Mappings - Introductory Abstract Algebra (Undergraduate Advanced)
[University] Introduction to Abstract AlgebraMaster 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. Introduction3
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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