Discrete Mathematics: Open Doors to Great Careers

Learn the core topics of Discrete Math to open doors to Computer Science, Data Science, Actuarial Science, and more!
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  • Lectures 48
  • Length 4.5 hours
  • Skill Level All Levels
  • Languages English
  • Includes Lifetime access
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    Available on iOS and Android
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About This Course

Published 7/2016 English

Course 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 chunksI 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!

What are the requirements?

  • Basic understanding of algebra

What am I going to get from this course?

  • 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.

What is the target audience?

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

What you get with this course?

Not for you? No problem.
30 day money back guarantee.

Forever yours.
Lifetime access.

Learn on the go.
Desktop, iOS and Android.

Get rewarded.
Certificate of completion.

Curriculum

Section 1: Introduction
Introduction Lecture
Preview
03:05
Section 2: Propositional Logic
07:28

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.

07:59

The logical symbols of conjunction and disjunction are introduced.

Students will learn how to evaluate the truth-value of statements involving conjunction and disjunction.

10:50

The conditional symbol and the biconditional symbol are introduced.

Students will learn how to evaluate the truth-values of conditional and biconditional statements.

08:53

The notion of a statement form is introduced.

Students will learn how to find the truth-tables for statement forms.

Problem Set: Statement Forms
Article
14:10

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 Equivalence
Article
07:18

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 Contradiction
Article
15:27

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 Equivalences
Article
08:55

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
Article
06:32

The notion of a rule of inference is introduced.

Students will learn about some important rules of inference.

10:34

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 Inference
Article
Section 3: Predicate Logic
10:28

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.

06:02

Students will learn how to find the truth-set of a predicate.

Problem Set: Truth-set
Article
09:12

The universal quantifier symbol is introduced.

Students will learn how to prove and disprove statements involving the universal quantifier.

08:54

The existential quantifier symbol is introduced.

Students will learn how to prove and disprove statements involving the existential quantifier.

09:08

The notion of a universal conditional statement is introduced.

Students will learn how to prove and disprove universal conditional statements. 

Problem Set: Quantifiers
Article
12:01

Students will learn how to find the negation of a quantified statement.  

Problem Set: Negations and Quantified Statements
Article
07:23

Students are introduced to statements involving multiple quantifiers.

07:05

Students will learn how negations of multiply-quantified statements work.

Problem Set: Multiple Quantifiers
Article
13:09

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.

04:21

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 Quantifiers
Article
11:00

Students will learn how to construct arguments using rules of inference involving quantifiers.

Problem Set: Constructing Arguments Involving Quantified Statements
Article
Section 4: Proofs
08:31

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.

10:00

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 Proof
Article
07:13

Students will be able to perform proofs by contradiction.

08:38

Students will be able to perform proofs by contraposition.

Problem Set: Proofs by Contradiction and by Contraposition
Article
Section 5: Mathematical Induction
16:37

Students will be able to construct proofs using mathematical induction.

Problem Set: Mathematical Induction
Article
04:27

Students will be able to construct proofs using strong induction. 

11:03

An example of a proof by strong induction is provided.

10:17

An additional example of a proof by strong induction is provided. 

Problem Set: Strong Induction
Article
Section 6: Concluding Letter
Concluding Letter
Article
Bonus Lecture
Article

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Instructor Biography

Richard Han, PhD in Mathematics

Hi there! My name is Richard Han. 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, over two 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. My expertise includes calculus and linear algebra. I am an instructor on Udemy for the courses Philosophy of Language: Solidify Critical Thinking Skills and Linear Algebra for Beginners: Open Doors to Great Careers.

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