An Introduction to Discrete Maths

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8 STUDENTS
An Introduction to Discrete Maths

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Course Curriculum

Sets
Introduction to Sets 00:01:00
Definition of Set 00:09:00
Number Sets 00:10:00
Set Equality 00:09:00
Set-Builder Notation 00:10:00
Types of Sets 00:12:00
Subsets 00:10:00
Power Set 00:05:00
Ordered Pairs 00:05:00
Cartesian Products 00:14:00
Cartesian Plane 00:04:00
Venn Diagrams 00:03:00
Set Operations (Union, Intersection) 00:15:00
Properties of Union and Intersection 00:10:00
Set Operations (Difference, Complement) 00:12:00
Properties of Difference and Complement 00:07:00
De Morgan’s Law 00:08:00
Partition of Sets 00:16:00
Logic
Introduction 00:01:00
Statements 00:07:00
Compound Statements 00:13:00
Truth Tables 00:09:00
Examples 00:13:00
Logical Equivalences 00:07:00
Tautologies and Contradictions 00:06:00
De Morgan’s Laws in Logic 00:12:00
Logical Equivalence Laws 00:03:00
Conditional Statements 00:13:00
Negation of Conditional Statements 00:10:00
Converse and Inverse 00:07:00
Biconditional Statements 00:09:00
Examples 00:12:00
Digital Logic Circuits 00:13:00
Black Boxes and Gates 00:15:00
Boolean Expressions 00:06:00
Truth Tables and Circuits 00:09:00
Equivalent Circuits 00:07:00
NAND and NOR Gates 00:07:00
Quantified Statements – ALL 00:08:00
Quantified Statements – THERE EXISTS 00:07:00
Negations of Quantified Statements 00:08:00
Number Theory
Introduction 00:01:00
Parity 00:13:00
Divisibility 00:11:00
Prime Numbers 00:08:00
Prime Factorisation 00:09:00
GCD & LCM 00:17:00
Proof
Intro 00:06:00
Terminologies 00:08:00
Direct Proofs 00:09:00
Proofs by Contrapositive 00:11:00
Proofs by Contradiction 00:17:00
Exhaustion Proofs 00:14:00
Existence & Uniqueness Proofs 00:16:00
Proofs by Induction 00:12:00
Examples 00:19:00
Functions
Intro 00:01:00
Functions 00:15:00
Evaluating a Function 00:13:00
Domains 00:16:00
Range 00:05:00
Graphs 00:16:00
Graphing Calculator 00:06:00
Extracting Info from a Graph 00:12:00
Domain & Range from a Graph 00:08:00
Function Composition 00:10:00
Function Combination 00:09:00
Even and Odd Functions 00:08:00
One to One (Injective) Functions 00:09:00
Onto (Surjective) Functions 00:07:00
Inverse Functions 00:10:00
Long Division 00:16:00
Relations
Intro 00:01:00
The Language of Relations 00:10:00
Relations on Sets 00:13:00
The Inverse of a Relation 00:06:00
Reflexivity, Symmetry and Transitivity 00:13:00
Examples 00:08:00
Properties of Equality & Less Than 00:08:00
Equivalence Relation 00:07:00
Equivalence Class 00:07:00
Graph Theory
Intro 00:01:00
Graphs 00:11:00
Subgraphs 00:09:00
Degree 00:10:00
Sum of Degrees of Vertices Theorem 00:23:00
Adjacency and Incidence 00:09:00
Adjacency Matrix 00:16:00
Incidence Matrix 00:08:00
Isomorphism 00:08:00
Walks, Trails, Paths, and Circuits 00:13:00
Examples 00:10:00
Eccentricity, Diameter, and Radius 00:07:00
Connectedness 00:20:00
Euler Trails and Circuits 00:18:00
Fleury’s Algorithm 00:10:00
Hamiltonian Paths and Circuits 00:06:00
Ore’s Theorem 00:14:00
The Shortest Path Problem 00:13:00
Statistics
Intro 00:01:00
Terminologies 00:03:00
Mean 00:04:00
Median 00:03:00
Mode 00:03:00
Range 00:08:00
Outlier 00:04:00
Variance 00:09:00
Standard Deviation 00:04:00
Combinatorics
Intro 00:03:00
Factorials 00:08:00
The Fundamental Counting Principle 00:13:00
Permutations 00:13:00
Combinations 00:12:00
Pigeonhole Principle 00:06:00
Pascal’s Triangle 00:08:00
Sequence and Series
Intro 00:01:00
Sequence 00:07:00
Arithmetic Sequences 00:12:00
Geometric Sequences 00:09:00
Partial Sums of Arithmetic Sequences 00:12:00
Partial Sums of Geometric Sequences 00:07:00
Series 00:13:00
Assignment
Assignment – An Introduction to Discrete Maths 00:00:00

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Course Info

8 Enrolled
  • Personal Development
PRIVATE COURSE
  • PRIVATE
  • 1 year
  • Number of Units123
  • Number of Quizzes0
  • 18 hours, 56 minutes

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