Set Theory and Number Systems - Mathematics (Undergraduate Foundation)

This course establishes the foundational language of mathematics. It covers the core principles of set theory and applies them directly to the structure of the real number system. Mastery of this material is non-negotiable for further study in any quantitative field. The principles of set theory are the structural basis for formal logic, database theory, and computer programming. Understanding number systems as structured sets is the prerequisite for all higher mathematics, including algebra and calculus. This course provides the essential logical framework for these disciplines. By the end of this course, you will be able to use formal notation to define sets and their relationships, perform standard set operations such as union and intersection, use Venn diagrams to analyse set identities, and classify numbers within the real number system. This course is designed for first-year university students of mathematics, computer science, and engineering. It is also required foundational material for any professional in data analysis, software development, or other technical fields requiring rigorous logical thought.

6 hrs

Enrolment valid for 12 months

This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.

MTH 101: Elementary Mathematics I - Algebra and Trigonometry

Master the mathematics every scientist, engineer, and computer scientist must know. This track covers the NUC Core syllabus for MTH 101: Elementary Mathematics I. From set theory and sequences to trigonometry and complex numbers, you will gain the exact tools used in higher mathematics, algorithm design, data analysis, physics, and engineering. This programme is for first-year university students in mathematics, computer science, engineering, or physics, as well as serious learners preparing for undergraduate study. It also serves professionals who need a rigorous mathematical foundation for technical fields. By the end, you will handle formal set notation, progressions, quadratic models, combinatorics, induction proofs, binomial expansions, trigonometric analysis, and complex arithmetic. You will be equipped to solve real problems in science, engineering, computing, and finance, and ready for advanced study in calculus, statistics, and applied mathematics.

Course Chapters

1. Introduction

This chapter establishes the essential groundwork for the course. It provides precise definitions of a set and its fundamental properties, establishing the correct notation and terminology required for all subsequent material on the subject. Key topics covered are the formal definition of a set, determining a set's cardinality, the distinction between finite and infinite sets, and the roles of the empty and universal sets.

Concept Overviews

5 Lessons

57:05

Problem Walkthroughs

2 Lessons

10:05

2. Set Inclusion, Sets of Numbers and Power Sets

This chapter examines the relationships between sets. It covers the concepts of subsets and set equality, which are essential for comparing sets, and introduces the power set, a fundamental structure in advanced mathematics. Topics include defining subsets and proper subsets, verifying set equality, and constructing the power set of a given set. Worked examples demonstrate these core skills.

Concept Overviews

4 Lessons

49:23

Problem Walkthroughs

3 Lessons

12:55

3. Basic Operations on Sets

This chapter details the primary operations used to combine and modify sets. It provides the formal framework for manipulating sets, a skill essential for logic and problem-solving. Key operations covered are union, intersection, and complement. Their formal definitions, properties, and direct applications in worked calculations are demonstrated.

Concept Overviews

7 Lessons

1:02:27

Problem Walkthroughs

1 Lesson

6:25

4. Venn Diagrams

This chapter introduces Venn diagrams as the standard method for the visual representation of sets. This tool is critical for translating abstract set notation into a concrete graphical form for analysis. Topics include representing sets visually, analysing relationships, solving cardinality problems for two and three sets, and using diagrams to prove identities.

Concept Overviews

3 Lessons

32:53

Problem Walkthroughs

4 Lessons

28:11

5. Conclusion

This chapter consolidates the core concepts of the course. It provides a structured summary of set theory and the real number system, reinforcing the essential principles required for progression. The conclusion summarises key definitions and operations. It also outlines how these concepts will be applied directly in subsequent mathematics and computer science courses.

Concept Overviews

1 Lesson

7:56