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.

4 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 203: Sets, Logic and Algebra I
MTH 203: Sets, Logic and Algebra I
Abstract algebra is the structural foundation of modern advanced mathematics. This track delivers the complete NUC CCMAS MTH 203 curriculum, rigorously transitioning you from computational arithmetic to abstract mathematical reasoning. It provides the necessary prerequisite framework for understanding complex mathematical systems and their applications. This programme is targeted at undergraduate students in mathematics, computer science, and physics requiring a firm grounding in fundamental algebraic structures. It also serves professionals in fields like cryptography or theoretical computer science who need a rigorous theoretical refresher. You will master the precise definitions, properties, and relations of core algebraic structures, including groups, subgroups, rings, and fields. You will gain competence in constructing formal proofs using set theory and logic, and understand how homomorphisms preserve mathematical structure. Completion establishes the critical theoretical base demanded for advanced studies in algebra, coding theory, and algorithm design.

Abstract algebra is the structural foundation of modern advanced mathematics. This track delivers the complete NUC CCMAS MTH 203 curriculum, rigorously transitioning you from computational arithmetic to abstract mathematical reasoning. It provides the necessary prerequisite framework for understanding complex mathematical systems and their applications. This programme is targeted at undergraduate students in mathematics, computer science, and physics requiring a firm grounding in fundamental algebraic structures. It also serves professionals in fields like cryptography or theoretical computer science who need a rigorous theoretical refresher. You will master the precise definitions, properties, and relations of core algebraic structures, including groups, subgroups, rings, and fields. You will gain competence in constructing formal proofs using set theory and logic, and understand how homomorphisms preserve mathematical structure. Completion establishes the critical theoretical base demanded for advanced studies in algebra, coding theory, and algorithm design.

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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.
Concept Overviews
9 Lessons
1:43:34
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.
Concept Overviews
10 Lessons
1:21:45