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Discrete Mathematics: Open Doors to Great Careers 2

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Learn the core topics of Discrete Math to open doors to Computer Science, Data Science, Actuarial Science, and more!

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- 6 hours on-demand video
- 24 Articles
- 44 Supplemental Resources
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- 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.

Requirements

- The Udemy Course "Discrete Mathematics: Open Doors to Great Careers"

Description

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**The sequel to the course Discrete Mathematics: Open Doors to Great Careers.**

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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:

**Set Theory****Functions****Relations****Partial Order Relations****Algorithms****Algorithm Efficiency**

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 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

Expand All 65 Lectures
Collapse All 65 Lectures
05:51:11

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Introduction
1 Lecture
03:11

Preview
03:11

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Set Theory
12 Lectures
01:04:59

Students will be introduced to the notions of set, element, set equality, subset, and proper subset.

Preview
09:19

Students will learn how to find the union, intersection, difference, and complements of sets.

Operations on Sets

16:19

Problem Set: Operations on Sets

00:01

Students will learn how to find the union of any number of sets and the intersection of any number of sets.

General Unions and Intersections

12:06

Problem Set: General Unions and Intersections

00:01

The notion of a partition is introduced.

Students will be able to determine if a collection of sets forms a partition of a given set.

Preview
07:24

Problem Set: Partitions

00:00

The notion of the power set of a set is introduced.

Students will be able to find the power set of a given set.

Preview
03:03

The notion of the Cartesian product of a collection of sets is introduced.

Students will be able to find the Cartesian product of a collection of sets.

Cartesian Product

06:06

Problem Set: Power Set and Cartesian Product

00:01

In this lecture, students are introduced to set identities.

Students will be able to prove set identities.

Set Identities

10:36

Problem Set: Set Identities

00:01

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Functions
14 Lectures
01:42:50

The notion of a function is introduced.

Students will understand what the domain and range of a function are, and students will understand what the image of an element is and what the preimage of an element is.

Functions

11:27

In this lecture, we look at some examples of functions, including the floor function.

Students will be able to find the domain and range of a function and the preimage of a given element in the codomain.

Examples of Functions

13:35

Problem Set: Functions

00:00

The one-to-one and onto properties are introduced.

Students will be able to prove that a function is one-to-one or that a function is not one-to-one. Students will also be able to prove that a function is onto or that a function is not onto.

Preview
11:30

Problem Set: One to One and Onto Properties

00:02

The notion of a one-to-one correspondence and the notion of the inverse function of a given function are introduced.

Students will be able to prove that a function is a one-to-one correspondence. Students will also be able to find the inverse function of a given function.

Preview
17:32

Problem Set: One-to-one Correspondence and Inverse Functions

00:01

The notion of the composition of two functions is introduced.

Students will be able to find the composition of two functions.

Composition of Functions

14:39

Problem Set: Composition of Functions

00:01

In this lecture, we apply functions to the task of measuring the sizes of sets.

Students will be able to show that two sets have the same cardinality.

Preview
09:02

Problem Set: Cardinality

00:00

The notion of a countable set is introduced. An example of an uncountable set is discussed.

Students will be able to show that a set is countable or that a set is uncountable.

Countable and Uncountable Sets

15:22

In this lecture, an additional example of an uncountable set is discussed. The Cantor diagonalization process is also introduced.

Students will be able to apply the Cantor diagonalization process to show that a set is uncountable.

The Cantor Diagonalization Process

09:34

Problem Set: Countable Sets, Uncountable Sets, Cantor Diagonalization Process

00:02

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Relations
14 Lectures
01:11:09

The notion of a relation is introduced.

Students will understand what the domain and codomain of a relation are, and students will understand what it means for x to be related to y.

Preview
05:43

We explore additional examples of relations. The notion of a relation on a set A is introduced. Also, the notion of congruence modulo 5 is introduced.

Relations: Additional Examples

09:15

Problem Set: Relations

00:00

In this lecture, we explore relationships between 3 or more things.

Students will see examples of n-ary relations.

n-ary Relations

05:52

The properties of reflexivity, symmetry, and transitivity are introduced.

