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


  1. INTRODUCTION to DISCRETE STRUCTURES click here

  2. PROBLEM SOLVING

    1. Problem Solving click here
    2. Extrapolation click here

  3. LOGIC

    1. Introduction to Logic click here

    2. Propositional Logic
      1. Introduction to Propositional Logic Click here
      2. Proposition
      3. From English to Proposition
      4. Reasoning with Propositions
      5. Interactive Exercises ---Has been repaired -- 1-20-07
  4. Predicate Logic
    1. Why Predicate Logic ? Click here
    2. Well Formed Formula (Wff) of Predicate Logic
    3. From Wff to Proposition Click here
    4. English to Logic Translation Click here
    5. Exercises Click here
    6. Reasoning with Predicate Logic
    7. Interactive Exercises ---Has been repaired -- 1-20-07

  • SETS

    1. Basics
      1. Introduction to Sets Click here
      2. Representation of Set Click here
      3. Equality, Subset, Etc Click here
      4. Exercises Click here
    2. Mathematical Reasoning Click here

    3. Set Operations
      1. Set Operations Click here
      2. Exercises Click here
      3. Properties of Set Operation Click here
      4. Exercises Click here

    4. Interactive Exercises on Reasoning about Sets Click here

  • RECURSION

    1. Recursive Definition
      1. Recursive Definition click here
      2. Generalized Set Operations Click here
      3. Exercises Click here
      4. More Examples on Recursive Definition click here --- Optional
      5. Recursive Definition of Function click here
    2. Recursive Algorithm click here
    3. Exercises Click here


    4. Proof by Induction
      1. First Principle of Mathematical Induction click here
      2. Exercises Click here
      3. Example of Use of Mathematical Induction --- Program Correctness click here
      4. Second Principle of Mathematical Induction click here
      5. Exercises Click here
      6. Interactive Exercises on Induction click here --- New -- January 26, 2007.
      7. Proof Checker for Mathematical Induction click here --- Repaired on January 26, 2007.

  • RELATION

    1. Introduction to Relation click here

    2. Definitions
      1. Binary Relation click here
      2. Definition of Relation (general relation) click here
      3. Equality of Relations click here
      4. Recursive Definition of Relation click here
      5. Exercises Click here
    3. Properties of Binary Relation, and Operations
      1. Digraph click here
      2. Digraph Representation of Binary Relation click here
      3. Properties of Binary Relation click here
      4. Exercises Click here
      5. Operations on Binary Relations click here
    4. Special Relations
      1. Closures of Binary Relation click here
      2. Exercises Click here
      3. Equivalence Relation click here
      4. Exercises Click here
      5. Order Relation click here
      6. Exercises Click here
  • FUNCTION

    1. Definitions click here
    2. Exercises Click here
    3. Growth of Function click here
    4. Exercises Click here


  • INDEX click here

  • Links to Related Web Sites click here

    For any trouble contact     cs381@cs.odu.edu




    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






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