Discrete Mathematics Online Course for Academic Credit

Roger Williams University Course Catalog Listing: DMAT 225 - Computational Discrete Mathematics

DMAT 225 - Computational Discrete Mathematics - Learning Outcomes

• 1. To develop understanding and ability in symbolic logic
• 2. To understand and formulate basic mathematical proofs
• 3. To understand and formulate mathematical conjecture and algorithmic experimentation
• 4. To understand and compute the core concepts of Set Theory
• 5. To develop understanding of introductory Number Theory and Cryptography
• 6. To understand and formulate induction and recursion proofs and computations
• 7. To understand and compute with the Principals of Counting and Recurrence Relations
• 8. To develop understanding of introductory Graph and Tree Theory

DMAT 225 - Computational Discrete Mathematics - Syllabus of Topics

1.	Getting Started
	1.1.  Email and Chat
	1.2.  Learning About the Course
	1.3   Required Hardware
	1.4.  Software Fundamentals

2.	Logical Reasoning
	2.1.	Propositional Logic
	2.2.	Equivalences
	2.3.	Inference
	2.4.	Introduction to Proofs
	2.5.	Proof Methods and Strategies
	2.6.	Conjecture and Experimentation

3.	Set Theory
	3.1.	Sets and Set Operations
	3.2.	Functions
	3.3.	Sequences and Summations
	3.4.	Matrices

4.	Algorithms
	4.1.	Introduction
	4.2.	Growth of Functions
	4.3.	Complexity of Algorithms
	
5.	Number Theory
	5.1.	Modular Arithmetic
	5.2.	Divisibility
	5.3.	Primes
	5.4.	Greatest Common Divisors
	5.5.	Congruences
	5.6.	Cryptography

6.	Recursion
	6.1.	Danger in Recursion in Programming
	6.2.	Induction
	6.3.	Recursion and Algorithms
	
7.	Counting
	7.1.	Basics of Counting
	7.2.	Pigeonhole Principle
	7.3.	Permutations
	7.4.	Combinations
	7.5.	Recurrence Relations
	7.6.	Divide-and-Conquer Algorithms
	
8.	Relations
	8.1.	Properties of Relations
	8.2.	Closure
	8.3.	Equivalence
	
9.	Graph Theory
	9.1.	Graphs and Graph Models
	9.2.	Generating Graphs
	9.3.	Representing Graphs and Graph Isomorphism
	9.4.	Connectivity
	9.5.	Euler and Hamilton Paths
	9.6.	Graph Coloring
	9.7.	Trees



	

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