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Ultimate Guide to Discrete Mathematics

What Will I Learn? You will learn and develop the ability to think, read and write abstractly and Mathematically. You …

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What Will I Learn?

You will learn and develop the ability to think, read and write abstractly and Mathematically.

You will learn tautologies, contradictions, De Morgan's Laws in Logic, logical equivalence, and formulating quantified statements.

You will know how to write, read and prove Mathematical statements using a variety of methods.

You will learn the fundamentals of Set Theory including set builder notation, and set operations and properties.

You will lear how to create truth tables and tell the falsehood and truthfulness of a compound statements.

Course Overview

A survey in the Uk shows that the total number of skills required for a single job has increased by 10% year-over-year since 2017. Furthermore, one in three skills in an average 2017 job posting are already obsolete. Due to ongoing business disruption and rapidly evolving needs, emerging skills gaps have accelerated due to the COVID-19 pandemic.

And to help you bridge that gap, Course Cloud has prepared this comprehensive Ultimate Guide to Discrete Mathematics online course. Ultimate Guide to Discrete Mathematics covers a collection of necessary skills required to help you achieve your goals. In addition, our industry professionals will guide you through the process of establishing a solid foundation in Ultimate Guide to Discrete Mathematics.

The Ultimate Guide to Discrete Mathematics course is broken down into manageable sections, each of which will provide you with a new level of expertise. Our exclusive training in Ultimate Guide to Discrete Mathematics will equip you with the skills required to set yourself up for career success.

The Ultimate Guide to Discrete Mathematics provides internationally accepted certification upon successful completion. This certificate will add value to your resume and let you stand out among your peers. So enrol now and work your way towards becoming a highly sought-after professional at Ultimate Guide to Discrete Mathematics.

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Certification

After successfully completing the course, you will be able to get the UK and internationally accepted certificate to share your achievement with potential employers or include it in your CV. The PDF Certificate + Transcript is available at £6.99 (Special Offer - 50% OFF). In addition, you can get a hard copy of your certificate for £12 (Shipping cost inside the UK is free, and outside the UK is £9.99).

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 – Ultimate Guide to Discrete Mathematics	00:00:00