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Week 9 - The fundamental Correspondence
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HT24
Mathematics Fall 24
Second level courses
MM7043 HT24
Week 9 - The fundamental Correspondence
Section outline
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Week 8 - The primitive element theorem
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Week 10: Cyclotomic and abelian extensions
DF 14.2
Exercises: 3, 4, 5, 6, 7, 10, 12
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Week 8 - The primitive element theorem
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General
Examination & Grading
Some Recent Exams
Other texts (not required for the course)
Introduction & Overview
Week 1 - Introduction and review
Week 2 - Field Extension, finite, finitely generated and algebraic
Week 3 - splitting field
Week 4 -Separability
Week 5 - Embeddings
Week 6 - Finite fields
Week 7 - Root of Unity and cyclotomic extensions
Week 8 - The primitive element theorem
Week 9 - The fundamental Correspondence
Week 10: Cyclotomic and abelian extensions
Week 11: Construction by straightedge and compass
Week 12: Solvability by radicals
Week 13: Computing the Galois group I
Week 14: Computing Galois groups II
Week 14 - A proof of quadratic reciprocity
Artin's Example in Lang's Algebraic Number Theory
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Week 10: Cyclotomic and abelian extensions