• 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