Elementary Number Theory - 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
Welcome to the course and review of number systems.
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2. Divisibility
Definition and Euclidean algorithm, notations, and simple consequences.
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3. Greatest Common Divisor (GCD)
Definition, computation using Euclidean algorithm.
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4. Congruence and Residue Systems
Definition, notation, and properties of congruence, complete and reduced residue systems, including examples.
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5. Polynomials
Polynomials with integer coefficients, polynomial congruence modulo n, and basic operations.
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