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Core Module in Algebra

Dr Juana Sanchez-Ortega
1st semester 2019
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.