• Learning Outcomes for 3450:208 Introduction to Discrete Mathematics 

    Students are expected to be able to

    • communicate mathematical results through the proper use of mathematical notation and words
    • use symbolic logic and various proof-writing techniques, including Mathematical Induction
    • describe the basic properties and operations of sets, functions and relations
    • learn the basics of logic circuits, number systems, set theory, sequences, algorithms, and probability.
  • Topical Outline
    • Logical Form and Logical Equivalence
    • Conditional Statements
    • Valid and Invalid Arguments
    • Application:  Digital Logic Circuits
    • Application:  Number Systems and Circuits Addition
    • Basic Definitions of Set Theory
    • Properties of Sets
    • Disproofs, Algebraic Proofs, and Boolean Algebras
    • Counting Elements of disjoint Sets:  The Addition Rule
    • Direct Proof and Counterexample I:  Introduction
    • Direct Proof and Counterexample III:  Divisibility
    • Direct Proof and Counterexample IV:  Division into Cases and the Quotient-Remainder Theorem
    • Application:  Algorithms
    • Sequences
    • Mathematical Induction I
    • Mathematical Induction II
    • Strong Mathematical Induction and the Well-Ordering Principle
    • Solving Recurrence Relations by Iteration
    • Second-Order Linear Homogenous Recurrence Relations with Constant Coefficients
    • Big Oh, Omega and Theta Notations
    • Application:  Efficiency of Algorithms I
    • Exponential and Logarithmic Functions:  Graphs and Orders
    • Application:  Efficiency of Algorithms II
    • Possibility Trees and the Multiplication Rule
    • Counting Elements of Disjoint Sets:  The Addition Rule
    • Counting Subsets of a Set:  Combinations
    • Combinations with Repetition Allowed