Set Theory - Mathematics (Undergraduate Foundation)

Mathematics begins with sets. This course covers everything from basic definitions and membership notations to complex set algebra and De Morgan's laws. You will master cardinality, power sets, and the classification of number systems including rational, irrational, and complex numbers. The curriculum moves from simple operations like union and intersection into element-wise proofs, Cartesian products, and the mechanics of relations and functions. Set theory is the language of modern data and logic. These concepts are essential for computer programming, database management, and statistical analysis. Understanding functions and mappings allows you to model real-world dependencies in engineering, economics, and the sciences. Mastering these foundations provides the exact logical framework needed to solve complex problems in technology and research. Upon completion, you will be able to simplify set expressions and solve grouping problems using Venn diagrams and the inclusion-exclusion principle. You will know how to perform element-wise proofs and calculate set cardinalities. You will also gain the ability to evaluate composite functions and prove whether a mapping is one-to-one, onto, or bijective. This course is designed for undergraduate students and secondary school leavers entering STEM disciplines. It provides a necessary logical foundation for anyone moving into calculus, data science, or advanced mathematics. The clear, direct instruction ensures that any student can develop the systematic thinking required for professional technical roles.

20 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 foundational mathematical structures essential for success in quantitative undergraduate degrees and professional technical roles. This comprehensive learning track delivers a rigorous treatment of algebra and trigonometry, moving rapidly from fundamental set theory and real number operations to advanced topics including matrix algebra, complex numbers, and analytical trigonometry. You will establish the critical problem-solving framework required for advanced study in calculus, engineering mechanics, and data science. This programme is primarily designed for first-year university students in STEM disciplines requiring strong analytical bases, particularly engineering, physics, computer science, and economics. It also serves as an intensive, high-level refresher for professionals returning to academia or shifting into data-driven roles demanding precise numerical literacy and logical structuring. Prior competence in standard secondary school mathematics is assumed; focus is placed strictly on mastery and application of core definitions. Upon completion, you will possess the skills to construct rigorous logical arguments using set theory and mathematical induction, model complex relationships with functions and matrices, and analyze periodic systems using advanced trigonometry. You will demonstrate competence in solving diverse equation types, from quadratics to linear systems, and manipulating complex numbers in engineering applications. This track prepares you directly for the mathematical demands of second-year university studies and technical professional certification exams.

Course Chapters

1. Introduction

This chapter introduces the fundamental language and notation of set theory. Mastering these primary definitions is mandatory for structuring logical arguments and categorising data in all advanced mathematical and computational disciplines. You will master four objectives: defining sets and elements with precision; using roster and set-builder notation; identifying finite and infinite collections; and applying basic symbols for membership and subsets.

Concept Overviews

7 Lessons

1:52:52

2. Subsets

This chapter defines the hierarchical inclusion of sets and the precise conditions for set equality. Mastery of subset logic is critical for constructing rigorous proofs and managing data inheritance in computational architecture. You will master four objectives: distinguishing between proper and improper subsets; proving set equality through mutual inclusion; calculating the total number of subsets for finite collections; and defining the universal set and empty set within inclusion frameworks.

Concept Overviews

7 Lessons

1:38:01

Problem Walkthroughs

2 Lessons

27:33

3. Sets of Numbers

This chapter defines the rigorous classification of numerical collections and their hierarchical inclusion. Mastery of these standard sets is mandatory for defining domains in calculus, establishing computational constraints, and ensuring logical consistency in mathematical proofs. You will master four objectives: categorising natural, integer, rational, and irrational numbers; identifying the real and complex number systems; applying interval notation for continuous subsets; and mapping the nested relationship between numerical sets.

Concept Overviews

7 Lessons

1:57:16

Problem Walkthroughs

1 Lesson

8:28

4. Operations on Sets

This chapter covers the algebraic manipulation of sets to form new collections through rigorous logical rules. Mastering these operations is foundational for database querying, probability theory, and complex data stratification in engineering and analytical systems. You will master four objectives: performing unions, intersections, and set differences; calculating absolute and relative complements; applying De Morgan's laws to simplify set expressions; and identifying disjoint sets.

Concept Overviews

6 Lessons

1:11:30

Problem Walkthroughs

4 Lessons

39:07

5. Algebra of Sets

This chapter covers the fundamental laws governing set operations and the formal proof of set identities. Mastering this symbolic logic is essential for simplifying complex boolean expressions and ensuring the validity of analytical arguments in computer science and mathematical engineering. You will master four objectives: applying idempotent, associative, and commutative laws; implementing distributive and absorption laws; proving identities using De Morgan's laws; and simplifying expressions using identity and complement laws.

Concept Overviews

10 Lessons

58:57

Problem Walkthroughs

2 Lessons

10:46

6. Venn Diagrams

This chapter introduces the visual representation of set relationships and the spatial logic of inclusions. Mastery of Venn diagrams is essential for mapping data overlaps, solving combinatorial problems, and verifying set identities through geometric interpretation. You will master four objectives: constructing diagrams for two and three sets; shaded representation of unions and intersections; interpreting regions of relative and absolute complements; and solving practical survey problems using the principle of inclusion-exclusion.

Concept Overviews

5 Lessons

1:02:38

Problem Walkthroughs

4 Lessons

1:17:35

7. Cartesian Products

This chapter defines the construction of ordered pairs and the product of distinct sets. Understanding these mappings is mandatory for defining relations, functions, and the multidimensional coordinate systems used in database schema design and linear algebra. By the end of this chapter, you will master: constructing ordered pairs and n-tuples; calculating the cardinality of product sets; applying the non-commutative property; and executing distributive operations over unions and intersections.

Concept Overviews

4 Lessons

1:05:19

Problem Walkthroughs

1 Lesson

6:37

8. Relations, Mappings and Functions

This chapter explains how elements from different sets interact through specific rules. These principles are the building blocks for computer programming and advanced calculus. You will learn to link data points accurately and transform inputs into valid outputs. You will master identifying relations and functions; performing algebraic and composite operations; classifying injective, surjective, and bijective mappings; and calculating inverse functions.

Concept Overviews

9 Lessons

3:11:31

Problem Walkthroughs

5 Lessons

47:59