Mappings - Introductory Abstract Algebra (Undergraduate Advanced)

This course focuses on mappings—one of the core tools in modern mathematics and abstract algebra. We cover functions, injectivity, surjectivity, bijections, and composition. You'll see how mappings connect sets, preserve structure, and lay the groundwork for understanding homomorphisms in algebraic systems. Straightforward, precise, and built for learners taking their first steps into abstract algebra.

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.
[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.

Course Chapters

1. Introduction
3

Definition of mappings, domain and co-domain, image and range, equality of mappings, constant mappings, identity mappings.

Chapter lessons

1-1. Welcome

Welcome to the course and outline of content.

1-2. Mapping

Definition and general examples of mappings.

1-3. Constant mapping

Meaning and examples of constant mappings.

2. Injections

Definition of injective mappings, examples of injections.

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3. Surjections

Definition of surjective mappings, examples of surjections.

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4. Bijections

Definition of bijective mappings, examples of bijections.

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5. Inverse Mappings

Definition of inverse mappings, examples of inverse mappings.

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6. Composition of Mappings

Definition of composition, examples of mapping compositions.

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