Discrete Math Series : Set Theory & Algebra masterclass from Udemy

You’ve just stumbled upon the most in-depth Discrete Math course series online. With over 15,000 students enrolled and thousands of 5 star reviews to date in the area of computer science, my computer science courses are enjoyed by students from 130 countries.

Whether you want to:

- build the skills in set theory topic of discrete math

- crack interview or competitive exam questions on set theory topic of discrete math

...this complete Masterclass on set theory is the course you need to do.

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The number one reason is its simplicity. According to many students in udemy, my courses are simple to understand as I always teach concepts from scratch in a simple language.

The second reason is you get a mentor for computer science through this course. I get lot of doubts from students regarding their career in computer science like which elective subject to choose, which book to refer, etc.

The third reason is, you are not just watching my videos, you can also ask doubts if you get one while watching the lectures.

Which text book should you refer ?I have used Henneth H Rosen textbook. Its a great textbook. You can follow it. But I have referred lot of other textbooksas well. So its upto you on which textbook you are comfortable with but follow a standard author book. If you complete this course, you will find it much easier to understand these textbooks. But anyway if you complete this course with good detailed notes, you don't need to read any textbook as I am reading them for you and giving the contents in an easy to understand manner.Why should you take this course?You will be joining over 15000 students who are already enrolled in one of my courses.

There are 4000+ reviews left by students. My Courses are rated as the best course to learn computer science for beginners.What makes this course a standout?

Like you, thousands of others were frustrated and fed up with incomplete Youtube tutorials which assume you already know a bunch of stuff and also bulk textbooks able to send even the most intuitive person to sleep.

Like you, they were tired of low-quality lessons, poorly explained topics and all-round confusing info presented in the wrong way. That’s why so many find success in my courses. It’s designed in a simple manner so that anybody will be able to understand.

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What's inside

Learning objectives

Master discrete mathematics
Master set theory and algebra

Get ready for advanced topics of discrete mathematics like group theory , functions
Get ready for research in computer science

Master discrete mathematics
Master set theory and algebra
Get ready for advanced topics of discrete mathematics like group theory , functions
Get ready for research in computer science

