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An Introduction to Basic Set Theory

Gain insights into fundamental set theory concepts and operations. Explore relations, functions, set ordering, and cardinality using Python. Delve into Cantor’s diagonalization and its applications in various fields.

5.0

35 Lessons

6h 30min

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LEARNING OBJECTIVES

An understanding of basic mathematical structures and concepts of set theory
Familiarity with the set operations and their properties
Working knowledge of the Cartesian product of sets, relations, and functions
An understanding of the cardinality of finite and infinite sets
Familiarity with the countable and uncountable sets
Hands-on experience with Cantor’s diagonalization method

Learning Roadmap

35 Lessons36 Quizzes4 Assessments

Introduction

Get familiar with basic set theory, set properties, operations, and Python-based examples.

Background and Motivation

Fundamentals

Look at the essence of sets, subsets, power sets, universal sets, and Venn diagrams.

Introduction to Sets

Subsets and Power Sets

Universal Sets and Venn Diagrams

Basic Set Operations

12 Lessons

Work your way through fundamental operations, laws, and principles in set theory.

Assessment 1

Assessment

Relations

7 Lessons

Grasp the fundamentals of binary, reflexive, symmetric, transitive, and order relations with examples.

Assessment 2

Assessment

Functions

6 Lessons

Take a closer look at functions, their types, compositions, and inverses with practical examples.

Assessment 3

Assessment

Indexing and Ordering of Sets

2 Lessons

Simplify complex topics of set indexing, sequences, tuples, and their practical applications.

Cardinality of Sets

2 Lessons

Build on understanding countable and uncountable sets, demonstrating varied cardinalities in set theory.

Assessment 4

Assessment

Concluding Remarks

2 Lessons

Learn how to use set theory fundamentals and logical operations for advanced applications.

Certificate of Completion

Showcase your accomplishment by sharing your certificate of completion.

Developed by MAANG Engineers

Every Educative lesson is designed by a team of ex-MAANG software engineers and PhD computer science educators, and developed in consultation with developers and data scientists working at Meta, Google, and more. Our mission is to get you hands-on with the necessary skills to stay ahead in a constantly changing industry. No video, no fluff. Just interactive, project-based learning with personalized feedback that adapts to your goals and experience.

ABOUT THIS COURSE

This course aims to introduce fundamental concepts of set theory. It provides hands-on experience through practical tasks using Python programming language (Python 3.8) to enhance engagement. You’ll start with the basics of sets, their properties, and set operations. Additionally, you’ll learn about relations, functions, ordering of sets, and cardinality of sets. You’ll also explore Cantor’s diagonalization method as a tool to demonstrate the uncountability of sets. After completing this course, you’ll have a solid understanding of the foundations of set theory that are vital for understanding many mathematics and computer science concepts, such as discrete mathematics, design of algorithms, theory of automata, and problem-solving. These concepts can also be applied in other significant areas including Physics, Statistics, and Probability.

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