Students will be able to determine if a given relation satisfies these properties.

Properties of Relations

08:38

We explore the properties of the relation of congruence modulo 5.

Students will further reinforce their understanding of the properties of relations.

Properties of Relations: Additional Example

09:18

Problem Set: Properties of Relations

00:01

The notion of equivalence relation is introduced.

Students will be able to prove that a given relation is an equivalence relation.

Preview
07:14

Problem Set: Equivalence Relations

00:01

The notion of a partition induced by an equivalence relation is introduced. The notion of an equivalence class is also introduced.

Students will be able to find the partition induced by an equivalence relation on a set.

Partition Induced by an Equivalence Relation

04:21

We explore the partition induced by congruence modulo 5 on the set of integers.

Partition Induced by an Equivalence Relation: Additional Example

14:13

Problem Set: Partition Induced by an Equivalence Relation

00:02

The notion of an equivalence relation induced by a partition is introduced.

Equivalence Relation Induced by a Partition

06:28

Problem Set: Equivalence Relation Induced by a Partition

00:02

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Partial Order Relations
8 Lectures
33:13

The notion of a partial order relation is introduced.

Students will understand the properties of a partial order relation and what it means for two elements to be comparable.

Preview
09:12

Problem Set: Partial Order Relations

00:01

We explore the 'prerequisite' relation on a set of math courses.

Students will be able to represent a partially ordered set using a directed graph.

Partial Order Relations: Additional Example

03:54

The notion of a Hasse diagram of a partial order relation is introduced. The notions of a maximal and of a minimal element are also introduced.

Students will be able to represent a partially ordered set using a Hasse diagram.

Preview
06:18

Problem Set: Hasse Diagrams

00:01

The notion of a topological sorting for a partial order relation is introduced.

Topological Sorting

03:38

In this lecture, we find a topological sorting for the prerequisite relation on a set of math courses.

Students will be able to find a topological sorting for a given partial order relation.

Example of Topological Sorting

10:08

Problem Set: Topological Sorting

00:01

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Algorithms
14 Lectures
01:15:21

In this lecture, we explore a simple example of an algorithm.

Preview
08:32

The definition of an algorithm is introduced, and the while loop is introduced. The general form of an algorithm is also explained.

Students will understand while loops and the general form of an algorithm.

Preview
07:41

Problem Set: Algorithms

00:00

The definition of correctness of a while loop is introduced.

Students will understand what it means for a while loop to be correct with respect to its pre-condition and post-condition.

Correctness of Algorithms

03:16

The notion of a loop invariant is introduced, and the Loop Invariant Theorem is introduced.

Students will understand how a loop invariant is used to prove the correctness of a while loop.

The Loop Invariant Theorem

06:34

We prove the correctness of the division algorithm.

Students will be able to prove the correctness of a given algorithm.

Proving the Correctness of the Division Algorithm

16:40

Problem Set: Correctness of Algorithms

00:01

The definition of the efficiency of an algorithm is introduced.

Students will understand what the efficiency of an algorithm means.

Preview
01:22

We explore the linear search algorithm.

Linear Search Algorithm

11:30

In this lecture, we explore the efficiency of the linear search algorithm. The notions of best-case efficiency and worst-case efficiency are introduced.

Students will be able to measure the efficiency of algorithms.

Efficiency of the Linear Search Algorithm

07:56

The notion of the order of a function is introduced.

Students will be able to determine the order of a given function.

Order

03:04

We explore the binary search algorithm.

Binary Search Algorithm

05:13

In this lecture, we explore the efficiency of the binary search algorithm.

Students will reinforce their ability to measure the efficiency of algorithms. Students will understand what it means for an algorithm to be more efficient than another algorithm.

Efficiency of the Binary Search Algorithm

03:30

Problem Set: Efficiency of Algorithms

00:01

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Concluding Letter
2 Lectures
00:29

Concluding Letter

00:20

Bonus Lecture

00:09

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About the Instructor

PhD in Mathematics

*Philosophy of Language: Solidify Critical Thinking Skills* and *Linear Algebra for Beginners: Open Doors to Great Careers*.

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