CS381 Introduction to Discrete Structures
CS381 Discrete Structures/Discrete Mathematics Web Course Material
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
- INTRODUCTION to DISCRETE STRUCTURES
click here
- PROBLEM SOLVING
- Problem Solving
click here
- Extrapolation
click here
- LOGIC
- Introduction to Logic
click here
-
Propositional Logic
-
Introduction to Propositional Logic
Click
here
- Proposition
- From English to Proposition
- Reasoning with Propositions
-
Interactive Exercises
---Has been repaired -- 1-20-07
-
Predicate Logic
-
Why Predicate Logic ?
Click
here
- Well Formed Formula (Wff) of Predicate Logic
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From Wff to Proposition
Click
here
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English to Logic Translation
Click
here
-
Exercises
Click
here
-
Reasoning with Predicate Logic
-
Interactive Exercises
---Has been repaired -- 1-20-07
SETS
- Basics
- Mathematical Reasoning Click here
- Set Operations
- Set Operations Click here
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Exercises
Click
here
- Properties of Set Operation Click here
-
Exercises
Click
here
-
Interactive Exercises on Reasoning about Sets Click here
RECURSION
- Recursive Definition
- Recursive Definition
click here
- Generalized Set Operations
Click here
- Exercises
Click here
- More Examples on Recursive Definition
click here
--- Optional
- Recursive Definition of Function click here
- Recursive Algorithm click here
-
Exercises
Click
here
- Proof by Induction
- First Principle of Mathematical Induction click here
-
Exercises
Click
here
- Example of Use of Mathematical Induction --- Program Correctness
click here
- Second Principle of Mathematical Induction click here
-
Exercises
Click
here
- Interactive Exercises on Induction click here --- New -- January 26, 2007.
- Proof Checker for Mathematical Induction click here --- Repaired on January 26, 2007.
RELATION
- Introduction to Relation
click here
- Definitions
- Binary Relation
click here
- Definition of
Relation (general relation)
click here
- Equality of Relations
click here
- Recursive Definition of Relation
click here
-
Exercises
Click
here
- Properties of Binary Relation, and Operations
- Digraph
click here
- Digraph Representation of Binary Relation
click here
- Properties of Binary Relation
click here
-
Exercises
Click
here
- Operations on Binary Relations
click here
- Special Relations
FUNCTION
- Definitions
click here
-
Exercises
Click
here
- Growth of Function
click here
-
Exercises
Click
here
INDEX
click here
Links to Related Web Sites
click here
This material was originally given in Fall 1999 as an Internet course.
People who contributed to this project (alphabetical order)
-
Minyi He
-
Li Li
-
Anjlica Malla
-
Guillaume Nerzic
-
Mohamed Owis
-
Lan Wang
-
Lei Wang
-
Chunxiang Xu
-
Jia Zhu
This work was partially supported by NSF Grnat No. DUE-9981039