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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.

Beginner

35 Lessons

6h 30min

Certificate of Completion

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Explanations

AI-POWERED

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This course includes

4 Assessments

23 Playgrounds

36 Quizzes

Course Overview

What You'll Learn

Course Content

Recommendations

Course Overview

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 h...Show More

What You'll Learn

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

An understanding of basic mathematical structures and concepts of set theory

Course Content

Introduction

1 Lessons

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

Background and Motivation

Fundamentals

3 Lessons

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.

Union

Intersection

Commutative and Associative Laws

The Inclusion-Exclusion Principle

Difference

Complement

The First Distributive Law

The Second Distributive Law

DeMorgan’s First Law

DeMorgan’s Second Law

Cartesian Product

Set Identities

Assessment 1

Assessment

Relations

7 Lessons

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

Binary Relations

Reflexive and Symmetric Relations

Transitive and Antisymmetric Relations

Equivalence Relations

Partition of a Set

Order Relations

Supremum, Infimum, and Other Orderings

Assessment 2

Assessment

Functions

6 Lessons

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

Functions, Domain, and Range

Restricted Functions

Composite Functions

Injective and Surjective Functions

Bijective Functions

Inverse of a Function

Assessment 3

Assessment

Indexing and Ordering of Sets

2 Lessons

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

Indexed Family of Sets

Sequences and Tuples

10.

Cardinality of Sets

2 Lessons

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

Countable Sets

Uncountable Sets

Assessment 4

Assessment

12.

Concluding Remarks

2 Lessons

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

Conclusion and Further Directions

Appendix

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