wang
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Lei Wang
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Chunxiang Xu
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Jia Zhu
This work was partially supported by NSF Grnat No. DUE-9981039