Discrete Mathematics by Udemy
Master Discrete Math for Computer Science and Mathematics Students
Course Highlights
- You will learn and develop the ability to think, read and write abstractly and Mathematically.
- You will learn the fundamentals of Set Theory including set builder notation, and set operations and properties.
- You will learn tautologies, contradictions, De Morgan's Laws in Logic, logical equivalence, and formulating quantified statements.
- You will lear how to create truth tables and tell the falsehood and truthfulness of a compound statements.
- You will know how to write, read and prove Mathematical statements using a variety of methods.
- You will understand boolean expressions, black boxes, logical gates and digital circuits.
- You will understand the Fundamental Theorem of Arithmetics, modular arithmetic, and learn how to find GCD & LCM.
- You will acquire a solid foundation in functions, function composition & combination, bijective and inverse functions.
- You will learn how to find equivalence relations and equivalence classes.
- You will learn essential concepts in Statistics and Combinatorics.
- You will master arithmetic and geometric sequences, and partial sums.
- You will learn the fundamental concepts in Graph Theory like incidence and adjacency matrices, walks, eccentricity, connectedness, and Ore's Theorem.
Skills you will learn!
Curriculum
36 Topics
Intro
Definition of a Set
Quiz
Number Sets
Quiz
Set Equality
Quiz
Set-Builder Notation
Quiz
Types of Sets
Quiz
Subsets
Quiz
Power Set
Quiz
Ordered Pairs
Quiz
Cartesian Products
Quiz
Cartesian Plane
Quiz
Venn Diagrams
Quiz
Set Operations (Union Intersection)
Quiz
Properties of Union and Intersection
Quiz
Set Operations (Difference Complement)
Quiz
Properties of Difference and Complement
Quiz
De Morgan’s Law
Quiz
Partition of Sets
Quiz
Extra Practice Problems
45 Topics
Introduction
Statements
Quiz
Compound Statements
Quiz
Truth Tables
Quiz
Examples
Quiz
Logical Equivalences
Quiz
Tautologies and Contradictions
Quiz
De Morgan’s Laws in Logic
Quiz
Logical Equivalence Laws
Quiz
Conditional Statements
Quiz
Negation of Conditional Statements
Quiz
Converse and Inverse
Quiz
Biconditional Statements
Quiz
Examples
Quiz
Digital Logic Circuits
Quiz
Black Boxes and Gates
Quiz
Boolean Expressions
Quiz
Truth Tables and Circuits
Quiz
Equivalent Circuits
Quiz
NAND and NOR Gates
Quiz
Quantified Statements - ALL
Quiz
Quantified Statements - THERE EXISTS
Quiz
Negations of Quantified Statements
Quiz
11 Topics
Introduction
Parity
Quiz
Divisibility
Quiz
Prime Numbers
Quiz
Prime Factorization
Quiz
GCD & LCM
Quiz
9 Topics
Intro
Terminologies
Direct Proofs
Proofs by Contrapositive
Proofs by Contradiction
Exhaustion Proofs
Existence & Uniqueness Proofs
Proofs by Induction
Examples
30 Topics
Intro
Functions
Quiz
Evaluating a Function
Quiz
Domains
Quiz
Range
Quiz
Graphs
Quiz
Graphing Calculator
Extracting Info from a Graph
Quiz
Domain & Range from a Graph
Quiz
Function Composition
Quiz
Function Combination
Quiz
Even and Odd Functions
Quiz
One to One (Injective) Functions
Quiz
Onto (Surjective) Functions
Quiz
Inverse Functions
Quiz
Long Division
Quiz
17 Topics
Intro
The Language of Relations
Quiz
Relations on Sets
Quiz
The Inverse of a Relation
Quiz
Reflexivity Symmetry and Transitivity
Quiz
Examples
Quiz
Properties of Equality & Less Than
Quiz
Equivalence Relation
Quiz
Equivalence Class
Quiz
35 Topics
Intro
Graphs
Quiz
Subgraphs
Quiz
Degree
Quiz
Sum of Degrees of Vertices Theorem
Quiz
Adjacency and Incidence
Quiz
Adjacency Matrix
Quiz
Incidence Matrix
Quiz
Isomorphism
Quiz
Walks Trails Paths and Circuits
Quiz
Examples
Quiz
Eccentricity Diameter and Radius
Quiz
Connectedness
Quiz
Euler Trails and Circuits
Quiz
Fleury’s Algorithm
Quiz
Hamiltonian Paths and Circuits
Quiz
Ore's Theorem
Quiz
The Shortest Path Problem
Quiz
17 Topics
Intro
Terminologies
Quiz
Mean
Quiz
Median
Quiz
Mode
Quiz
Range
Quiz
Outlier
Quiz
Variance
Quiz
Standard Deviation
Quiz
13 Topics
Intro
Factorials
Quiz
The Fundamental Counting Principle
Quiz
Permutations
Quiz
Combinations
Quiz
Pigeonhole Principle
Quiz
Pascal's Triangle
Quiz
14 Topics
Intro
Sequence
Quiz
Arithmetic Sequences
Quiz
Geometric Sequences
Quiz
Partial Sums of Arithmetic Sequences
Quiz
Partial Sums of Geometric Sequences
Quiz
Series
Quiz
Bonus Lecture
Discrete Mathematics
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