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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