ADVANCED ALGEBRA A
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Bibliography
- Delivery method
- Teaching methods
- Contacts/Info
Knowledge of basic algebraic structures and their properties: groups, rings, polynomials, fields. Knowledge of basic results in linear algebra and matrix calculus.
Written examination immediately followed by an oral examination.
Knowledge of Galois Theory with applications.
Ruler and compass constructions. Splitting field of a polynomial. Multiple roots. Perfect fields. (20 hours)
The Galois group. The Galois correspondence. Normal and separable extensions of a field. (20 hours)
Finite soluble groups. Simplicity of the alternating group. The criterion for the solubility by radicals of an equation. The Galois group as the permutation group of the roots of a polynomial. General equation of degree n. (20 hours)
Finite fields. (4 hours)
Ruler and compass constructions. Splitting field of a polynomial. Multiple roots. Perfect fields. (20 hours)
The Galois group. The Galois correspondence. Normal and separable extensions of a field. (20 hours)
Finite soluble groups. Simplicity of the alternating group. The criterion for the solubility by radicals of an equation. The Galois group as the permutation group of the roots of a polynomial. General equation of degree n. (20 hours)
Finite fields. (4 hours)
John M. Howie, Field and Galois Theory, Springer
N. Jacobson, Basic Algebra I, Dover
Frontal lectures and guided exercise sessions
For further detail go to the web page of the course.
Borrowed from
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