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Materials for MATH 225
Discrete Mathematics and Statistics

Syllabus Addendum

Week 01 Set Theory
Sets, Cardinality of Sets, Equal and Equivalent Sets, Subsets,
Union, Intersection, Complement, Differences of Sets,
Venn Diagram, De Morganís Laws, Ordered Pairs and
Cartesian Products

Week 1 PowerPoint

Week 02 Logic
Propositions, Conjunctions of Propositions and their Truth Tables
Disjunctions of Propositions and their Truth Tables
Order of Operations among the Conjunction,
Disjunction and Negation,
Conditional Propositions and Logical Equivalence
Contraposition or Transposition of Conditional Propositions
Biconditional Propositions and Logical Equivalence

Week 2 PowerPoint

Week 3 Graph Theory, Paths, Circuits and Trees
Graphs, Graph Types, Introduction to Trees and Coding,
Searching and Spanning Trees, Paths and Cycles

Week 3 PowerPoint

Week 04 Matrices
Relations, Sequences, Special Sequences, Matrices and Matrix Operations

Week 4 PowerPoint

Week 05 Algorithms
Augmented Matrices
Different Types of Algorithms,
Big O Calculations for Matrix Operations,
Searching Algorithms, Sorting Algorithms, Big O Notation,
Array Sorting and Runtime for Different Sorting Algorithms
Comparing Different Runtimes

Week 5 PowerPoint
Week 5 Excel Solver Demo

Week 06 Probability
Events and Sample Spaces in Probability, Complement of Events,
Types of Probability, Addition Rule in Probability,
Multiplication Rule in Probability

Week 6 PowerPoint
Week 6 Excel Powerball and Kentucky Derby data

Week 07 Statistics
Introduction, Graphs

Week 7 PowerPoint
Week 7 Excel Container data

Week 8 - Have a great Thanksgiving!

Week 09 Statistics
Frequencies, Fractiles,
Measurements, Central Tendency, Dispersion

Week 9 PowerPoint
Week 9 Excel Cephalic Index and Beans data

Week10 Statistics
Probability Distribution, Confidence Intervals
Correlation and Regression

Week 10 PowerPoint
Week 10 Olympics data

Week11 Summary

Week 11 PowerPoint

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