Core Module in Algebra
20 credits / 30 lectures
This course focuses on Galois Theory, which provides a connection between group and field theory, studied in previous years. We will study ancient geometrical problems such as "squaring the circle" and we will finish by proving that a solution by radicals of a quintic equation is not possible. To be more precise we will study
- field extensions,
- ruler and compasses constructions,
- splitting fields,
- normal and separable extensions,
- finite fields,
- the Galois correspondence, and,
- cubics, quartics and ‘insoluble’ quintics.
Prerequisites:The undergraduate module 3AL (Modern Abstract Algebra), or equivalent, is required. The 3rd year module 3TA (Topics in Algebra) is recommended.