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