Galois theory
4 points * Second semester * Clayton * Prerequisites: MAT2020 and one of MAP2021 or MAP3031
Objectives On the completion of this subject students will be able to review the fundamentals of previous algebra subjects; link these previous subjects with other subjects; prove the fundamental theorem of algebra; develop Galois theory to sufficient depth to answer the following questions: Can a cube be doubled? Can an angle be trisected? Can a general polynomial equation be solved?
Synopsis Classical problems in geometry and algebra. Polynomial rings, irreducible polynomials, field extensions. Degree of an extension and unsolvable construction problems. Automorphisms of field extensions, Galois theory. Unsolvability of the quintic equation.
Assessment Examinations (1.5 hours): 70% * Assignments: 30%
Prescribed texts
Fraleigh J B A first course in abstract algebra Addison-Wesley, 1994
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