Name: Discrete Mathematics: Open Doors to Great Careers
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Created byRichard Han

Last updated 1/2018

English

What you'll learn

Refresh your math knowledge.
Gain a firm foundation in Discrete Mathematics for furthering your career.
Learn one of the mathematical subjects crucial for Computer Science.
Learn one of the mathematical subjects needed for Data Science.

Course content

6 sections • 48 lectures • 4h 37m total length

Introduction Lecture3:05

Statements7:28
In this lecture, we introduce the notions of a statement, statement variables, the negation symbol, and a truth-table.

Students will be introduced to the building blocks of logic.
Conjunction and Disjunction7:59
The logical symbols of conjunction and disjunction are introduced.
Students will learn how to evaluate the truth-value of statements involving conjunction and disjunction.
Conditional and Biconditional10:50
The conditional symbol and the biconditional symbol are introduced.
Students will learn how to evaluate the truth-values of conditional and biconditional statements.
Statement Forms8:53
The notion of a statement form is introduced.
Students will learn how to find the truth-tables for statement forms.
Problem Set: Statement Forms0:01
Logical Equivalence14:10
The notion of logical equivalence is introduced.
Students will learn how to show that two statement forms are logically equivalent and how to show that two statement forms are not logically equivalent.
Problem Set: Logical Equivalence0:01
Tautology and Contradiction7:18
In this lecture, the notion of a tautology and the notion of a contradiction are introduced.
Students will learn how to prove logical equivalences involving tautologies and contradictions.
Problem Set: Tautology and Contradiction0:01
Logical Equivalences15:27
In this lecture, we will look at a list of logical equivalences that can be used to prove other logical equivalences. We will also learn about the contrapositive of a conditional statement.

Students will learn how to use the laws in the list of logical equivalences to prove other logical equivalences.
Problem Set: Logical Equivalences0:01
Arguments8:55
In this lecture, the notions of argument, argument form, and validity are introduced.
Students will learn how to prove that an argument form is valid and how to prove that an argument form is invalid.
Problem Set: Arguments
Rules of Inference6:32
The notion of a rule of inference is introduced.
Students will learn about some important rules of inference.
Rules of Inference and Constructing Arguments10:34
In this lecture, we go through a list of rules of inference and apply them in constructing arguments.
Students will learn how to construct arguments using rules of inference.
Problem Set: Rules of Inference0:01

Predicate Calculus10:28
In this lecture, we introduce the notions of a predicate symbol, a variable, constant symbols, predicates, the domain of a variable, and the truth-set of a predicate.
Students will be introduced to the building blocks of predicate logic.
Finding the Truth-set of a Predicate6:02
Students will learn how to find the truth-set of a predicate.
Problem Set: Truth-set
Universal Quantifier9:12
The universal quantifier symbol is introduced.
Students will learn how to prove and disprove statements involving the universal quantifier.
Existential Quantifier8:54
The existential quantifier symbol is introduced.
Students will learn how to prove and disprove statements involving the existential quantifier.
Universal Conditional Statement9:08
The notion of a universal conditional statement is introduced.
Students will learn how to prove and disprove universal conditional statements.
Problem Set: Quantifiers
Negations and Quantified Statements12:01
Students will learn how to find the negation of a quantified statement.
Problem Set: Negations and Quantified Statements0:01
Multiple Quantifiers7:23
Students are introduced to statements involving multiple quantifiers.
Negations and Multiply-Quantified Statements7:05
Students will learn how negations of multiply-quantified statements work.
Problem Set: Multiple Quantifiers0:01
Rules of Inference Involving Universal Quantifier13:09
The rules of inference universal instantiation, universal modus ponens, universal modus tollens, and universal generalization are introduced.
Students will learn how rules of inference involving the universal quantifier work.
Rules of Inference Involving Existential Quantifier4:21
The rules of inference existential instantiation and existential generalization are introduced.
Students will learn how rules of inference involving the existential quantifier work.
Problem Set: Rules of Inference Involving Quantifiers0:01
Constructing Arguments Involving Quantified Statements11:00
Students will learn how to construct arguments using rules of inference involving quantifiers.
Problem Set: Constructing Arguments Involving Quantified Statements0:01

Methods of Proof8:31
Students will be able to prove existential statements by providing an example. Students will also learn how to disprove universal statements by providing a counter-example.
Proving Universal Statements10:00
Students will learn how to prove universal statements by using the method of exhaustion and by using the method of direct proof.
Problem Set: Methods of Proof0:01
Proof by Contradiction7:13
Students will be able to perform proofs by contradiction.
Proof by Contraposition8:38
Students will be able to perform proofs by contraposition.
Problem Set: Proofs by Contradiction and by Contraposition0:02

Mathematical Induction16:37
Students will be able to construct proofs using mathematical induction.
Problem Set: Mathematical Induction0:01
Strong Induction4:27
Students will be able to construct proofs using strong induction.
Strong Induction: Example11:03
An example of a proof by strong induction is provided.
Strong Induction: Additional Example10:17
An additional example of a proof by strong induction is provided.
Problem Set: Strong Induction0:01

Requirements

Basic understanding of algebra

Description

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The prerequisite to the course Discrete Mathematics: Open Doors to Great Careers 2.

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Would you like to learn a mathematics subject that is crucial for many high-demand lucrative career fields such as:

Computer Science
Data Science
Actuarial Science
Financial Mathematics
Cryptography
Engineering
Computer Graphics
Economics

If you're looking to gain a solid foundation in Discrete Mathematics, allowing you to study on your own schedule at a fraction of the cost it would take at a traditional university, to further your career goals, this online course is for you. If you're a working professional needing a refresher on discrete mathematics or a complete beginner who needs to learn Discrete Mathematics for the first time, this online course is for you.

Why you should take this online course: You need to refresh your knowledge of discrete mathematics for your career to earn a higher salary. You need to learn discrete mathematics because it is a required mathematical subject for your chosen career field such as computer science or electrical engineering. You intend to pursue a masters degree or PhD, and discrete mathematics is a required or recommended subject.

Why you should choose this instructor: I earned my PhD in Mathematics from the University of California, Riverside. I have extensive teaching experience: 6 years as a teaching assistant at University of California, Riverside, four years as a faculty member at Western Governors University, #1 in secondary education by the National Council on Teacher Quality, and as a faculty member at Trident University International.

In this course, I cover core topics such as:

Propositional Logic
Predicate Logic
Proofs
Mathematical Induction

After taking this course, you will feel CARE-FREE AND CONFIDENT. I will break it all down into bite-sized no-brainer chunks. I explain each definition and go through each example STEP BY STEP so that you understand each topic clearly. I will also be AVAILABLE TO ANSWER ANY QUESTIONS you might have on the lecture material or any other questions you are struggling with.

Practice problems are provided for you, and detailed solutions are also provided to check your understanding.

30 day full refund if not satisfied.

Grab a cup of coffee and start listening to the first lecture. I, and your peers, are here to help. We're waiting for your insights and questions! Enroll now!

Who this course is for:

Working Professionals
Anyone interested in gaining mastery of the core topics in Discrete Mathematics
Adult Learners
College Students

What you'll learn

Explore related topics

Course content

Introduction1 lecture • 3min

Propositional Logic16 lectures • 1hr 38min

Predicate Logic17 lectures • 1hr 39min

Proofs6 lectures • 34min

Mathematical Induction6 lectures • 42min

Concluding Letter2 lectures • 1min

Requirements

Description

Who this course is for: