Discrete Mathematics: Open Doors to Great Careers
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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!
4.1 (71 ratings)
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
945 students enrolled
Created by Richard Han
Last updated 11/2016
English
Current price: $10 Original price: $20 Discount: 50% off
5 hours left at this price!
30-Day Money-Back Guarantee
Includes:
  • 4.5 hours on-demand video
  • 18 Articles
  • 36 Supplemental Resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
What Will I 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.
View Curriculum
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 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!

Who is the target audience?
  • Working Professionals
  • Anyone interested in gaining mastery of the core topics in Discrete Mathematics
  • Adult Learners
  • College Students
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Curriculum For This Course
48 Lectures
04:37:25
+
Introduction
1 Lecture 03:05
+
Propositional Logic
16 Lectures 01:38:12

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.

Preview 07:28

The logical symbols of conjunction and disjunction are introduced.

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

Conjunction and Disjunction
07:59

The conditional symbol and the biconditional symbol are introduced.

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

Conditional and Biconditional
10:50

The notion of a statement form is introduced.

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

Statement Forms
08:53

Problem Set: Statement Forms
00:01

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.

Preview 14:10

Problem Set: Logical Equivalence
00:01

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.

Tautology and Contradiction
07:18

Problem Set: Tautology and Contradiction
00:01

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.

Logical Equivalences
15:27

Problem Set: Logical Equivalences
00:01

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.

Arguments
08:55

Problem Set: Arguments
00:00

The notion of a rule of inference is introduced.

Students will learn about some important rules of inference.

Rules of Inference
06:32

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.

Rules of Inference and Constructing Arguments
10:34

Problem Set: Rules of Inference
00:01
+
Predicate Logic
17 Lectures 01:38:50

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.

Preview 10:28

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

Finding the Truth-set of a Predicate
06:02

Problem Set: Truth-set
00:00

The universal quantifier symbol is introduced.

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

Universal Quantifier
09:12

The existential quantifier symbol is introduced.

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

Existential Quantifier
08:54

The notion of a universal conditional statement is introduced.

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

Preview 09:08

Problem Set: Quantifiers
00:00

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

Negations and Quantified Statements
12:01

Problem Set: Negations and Quantified Statements
00:01

Students are introduced to statements involving multiple quantifiers.

Multiple Quantifiers
07:23

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

Negations and Multiply-Quantified Statements
07:05

Problem Set: Multiple Quantifiers
00:01

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.

Preview 13:09

The rules of inference existential instantiation and existential generalization are introduced.

Students will learn how rules of inference involving the existential quantifier work.

Rules of Inference Involving Existential Quantifier
04:21

Problem Set: Rules of Inference Involving Quantifiers
00:01

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

Constructing Arguments Involving Quantified Statements
11:00

Problem Set: Constructing Arguments Involving Quantified Statements
00:01
+
Proofs
6 Lectures 34:25

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.

Preview 08:31

Students will learn how to prove universal statements by using the method of exhaustion and by using the method of direct proof.

Proving Universal Statements
10:00

Problem Set: Methods of Proof
00:01

Students will be able to perform proofs by contradiction.

Proof by Contradiction
07:13

Students will be able to perform proofs by contraposition.

Proof by Contraposition
08:38

Problem Set: Proofs by Contradiction and by Contraposition
00:02
+
Mathematical Induction
6 Lectures 42:26

Students will be able to construct proofs using mathematical induction.

Preview 16:37

Problem Set: Mathematical Induction
00:01

Students will be able to construct proofs using strong induction. 

Strong Induction
04:27

An example of a proof by strong induction is provided.

Strong Induction: Example
11:03

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

Strong Induction: Additional Example
10:17

Problem Set: Strong Induction
00:01
+
Concluding Letter
2 Lectures 00:31
Concluding Letter
00:21

Bonus Lecture
00:10
About the Instructor
Richard Han
4.3 Average rating
402 Reviews
6,066 Students
6 Courses
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.