Elementary Number Theory - Introductory Abstract Algebra
[UI, Ibadan] MAT 211/213: Abstract AlgebraThis learning track brings together the essential building blocks of abstract algebra in one clear, structured path.
We begin with the fundamentals—set theory, relations, and mappings—to build the logical foundation for working with algebraic systems. Then we move into binary operations, groups, subgroups, and homomorphisms, helping you develop the tools to recognize structure and symmetry. The track wraps up with rings, fields, and key ideas from elementary number theory that tie everything together.
Curated for second-year undergraduates in engineering and physical sciences at the University of Ibadan, but equally valuable for any learner stepping into abstract algebra for the first time. Clear, focused, and paced to guide you with both depth and intuition.
This learning track brings together the essential building blocks of abstract algebra in one clear, structured path. We begin with the fundamentals—set theory, relations, and mappings—to build the logical foundation for working with algebraic systems. Then we move into binary operations, groups, subgroups, and homomorphisms, helping you develop the tools to recognize structure and symmetry. The track wraps up with rings, fields, and key ideas from elementary number theory that tie everything together. Curated for second-year undergraduates in engineering and physical sciences at the University of Ibadan, but equally valuable for any learner stepping into abstract algebra for the first time. Clear, focused, and paced to guide you with both depth and intuition.
Course Chapters
1Introduction
Welcome to the course and review of number systems.
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2Divisibility
Definition and Euclidean algorithm, notations, and simple consequences.
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3Greatest Common Divisor (GCD)
Definition, computation using Euclidean algorithm.
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4Congruence and Residue Systems
Definition, notation, and properties of congruence, complete and reduced residue systems, including examples.
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5Polynomials
Polynomials with integer coefficients, polynomial congruence modulo n, and basic operations.
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