Introduction to Set Theory - Mathematics (Senior Secondary)

This course introduces the fundamental principles of set theory, the branch of mathematics dedicated to the study of collections of objects. We will explore how to precisely define, describe, and denote sets. The course covers the different types of sets, including universal sets, empty sets, subsets, and power sets, providing the formal language used across all of modern mathematics. A command of set theory is non-negotiable for any serious student of mathematics, computer science, or statistics. It is the foundational language used to construct more complex ideas in logic, probability, and database theory. Understanding how to group and operate on collections of data is a critical skill for creating algorithms, analysing information, and building valid logical arguments. By the end of this course, you will be able to correctly use set notation to define any given set. You will identify different types of sets and their relationships, perform core set operations such as union, intersection, and complement, and use Venn diagrams to visually solve complex problems involving up to three sets. This course is built for secondary school students taking their first steps into abstract mathematical reasoning. It is an essential prerequisite for anyone planning to study computer science, data analysis, or any field that requires rigorous logical and structural thinking. No prior knowledge is required.

Enrolment valid for 12 months

Course Chapters

1. Introduction

This chapter introduces the core concepts of set theory. It defines what a set is and explains why the formal language of sets is a critical tool for clear and precise reasoning in mathematics and beyond. Key learning objectives include defining a set, identifying its elements, and appreciating the importance of a well-defined system to classify information.

Chapter lessons

1-1. Welcome

This lesson outlines the structure and goals of the course. It defines what a set is and explains why it is a foundational concept in modern mathematics.

1-2. Defining and describing sets

This lesson covers the different ways to represent a set, focusing on the listing (roster) method and the rule (set-builder notation) method.

2. Types of Sets and Their Relationships

This chapter explores the different classifications of sets and how they relate to one another. It covers key definitions such as the universal set, empty set, subsets, and disjoint sets. Key learning objectives include identifying and providing examples for various types of sets, and learning to determine the relationship between two or more given sets.

Chapter lessons

2-1. The universal set and the empty set

This lesson introduces two fundamental concepts: the universal set as the set of all possible elements, and the empty or null set, which contains no elements.

2-2. Finite and infinite sets

This lesson explains the distinction between finite sets, whose elements can be counted, and infinite sets, whose elements are countless.

2-3. Subsets, proper subsets, and the power set

This lesson covers the concept of subsets and proper subsets. It also introduces the power set, which is the set of all possible subsets of a given set.

3. Set Operations and Venn Diagrams

This chapter focuses on the practical application of set theory. It covers how to perform operations to combine or differentiate sets and how to use Venn diagrams to visualise these relationships and solve complex problems. Key learning objectives include performing union, intersection, and complement operations, and drawing and interpreting Venn diagrams to solve word problems involving up to three sets.

Chapter lessons

3-1. Union and intersection of sets

This lesson covers the two primary operations in set theory: union (combining all elements) and intersection (finding common elements).

3-2. Complement of a set

This lesson introduces the concept of the complement of a set, which includes all elements within the universal set that are not in the given set.

3-3. Introduction to venn diagrams

This lesson introduces Venn diagrams as a powerful visual tool for representing the relationships between two or three sets.

3-4. Solving problems with venn diagrams

This lesson provides a step-by-step guide to translating word problems into Venn diagrams and using them to find unknown quantities.

4. Conclusion and Next Steps

This concluding chapter summarises the core concepts of set theory. It reinforces the understanding of set notation, types of sets, and operations, preparing the student for future topics where these skills are required. Key outcomes include a review of the principles of set theory and an understanding of its importance as the language of modern mathematics, ready for application in other subjects.

Chapter lessons

4-1. Summary of what you have learned

This lesson provides a concise overview of the entire course, recapping set notation, the different types of sets, set operations, and the use of Venn diagrams.

4-2. How set theory connects to other subjects

This lesson explains how the principles of set theory are fundamental to other areas of study, such as probability, statistics, and computer database logic.