Course Archives Theoretical Statistics and Mathematics Unit
Course:
Field and Galois theory
Level:
Undergraduate
Time:
Currently not offered
Syllabus
Past Exams
Syllabus:
- Algebraic extensions: degree, Splitting fields and normal extensions, Algebraic closure.
- Separable extensions, Fundamental theorem of Galois theory.
- Finite fields, Cyclic extensions, Kummer theory.
- Ruler and compass constructions, Solvability by radicals.
- Transcendental extensions: Transcendence bases and transcendence degree
Reference Texts:
(a) M. Artin: Algebra.
(b) S. D. Dummit and M. R. Foote: Abstract Algebra.
(c) I. N. Herstein: Topics in Algebra.
(d) K. Hoffman and R. Kunze: Linear Algebra.
(e) C. Musili: Rings and Modules.
(f) P. Morandi: Field and Galois theory.
(g) N. Jacobson: Basic Algebra.
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Past Exams
Midterm
24.pdf
Semestral
24.pdf
Supplementary and Back Paper
24.pdf
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