Syllabus

Sets - Basics

Important : Introduction to Sets

Subset, Superset, Proper subset, Proper superset

Power set, Trivial Subsets

Set Operations

Properties of Sets

Use of Venn diagrams

Difference between subset and belongs to

Example Problem

Relations

Cartesian product

Relation Introduction

Number of relations possible on a set with n elements

Reflexive relation

Reflexive relation with examples

Minimum and Maximum cardinality of a reflexive relation

Number of reflexive relations possible on a set with n elements

Problem on closure properties of Reflexive relation

Problems on Reflexive relation - 1

Problems on Reflexive relation - 2

Problems on Reflexive relation - 3

Problems on Reflexive relation - 4

Problems on Reflexive relation - 5

Irreflexive relation

Irreflexive relation with examples

Relationship between reflexive and irreflexive relations

Minimum and Maximum cardinality of an irreflexive relation

Number of irreflexive relations possible on a set with n elements

Relationship between reflexive and irreflexive relations continued

Problems on Irreflexive relation

Problem on closure properties of Irreflexive relation

Symmetric relation

Symmetric relation with examples

Minimum and Maximum cardinality of a symmetric relation

Number of symmetric relations possible on a set with n elements

Problems on Symmetric relation

Relationship between reflexive and symmetric relations

Relationship between reflexive and symmetric relations continued

Problems on symmetric relation

Problem on closure properties of symmetric relation

Closure properties of symmetric relations continued

Anti symmetric relation

Relationship between Irreflexive and symmetric relations

Relationship between Irreflexive and symmetric relations with venn diagram

Anti symmetric relation with examples

Minimum and Maximum cardinality of an antisymmetric relation

Number of antisymmetric relations possible on a set with n elements

Relationship between symmetric and antisymmetric relations

Problems on Transitive relation

Relationship between symmetric and antisymmetric relations continued

Relationship between Irreflexive and antisymmetric relations

Closure properties of antisymmetric relations

Closure properties of antisymmetric relations continued

Problems on antisymmetric relations

Asymmetric relation

Asymmetric relation with example

Maximum cardinality of Asymmetric relation possible

Number of asymmetric relations possible on a set with n elements

Relationship between Asymmetric and Reflexive relations

Relationship between Asymmetric and Reflexive relation with venn diagram

Relationship between Asymmetric and Irreflexive relations

Relationship between Asymmetric and Symmetric relations

Relationship between Asymmetric and Antisymmetric relation

Closure properties of Asymmetric relations

Transitive relation

Transitive relation with examples

Minimum and Maximum cardinality of a transitive relation

Equivalence relation and Partially Ordered Relation

Equivalence relation explained

Examples on Equivalence relation

Partial Ordered Relation explained

Relation which is both equivalent and partially ordered

Examples on Partially ordered relation

POSET explained

Examples of POSET

Problem

Problem on Equivalence relation

Hasse diagram explained

Closure properties of Equivalence relations continued

Bonus Section

Totally Ordered Set - TOSET

Examples of TOSET

Hasse Diagam

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Provides a strong foundation in set theory and algebra, which are essential for understanding more advanced computer science topics such as data structures and algorithms

Offers comprehensive coverage of set theory, which is a frequently tested topic in computer science interviews and competitive examinations

Teaches concepts from scratch in a simple language, making it accessible to learners with little to no prior experience in discrete mathematics

Offers mentorship and guidance on career-related questions, such as elective subject choices and book recommendations, providing valuable support beyond the course material

Belongs to a series of courses, which may indicate a comprehensive and detailed approach to learning discrete mathematics and related topics

Prepares learners to understand standard textbooks, such as the one by Kenneth H. Rosen, by presenting the contents in an easy-to-understand manner

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Discrete Math Series : Set Theory & Algebra masterclass with these activities:

Review Basic Set Theory Concepts

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Solidify your understanding of fundamental set theory concepts to prepare for more advanced topics covered in the course.

Browse courses on Sets

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Review definitions of sets, subsets, and power sets.
Practice basic set operations like union, intersection, and complement.
Work through example problems involving Venn diagrams.

Review 'Discrete Mathematics and Its Applications' by Kenneth H. Rosen

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Reinforce your understanding of set theory and algebra by studying a widely-used textbook.

View Discrete Mathematics and Its Applications on Amazon

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Obtain a copy of 'Discrete Mathematics and Its Applications'.
Read the chapters on set theory and relations.
Work through the examples and exercises in the book.

Tutor other students in Set Theory

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Reinforce your understanding of set theory by helping other students learn the material.

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Offer to tutor classmates or students in lower-level courses.
Prepare explanations and examples to help students understand the concepts.
Answer questions and provide feedback to students.

Four other activities

Expand to see all activities and additional details

Show all seven activities

Create a Venn Diagram Tutorial

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Deepen your understanding of Venn diagrams by creating a tutorial explaining their use in set theory.

Show steps

Research different types of Venn diagrams and their applications.
Create a script or outline for your tutorial.
Record a video or create a written guide explaining Venn diagrams.
Share your tutorial with others and gather feedback.

Solve Set Theory Problems on Online Judge Platforms

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Sharpen your problem-solving skills by tackling set theory problems on platforms like HackerRank or LeetCode.

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Search for set theory problems on online judge platforms.
Attempt to solve the problems independently.
Review solutions and explanations for problems you struggled with.

Review 'Naive Set Theory' by Paul Halmos

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Expand your knowledge of set theory by reading a classic text on the subject.

View Naive Set Theory on Amazon

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Obtain a copy of 'Naive Set Theory'.
Read the book and take notes on key concepts.
Reflect on how the concepts relate to the course material.

Develop a Set Theory Calculator

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Apply your knowledge of set theory by building a calculator that performs set operations.

Show steps

Design the user interface for your calculator.
Implement the set operations (union, intersection, complement, etc.).
Test your calculator with various inputs.
Refine your calculator based on testing and feedback.

