Contents

1. Symbolic Logic
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   • Basic Concepts
   • Logical Equivalence
   • Conditional Statements
2. Switching Circuits and Boolean Algebra
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   • Switching Circuits
   • Boolean Algebra
   • Algebraic Equivalence
3. Boolean Functions
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   • Convert Boolean Function to Boolean Expression
   • Canonical Form
   • Minimal Representation
   • Logic Gates
4. Karnaugh Maps
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   • Grid Layout for Karnaugh Maps
   • Simplification Procedure
5. Propositional Logic
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   • Argument Forms
   • Converse, Inverse and Contrapositive
   • Rules of Inference
6. Predicate Calculus
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   • Predicate Quantifiers
   • Predicate Properties
7. Set and Its Connection with Boolean Algebra
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   • Basic Set Properties
   • Set Identities
   • Connection with Boolean Algebra
   • Russel's Paradox
8. Efficiency, Big
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   • Nested Evaluation of a Polynomial
   • Big Notation
   • Simple Features of
9. Mathematical Induction
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   • Principle of Mathematical Induction
   • Strong Principle of Mathematical Induction
10. Analysis of Algorithms
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    • Sequential Search
    • Binary Search
    • Complexity of Binary Search
    • Performance of Sorting Algorithms
11. Notation
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    • Definition of the Notation
    • Examples in Exaggerated Details
12. Number Bases
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    • Frequently Used Number Systems
    • Conversion to Numbers of Different Bases
13. Graphs and Their Basic Types
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    • Graphs and Directed Graphs
    • Basic Types and Features of Graphs
    • Planar Graphs
14. Eulerian and Hamiltonian Circuits
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    • Two Practical Problems
    • Eulerian and Hamiltonian Paths and Circuits
    • Fleury's Algorithm for Finding Eulerian Path or Circuit
15. Graph Isomorphism and Matrix Representations
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    • Graph Isomorphism and Isomorphic Invariants
    • The Adjacency Matrix
16. Trees
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    • Trees, Rooted Trees and Binary Trees
    • Traversal of Binary Trees
17. Spanning Trees
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    • The Concept of Spanning Trees
    • Spanning Tree Algorithm
    • Kruskal's Algorithm
18. Relations
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    • Binary Relations
    • Reflexivity, Symmetry and Transitivity
19. Equivalence Relations
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    • Equivalence Classes and Partitions
    • Property Closure
20. Partial Order Relations
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    • Partial Orderings
    • Hasse Diagrams
21. Recurrence Relations
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    • Recurrence Relations
    • Basic Concepts Related to Recurrence Relations
    • Simplest Case of General Solutions
22. Solution of Linear Homogeneous Recurrence Relations
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    • General Solutions for Homogeneous Problems
    • Derivation Hints for the Main Theorem
23. Basics of Linear Nonhomogeneous Recurrence Relations
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    • Connection between Homogeneous and Nonhomogeneous Problems
    • Examples of the First Glance
24. Solutions of Linear Nonhomogeneous Recurrence Relations
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    • A Case for Thought
    • Method of Undertermined Coefficients