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Discrete Mathematics

Video Introducing this tutorial


Sets :
Introduction
Definition of a Set
Quiz
3 questions
Number Sets
Quiz
3 questions
Set Equality
Quiz
3 questions
Set-Builder Notation
Quiz
3 questions
Types of Sets
Quiz
3 questions
Subsets
Quiz
3 questions
Power Set
Quiz
3 questions
Ordered Pairs
Quiz
3 questions
Cartesian Products
Quiz
3 questions
Cartesian Plane
Quiz
3 questions
Venn Diagrams
Quiz
3 questions
Set Operations (Union, Intersection)
Quiz
3 questions
Properties of Union and Intersection
Quiz
3 questions
Set Operations (Difference, Complement)
Quiz
3 questions
Properties of Difference and Complement
Quiz
3 questions
De Morgan’s Law
Quiz
3 questions
Partition of Sets
Quiz
3 questions
Extra Practice Problems

Logic :
Introduction
Statements
Quiz
3 questions
Compound Statements
Quiz
3 questions
Truth Tables
Quiz
3 questions
Examples
Quiz
3 questions
Logical Equivalences
Quiz
3 questions
Tautologies and Contradictions
Quiz
3 questions
De Morgan’s Laws in Logic
Quiz
3 questions
Logical Equivalence Laws
Quiz
3 questions
Conditional Statements
Quiz
3 questions
Negation of Conditional Statements
Quiz
3 questions
Converse and Inverse
Quiz
3 questions
Biconditional Statements
Examples
Digital Logic Circuits
Black Boxes and Gates
Boolean Expressions
Quiz
4 questions
Truth Tables and Circuits
Equivalent Circuits
NAND and NOR Gates
Quiz
4 questions
Quantified Statements - ALL
Quantified Statements - THERE EXISTS
Negations of Quantified Statements
Quiz
6 questions

Number Theory :
Introduction
Parity
Quiz
3 questions
Divisibility
Quiz
3 questions
Prime Numbers
Quiz
3 questions
Prime Factorization
Quiz
3 questions
GCD & LCM
Section 4 Quiz
3 questions

Proofs :
Intro
Terminologies
Direct Proofs
Quiz
2 questions
Proofs by Contrapositive
Proofs by Contradiction
Exhaustion Proofs
Existence & Uniqueness Proofs
Proofs by Induction
Examples

Functions :
Intro
Functions
Evaluating a Function
Domains
Range
Function Composition
Function Combination
Even and Odd Functions
One to One Functions
Inverse Functions
Section 6 Quiz
4 questions

Relations :
Intro
The Language of Relations
Relations on Sets
The Inverse of a Relation
Quiz
5 questions
Reflexivity, Symmetry and Transitivity
Examples
Properties of Equality & Less Than
Equivalence Relation
Equivalence Class
Section 7 Quiz
6 questions

Graph Theory :
Intro
Graphs
Quiz
3 questions
Subgraphs
Quiz
3 questions
Degree
Quiz
3 questions
Sum of Degrees of Vertices Theorem
Quiz
3 questions
Adjacency and Incidence
Quiz
3 questions
Adjacency Matrix
Quiz
3 questions
Incidence Matrix
Quiz
3 questions
Isomorphism
Quiz
3 questions
Walks, Trails, Paths, and Circuits
Quiz
3 questions
Examples
Quiz
3 questions
Eccentricity, Diameter, and Radius
Quiz
3 questions
Connectedness
Quiz
3 questions

Statistics :
Intro
Terminologies
Mean
Median
Mode
Range
Quiz
7 questions
Outlier
Variance
Standard Deviation
Chapter Quiz
8 questions

Combinatorics :
Intro
Factorials
Quiz
3 questions
The Fundamental Counting Principle
Quiz
3 questions
Permutations
Quiz
3 questions
Combinations
Quiz
3 questions
Pigeonhole Principle
Quiz
3 questions
Pascal's Triangle
Quiz
3 questions
Bonus Lecture

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