Conducted in
term:
2023/24Z
ECTS credits:
3
Language:
Polish
Organized by:
Doctoral School of Exact and Natural Sciences
Galois Theory 7404-MAT-TG
- Field extensions
- Geometric constructions
- The Fundamental Theorem of the Galois Theory
- Splitting field, algebraic closure and normality
- The Fundamental Theorem of Algebra
- The Galois group of a polynomial
- Finite fields
- Separability
- Cyclic extensions
- Cyclotomic extensions
- Radical extensions
- The general equation of degree n
Total student workload
30 hours - lecture
30 hours - preparation for lectures and study of literature
30 hours - preparation for exam
Learning outcomes - knowledge
After finishing the course a Ph student should know
* notions of algebraic/separable extension
* reasons, why a trisection of an angle is impossible
* reasons, why one cannot present a general formula for roots of polynomials of degree bigger than 4 (P8S_WG)
Learning outcomes - skills
After finishing the course a Ph student should be able to:
* present a construction of the splitting field of a polynomial,
* present a construction of the algebraic closure of a field,
* prove the Fundamental Theorem of the Galois Theory.
(P8S_UW)
Expository teaching methods
- informative (conventional) lecture
Prerequisites
Knowledge of basis notions and theorem of algebra concering groups and rings.
Course coordinators
Assessment criteria
Oral exam
Bibliography
- T. Hungerford, Algebra, Springer, 1974.
- J.Browkin, Teoria ciał, PWN, 1978.
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: