Set Theory - Introductory Abstract Algebra

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.

4 hrs

$ 10.00

Payment required for enrolment

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.

[UI, Ibadan] MAT 211/213: Abstract Algebra

This learning track brings together the essential building blocks of abstract algebra in one clear, structured path. We begin with the fundamentals—set theory, relations, and mappings—to build the logical foundation for working with algebraic systems. Then we move into binary operations, groups, subgroups, and homomorphisms, helping you develop the tools to recognize structure and symmetry. The track wraps up with rings, fields, and key ideas from elementary number theory that tie everything together. Curated for second-year undergraduates in engineering and physical sciences at the University of Ibadan, but equally valuable for any learner stepping into abstract algebra for the first time. Clear, focused, and paced to guide you with both depth and intuition.

Course Chapters

Introduction

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.Welcome4:19

Welcome to the course and outline of course.

2.Definition14:56

Meaning of set and set membership notation.

3.Description17:53

Different ways to clearly define the membership of a set.

4.Types of sets (1)5:40

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

5.Types of sets (2)11:16

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

6.Subsets26:40

Meaning and examples of subsets.

7.Venn diagrams6:39

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

8.Power set9:07

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

9.Equality of sets7:04

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

Number Systems

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

1.Introduction6:49

What number systems are and why they matter in mathematics.

2.Natural numbers and integers5:58

Meaning of and differences between natural numbers and integers.

3.Rational numbers18:05

Meaning of rational numbers and how to identify them.

4.Irrational numbers6:59

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

5.Real numbers7:28

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

6.Complex numbers7:29

Meaning and identification of complex numbers.

7.Special integers (1)9:40

Special integer subsets - positive, nonzero, etc.

8.Special integers (2)7:59

Special subsets of integers involving modular arithmetics.

9.Special rationals and reals2:18

Special subsets of rational numbers and real numbers.

10.Polynomials and rational functions9:00

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