Set Theory - Introductory Abstract Algebra (Undergraduate Advanced)

This course lays the groundwork for understanding the structures that power modern mathematics. We start with the basics of set theory—notation, logic, functions, and operations—and use it as a stepping stone into the world of abstract algebra. From there, we introduce groups, rings, and fields in a way that highlights both intuition and structure. Clear, rigorous, and designed with first-time learners in mind.

13

4 hrs

Payment required for enrolment
Enrolment valid for 12 months
This course is also part of the following learning tracks. You may join a track to gain comprehensive knowledge across related courses.
[University] Introduction to Abstract Algebra
[University] Introduction to Abstract Algebra
Master the foundational structures of modern mathematics. This learning track provides a direct path through abstract algebra, from basic sets to groups, rings, and fields. It delivers the analytical framework essential for advanced theoretical work. This programme is for undergraduate students in mathematics, computer science, or theoretical physics. It is also essential for professionals requiring a rigorous grasp of algebraic structures for work in cryptography, algorithm design, or quantum computing. Construct rigorous proofs and analyse the properties of groups, rings, and fields. This programme directly prepares you for postgraduate studies in pure mathematics and for advanced technical roles in cryptography and algorithm theory.

Master the foundational structures of modern mathematics. This learning track provides a direct path through abstract algebra, from basic sets to groups, rings, and fields. It delivers the analytical framework essential for advanced theoretical work. This programme is for undergraduate students in mathematics, computer science, or theoretical physics. It is also essential for professionals requiring a rigorous grasp of algebraic structures for work in cryptography, algorithm design, or quantum computing. Construct rigorous proofs and analyse the properties of groups, rings, and fields. This programme directly prepares you for postgraduate studies in pure mathematics and for advanced technical roles in cryptography and algorithm theory.

[UI, Ibadan] MAT 223: Real Analysis
[UI, Ibadan] MAT 223: Real Analysis
This learning track provides the complete theoretical machinery of single-variable calculus and analysis. We build the subject from first principles, establishing the rigorous logical framework required for advanced quantitative disciplines. This is the 'why' behind the mathematics that powers science and engineering. This track is built for second-year engineering and physical science students, particularly those at the University Of Ibadan. It is also structured for any student requiring the same rigorous theoretical foundation for advanced quantitative study. On completion, you will command the complete theoretical basis of single-variable calculus. You will construct formal proofs, rigorously analyse function behaviour, and determine the convergence of infinite series. This programme provides the non-negotiable prerequisite knowledge for advanced study in differential equations, complex analysis, and theoretical physics.

This learning track provides the complete theoretical machinery of single-variable calculus and analysis. We build the subject from first principles, establishing the rigorous logical framework required for advanced quantitative disciplines. This is the 'why' behind the mathematics that powers science and engineering. This track is built for second-year engineering and physical science students, particularly those at the University Of Ibadan. It is also structured for any student requiring the same rigorous theoretical foundation for advanced quantitative study. On completion, you will command the complete theoretical basis of single-variable calculus. You will construct formal proofs, rigorously analyse function behaviour, and determine the convergence of infinite series. This programme provides the non-negotiable prerequisite knowledge for advanced study in differential equations, complex analysis, and theoretical physics.

Course Chapters

1. Introduction
9

What sets are, why they matter, and how to describe them. Covers everyday and mathematical examples, basic notation, set membership, subsets, and types of sets like finite, infinite, empty, universal, etc.

Chapter lessons

1-1. Welcome
4:19

Welcome to the course and outline of course.

1-2. Definition
14:56

Meaning of set and set membership notation.

1-3. Description
17:53

Different ways to clearly define the membership of a set.

1-4. Types of sets (1)
5:40

Types of sets - finite, infinite sets and their order or cardinality.

1-5. Types of sets (2)
11:16

Types of sets - empty, singleton and universal and complement sets.

1-6. Subsets
26:40

Meaning and examples of subsets.

1-7. Venn diagrams
6:39

An introduction to Venn diagrams and their use in illustrating sets and their subsets.

1-8. Power set
9:07

Meaning and cardinality of the power set of a given set.

1-9. Equality of sets
7:04

Meaning, condition for and implications of the equality of two sets.

2. Number Systems
10

This chapter introduces key mathematical sets and notations that form the language of abstract algebra. You’ll explore sets like Z+, mZ, Z_m, Z*, R[x], and R(x), along with common subsets such as Q+, R*, Q*, and R+. These notations are essential for understanding mappings, relations, and algebraic structures.

Chapter lessons

2-1. Introduction
6:49

What number systems are and why they matter in mathematics.

2-2. Natural numbers and integers
5:58

Meaning of and differences between natural numbers and integers.

2-3. Rational numbers
18:05

Meaning of rational numbers and how to identify them.

2-4. Irrational numbers
6:59

Meaning of irrational numbers and how they differ from rational ones.

2-5. Real numbers
7:28

Meaning and identification of real numbers - and 'unreal' ones.

2-6. Complex numbers
7:29

Meaning and identification of complex numbers.

2-7. Special integers (1)
9:40

Special integer subsets - positive, nonzero, etc.

2-8. Special integers (2)
7:59

Special subsets of integers involving modular arithmetics.

2-9. Special rationals and reals
2:18

Special subsets of rational numbers and real numbers.

2-10. Polynomials and rational functions
9:00

Meaning and examples of polynomials and rational functions with real coefficients.