Rings and Fields - 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. Introduction
Definition of a ring, ring axioms, properties, examples.
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2. Some Special Rings
Commutative rings, Boolean rings, integral domains - properties and examples.
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3. Subrings
Definition, subring test, and illustrative examples; two-sided ideals.
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4. Ring Homomorphisms
Definition and illustration of ring homomorphisms.
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5. Fields
Division rings, fields - definition, properties and illustrative examples.
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