Elementary Number Theory - Introductory Abstract Algebra (Undergraduate Advanced)

This course brings in elementary number theory as a foundation for abstract algebra. We cover divisibility, prime numbers, greatest common divisors, modular arithmetic, and congruences—all with a focus on the ideas that connect naturally to groups, rings, and fields. Clean, intuitive, and designed for learners building a solid entry point into algebra through number theory.

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

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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