Core unitUnit 11 of 24
Abstract Algebra I
Explore algebraic structures such as groups, rings, and fields that reveal the symmetry of mathematics.
Difficulty
Beginner
Estimated study
200 hours
Duration
Self-paced
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About this unit
Unit overview
This unit introduces the structural viewpoint of modern algebra through groups, rings and fields. You will learn to work with algebraic operations, prove fundamental results and recognise how symmetry and structure connect apparently different mathematical problems.
Learning outcomes
What you’ll learn
- 01Verify whether a set and operation form a group, ring or field
- 02Work with subgroups, cyclic groups, cosets and quotient structures
- 03Use homomorphisms and isomorphisms to compare algebraic structures
- 04Construct rigorous proofs about finite groups and elementary rings