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Discrete Mathematics: Open Doors to Great Careers 2

Name: Discrete Mathematics: Open Doors to Great Careers 2
Rating: 4.2 (36 reviews)

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

Created byRichard Han

Last updated 5/2018

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

7 sections • 65 lectures • 5h 51m total length

Introduction Lecture3:11

Set Theory9:19
Students will be introduced to the notions of set, element, set equality, subset, and proper subset.
Operations on Sets16:19
Students will learn how to find the union, intersection, difference, and complements of sets.
Problem Set: Operations on Sets0:01
General Unions and Intersections12:06
Students will learn how to find the union of any number of sets and the intersection of any number of sets.
Problem Set: General Unions and Intersections0:01
Partitions7:24
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.
Problem Set: Partitions
Power Set3:03
The notion of the power set of a set is introduced.
Students will be able to find the power set of a given set.
Cartesian Product6:06
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.
Problem Set: Power Set and Cartesian Product0:01
Set Identities10:36
In this lecture, students are introduced to set identities.

Students will be able to prove set identities.
Problem Set: Set Identities0:01

Functions11:27
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.
Examples of Functions13:35
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.
Problem Set: Functions
One to One and Onto Properties11:30
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.
Problem Set: One to One and Onto Properties0:02
One-to-one Correspondence and Inverse Functions17:32
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.
Problem Set: One-to-one Correspondence and Inverse Functions0:01
Composition of Functions14:39
The notion of the composition of two functions is introduced.
Students will be able to find the composition of two functions.
Problem Set: Composition of Functions0:01
Cardinality9:02
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.
Problem Set: Cardinality
Countable and Uncountable Sets15:22
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.
The Cantor Diagonalization Process9:34
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.
Problem Set: Countable Sets, Uncountable Sets, Cantor Diagonalization Process0:02

Relations5:43
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.
Relations: Additional Examples9:15
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.
Problem Set: Relations
n-ary Relations5:52
In this lecture, we explore relationships between 3 or more things.
Students will see examples of n-ary relations.
Properties of Relations8:38
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: Additional Example9:18
We explore the properties of the relation of congruence modulo 5.
Students will further reinforce their understanding of the properties of relations.
Problem Set: Properties of Relations0:01
Equivalence Relations7:14
The notion of equivalence relation is introduced.
Students will be able to prove that a given relation is an equivalence relation.
Problem Set: Equivalence Relations0:01
Partition Induced by an Equivalence Relation4:21
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: Additional Example14:13
We explore the partition induced by congruence modulo 5 on the set of integers.
Problem Set: Partition Induced by an Equivalence Relation0:02
Equivalence Relation Induced by a Partition6:28
The notion of an equivalence relation induced by a partition is introduced.
Problem Set: Equivalence Relation Induced by a Partition0:02

Partial Order Relations9:12
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.
Problem Set: Partial Order Relations0:01
Partial Order Relations: Additional Example3:54
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.
Hasse Diagrams6:18
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.
Problem Set: Hasse Diagrams0:01
Topological Sorting3:38
The notion of a topological sorting for a partial order relation is introduced.
Example of Topological Sorting10:08
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.
Problem Set: Topological Sorting0:01

Algorithms8:32
In this lecture, we explore a simple example of an algorithm.
The Division Algorithm7:41
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.
Problem Set: Algorithms
Correctness of Algorithms3:16
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.
The Loop Invariant Theorem6:34
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.
Proving the Correctness of the Division Algorithm16:40
We prove the correctness of the division algorithm.
Students will be able to prove the correctness of a given algorithm.
Problem Set: Correctness of Algorithms0:01
Efficiency of Algorithms1:22
The definition of the efficiency of an algorithm is introduced.
Students will understand what the efficiency of an algorithm means.
Linear Search Algorithm11:30
We explore the linear search algorithm.
Efficiency of the Linear Search Algorithm7:56
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.
Order3:04
The notion of the order of a function is introduced.
Students will be able to determine the order of a given function.
Binary Search Algorithm5:13
We explore the binary search algorithm.
Efficiency of the Binary Search Algorithm3:30
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.
Problem Set: Efficiency of Algorithms0:01

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 this course is for:

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

Discrete Mathematics: Open Doors to Great Careers 2

What you'll learn

Explore related topics

Course content

Introduction1 lecture • 3min

Set Theory12 lectures • 1hr 5min

Functions14 lectures • 1hr 43min

Relations14 lectures • 1hr 11min

Partial Order Relations8 lectures • 33min

Algorithms14 lectures • 1hr 15min

Concluding Letter2 lectures • 1min

Requirements

Description

Who this course is for: