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Introduction
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Definition of a Set
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Number Sets
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Set Equality
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Set-Builder Notation
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Types of Sets
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Subsets
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Power Set
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Ordered Pairs
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Cartesian Products
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Cartesian Plane
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Venn Diagrams
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Set Operations (Union, Intersection)
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Properties of Union and Intersection
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Set Operations (Difference, Complement)
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Properties of Difference and Complement
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De MorganвЂ™s Law
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Partition of Sets
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Extra Practice Problems
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Introduction
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Statements
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Compound Statements
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Truth Tables
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Examples
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Logical Equivalences
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De MorganвЂ™s Laws in Logic
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Logical Equivalence Laws
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Conditional Statements
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Negation of Conditional Statements
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Converse and Inverse
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Biconditional Statements
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Examples
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Digital Logic Circuits
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Black Boxes and Gates
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Boolean Expressions
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Truth Tables and Circuits
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Equivalent Circuits
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NAND and NOR Gates
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Quantified Statements - ALL
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Quantified Statements - THERE EXISTS
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Negations of Quantified Statements
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Introduction
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Parity
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Divisibility
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Prime Numbers
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Prime Factorization
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GCD & LCM
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Intro
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Terminologies
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Direct Proofs
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Proofs by Contrapositive
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Exhaustion Proofs
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Existence & Uniqueness Proofs
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Proofs by Induction
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Examples
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Intro
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Functions
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Evaluating a Function
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Domains
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Range
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Function Composition
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Function Combination
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Even and Odd Functions
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One to One Functions
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Inverse Functions
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Intro
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The Language of Relations
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Relations on Sets
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The Inverse of a Relation
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Reflexivity, Symmetry and Transitivity
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Examples
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Properties of Equality & Less Than
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Equivalence Relation
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Equivalence Class
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Intro
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Graphs
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Subgraphs
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Degree
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Sum of Degrees of Vertices Theorem
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Incidence Matrix
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Isomorphism
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Walks, Trails, Paths, and Circuits
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Examples
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Connectedness
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Euler Trails and Circuits
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FleuryвЂ™s Algorithm
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Hamiltonian Paths and Circuits
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Ore's Theorem
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The Shortest Path Problem
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Intro
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Terminologies
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Mean
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Median
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Mode
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Range
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Outlier
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Variance
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Standard Deviation
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Intro
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Factorials
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The Fundamental Counting Principle
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Permutations
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Combinations
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Pigeonhole Principle
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Pascal's Triangle
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Intro
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Sequence
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Arithmetic Sequences
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Geometric Sequences
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Partial Sums of Arithmetic Sequences
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Partial Sums of Geometric Sequences
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Series
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Bonus Lecture