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
2
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.
Concept Overviews
2 Lessons
2. Types of Sets and Their Relationships
3
1
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.
Concept Overviews
3 Lessons
Problem Walkthroughs
1 Lesson
3. Set Operations and Venn Diagrams
4
2
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.
Concept Overviews
4 Lessons
Problem Walkthroughs
2 Lessons
4. Conclusion and Next Steps
2
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.
Concept Overviews
2 Lessons