Career center

Learners who complete Discrete Math Series : Set Theory & Algebra masterclass will develop knowledge and skills that may be useful to these careers:

Software Developer

A software developer creates and maintains computer programs, often working with complex systems. This course provides a deep dive into set theory and algebra, crucial for a strong understanding of data structures, algorithms, and database management, all of which are building blocks for many software applications. A software developer will find the course's focus on relations and their properties, alongside mastery of set operations, particularly useful for designing robust and efficient software systems. The course emphasizes a ground-up approach to discrete mathematics, which helps build the solid theoretical knowledge that every software developer should possess.

See salaries and explore the career path for Software Developer

Algorithm Designer

An algorithm designer develops efficient and effective algorithms for solving computational problems. This course builds a solid basis in discrete mathematics, which is essential for any algorithm designer. The focus on set theory and algebra provides a structured way of understanding how data can be manipulated and connected and will be a central part of developing algorithms. The course’s comprehensive treatment of relations and their properties, as well as set operations, is directly applicable to building and optimizing algorithmic solutions. Any aspiring algorithm designer should take this course to approach problems with a strong theoretical framework.

See salaries and explore the career path for Algorithm Designer

Database Administrator

A database administrator designs, implements, and maintains databases by ensuring data integrity, security, and availability. Set theory and algebra are foundational to this role as they underpin database schema design and query optimization. The course's deep coverage of set operations and relations is directly applicable to managing relational databases. A database administrator will find that this course allows them to understand how databases organize, connect, and retrieve information, making them more proficient at designing and managing databases effectively. The course can also prepare a database administrator for more complex database design and problem solving.

See salaries and explore the career path for Database Administrator

Machine Learning Engineer

A machine learning engineer develops and implements machine learning models. A strong grasp of discrete math including set theory and algebra helps build a solid understanding of the mathematics that underpins many machine learning algorithms. This course’s focus on set operations, relations, and their properties, provides a useful toolkit for working with data, as well as building the logic necessary to understand these models. The course emphasizes a ground-up approach, making it a good introduction for any aspiring machine learning engineer.

See salaries and explore the career path for Machine Learning Engineer

Cryptography Specialist

A cryptography specialist designs and implements algorithms to secure data and communications. Discrete math is the cornerstone of cryptography. This course provides the necessary background in set theory and algebra. The course’s exploration of relations and their properties, along with set operations, will help a cryptography specialist to approach the problems that they will face in their career, such as those faced in algorithm design. A cryptography specialist will find that the course provides the core mathematical knowledge they need to be successful.

See salaries and explore the career path for Cryptography Specialist

Data Scientist

Data scientists analyze complex data sets to extract meaningful insights and create predictive models. The mastery of set theory and algebra provided by this course helps build a foundation for understanding data structures and algorithms, which are crucial skills for any data scientist. The course's deep exploration of relations and their properties, as well as in-depth work with set operations, is particularly important for manipulating and interpreting data. Aspiring data scientists will find that this course helps them approach data from a more logical and structured standpoint, which is a great benefit.

See salaries and explore the career path for Data Scientist

Computer Science Researcher

A computer science researcher conducts theoretical and applied research in computer science to advance the field. This course may be especially useful for those exploring topics where discrete math is foundational, such as algorithms, complexity theory, and artificial intelligence. The course builds a strong basis in set theory and algebra. The detailed treatment of relations, their properties, and set operations is directly relevant to many areas of computer science research. This course may help those who wish to pursue theoretical computer science research by giving them the core mathematical concepts.

See salaries and explore the career path for Computer Science Researcher

Data Engineer

Data engineers build and maintain the infrastructure that allows data to be collected, processed, and used by others in their organizations. This course helps build a good understanding of set theory and algebra, which is directly applicable to how data is organized. The course's emphasis on set operations and relations can directly help a data engineer manage complex data pipelines. By understanding how sets operate, a data engineer can manipulate, refine, and prepare data for consumption by others, and this course may help to do just that.

