Notes on Discrete Mathematics

1. Logic and Sets
    1.1 Bits, Logical Values and Propositions
    1.2 Logical Operations
         1.2.1 The Eight Logical Operations
                   Logical Operations Summary
         1.2.2 Logical Operations in Mathematica
         1.2.3 Logical Operations in MATLAB
         1.2.4 Logical Operations in C
    1.3 Boolean Algebra
                   Boolean Algebra Summary
    1.4 Predicate Logic  
    1.5 Rules of Inference and Valid Arguments
    1.6 Valid Arguments Involving Predicates
    1.7 Lists
    1.8 Sets
         1.8.1 Sets and Set Operations
         1.8.2 Lists and Sets in Mathematica
    1.9 Mathematical Induction
    1.10 Recursion


2. Algorithms
    2.1 Algorithms and their Complexity
        2.1.2 Solutions to Problems 1 - 11
    2.2 Comparison of Algorithms

3. Numerical Operations
    3.1 Numerical operations - Floor, Ceiling and Mod
         3.1.1 Definitions and Applications
         3.1.2 Numerical operations in Mathematica
    3.2 Summation
    3.3 Hashing
         3.3.1 Hashing - concepts
         3.3.2 A C program with a simple hashing algorithm
    3.4 Modular Arithmetic
    3.5 Two's Complement Representation of Negative Numbers
    3.6 RSA cryptography
         3.6.1 The Method
         3.6.2 RSA Cryptography in Mathematica

4. Permutations and Combinations
    4.1 The Sum and Product Rules
    4.2 Permutations
    4.3 Combinations
    4.4 Generating Permutations & Combinations

5. Recurrence Relations
    5.1 Recurrence Relations
    5.2 First Order Recurrence Relations
    5.3 Second Order Recurrence Relations
    5.4 Inhomogeneous equations
    5.5 Divide & Conquer Difference Equations
    5.6 Solving Recurrence Relations in Mathematica

6. Relations
    6.1 Equivalence Relations
    6.2 Partial Orderings

7. Graphs
    7.1 Graph Models
    7.2 Eulerian Paths
    7.3 Shortest Paths
    7.4 Graph coloring and scheduling
 
8. Trees
    8.1 Properties of trees
    8.2 Trees and expressions
    8.4 Minimum Spanning Trees
    8.5 Graphs and Electric Circuits
 
9. Boolean Algebra
    9.1 Disjunctive normal form
    9.2 Karnaugh Maps

10. An Introduction to Mathematica

  Mathematics 276 Directory