See salaries and explore the career path for Data Engineer

Systems Analyst

A systems analyst evaluates and designs computer systems and processes to meet business needs. The course's in-depth treatment of set theory and algebra builds a foundation for logical and structured thinking, which is essential for systems analysis. A systems analyst may find that the course's focus on set operations and relations will be valuable when modeling complex systems and procedures. Specifically, the detailed study of relations can help a systems analyst describe complex connections and dependencies that exist in real-world systems. The course's structured approach may assist a systems analyst in their day-to-day work.

See salaries and explore the career path for Systems Analyst

Quantitative Analyst

A quantitative analyst, often known as a quant, uses mathematical and statistical methods to solve complex problems in finance and economics. This course may help a quant to better understand and use the mathematical tools they use every day. The course's focus on set theory and algebra helps build a strong theoretical foundation for understanding advanced mathematical concepts used in financial modeling. The deep coverage of relations and their properties, as well as set operations, may be valuable when modeling complex systems. Anyone who wishes to become a quant will find this course may help them solidify their understanding of basic mathematical concepts.

See salaries and explore the career path for Quantitative Analyst

Mathematical Modeler

Mathematical modelers create mathematical representations of real-world systems to understand, predict, or control their behavior. The course’s study of set theory and algebra helps build the foundation of logical and structured thought required to create effective mathematical models. A mathematical modeler will find that the course's examination of relations and their properties, along with set operations, may be particularly helpful. The course can provide a core understanding of mathematical principles required for a career as a mathematical modeler.

See salaries and explore the career path for Mathematical Modeler

Operations Research Analyst

An operations research analyst applies mathematical and analytical methods to help organizations make better decisions. The course’s focus on discrete math may allow an operations research analyst to understand the mathematical structure of problems, and find better solutions. The detailed study of sets, relations, and their properties may give the operations research analyst the logical and problem solving framework necessary for success. The course may provide the background knowledge needed to excel in operations research.

See salaries and explore the career path for Operations Research Analyst

Network Engineer

A network engineer designs, implements, and maintains computer networks, ensuring that they are both reliable and efficient.This course provides a solid mathematical foundation via set theory and algebra, which is important when working with complex networks. A network engineer will find that the course's comprehensive work with relations and their properties may be useful when modeling and analyzing the connections within network topologies. The concepts from the course may be helpful when designing and troubleshooting a computer network.

See salaries and explore the career path for Network Engineer

Robotics Engineer

A robotics engineer designs, builds, and tests robots, using math and physics to create practical systems. This course builds a foundation in set theory and algebra, which are crucial for many aspects of robotics, such as planning and control. The course's exploration of relations and set operations gives a robotics engineer tools to describe robotic systems, make plans, and design robotic logic. The course may give individuals a basis to understand the complex math that underlies robotic systems.

See salaries and explore the career path for Robotics Engineer

Game Developer

A game developer creates video games, including the gameplay, levels, and overall experience. This course helps provide a basic grasp of set theory and algebra, which are useful for some game development tasks; for example, collision detection systems often rely on these principles. The detailed study of relations and set operations can help a game developer think about the various objects in their games and how they relate to each other. The course may be helpful in developing the logic required to build a game, by providing a core theoretical knowledge of discrete math.

See salaries and explore the career path for Game Developer

Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Discrete Math Series : Set Theory & Algebra masterclass.

Discrete Mathematics and Its Applications

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Comprehensive resource for discrete mathematics, covering set theory, relations, functions, and more. It is commonly used as a textbook in universities and provides a solid foundation for the course. Reviewing relevant chapters will enhance your understanding of the course material. This book useful reference tool for discrete math.

Discrete Mathematics and Its Applications

Paperback

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Discrete Mathematics and Its Applications

Kindle Edition

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Naive Set Theory

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Provides a concise and elegant introduction to set theory. It is particularly useful for understanding the foundational concepts and axioms of set theory. While it may be more valuable as additional reading, it offers a deeper understanding of the subject. This book is commonly used as a textbook at academic institutions.

Naive Set Theory

Paperback

Discrete Math Series

Set Theory & Algebra masterclass

What's inside

Learning objectives

Syllabus

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Activities

Career center

Reading list

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