# Course plan and lecture notes

The following is a preliminary course plan and is subject to change. Changes will be recorded here. Notes from all lectures.

Some students have typed some notes and kindly shared them with the rest of the class. Typed notes

Day Book chapters Lecture notes
Thursday 11.01 Chapters 11.1-11.2 0.Background and motivation + 1.PIDs and UFDs
Friday 12.01 Chapters 11.3-11.4 2.Euclidean domains and polynomial rings
Thursday 18.01 Chapter 15.1 3.Polynomial rings over fields and irreducibility in $\mathbb Z [x]$
Friday 19.01 Chapter 15.2 4.Field extensions by root adjunction
Thursday 25.01 Problem Set 1 Problem Set 1 Solutions
Friday 26.01 Chapter 15.3 5.Algebraic extensions of fields
Thursday 01.02 Chapter 15.4 6(a).The algebraic closure of a field
Friday 02.02 Chapters 15.4-16.1 6(b).The algebraic closure of a field + 7(a).Splitting fields
Thursday 08.02 Chapters 16.1-16.2 7(b).Splitting fields + 8.Normal extensions
Friday 09.02 Chapter 16.3 9.Root multiplicity
Thursday 15.02 Problem Set 2 Problem Set 2 Solutions
Friday 16.02 Chapter 16.4 10(a).Finite fields
Thursday 22.02 Chapters 16.4-16.5 10(b).Finite fields + 11(a).Separable extensions
Friday 23.02 Chapter 16.5 11(b).Separable extensions
Thursday 29.02 Chapter 17.1 12(a).Galois groups
Friday 01.03 Chapter 17.1 12(b).Galois groups
Thursday 07.03 Problem Set 3 Problem Set 3 Solutions
Friday 08.03 Chapter 17.1 12(c).Galois groups
Thursday 14.03 Chapter 17.2 13.Fundamental theorem of Galois theory
Friday 15.03 Chapter 18.1 14(a).Roots of unity and cyclotomic polynomials
Thursday 21.03 Problem Set 4 Problem Set 4 Solutions
Friday 22.03 Chapter 18.1 14(b).Roots of unity and cyclotomic polynomials
Thursday 04.04 Chapter 18.1-18.2 14(c).Roots of unity and cyclotomic polynomials + 15(a).Cyclic extensions
Friday 05.04 Chapter 18.2-18.3 15(b).Cyclic extensions + 16(a).Polynomials solvable by radicals
Thursday 11.04 Chapter 18.3 16(b).Polynomials solvable by radicals
Friday 12.04 Chapter 18.3-18.5 16(c).Polynomials solvable by radicals + 17(a).Constructions with ruler and compass
Thursday 18.04 Problem Set 5 Problem Set 5 Solutions
Friday 19.04 Chapter 18.5 17(b).Constructions with ruler and compass
Thursday 25.04 No lecture No lecture
Friday 26.04 No lecture No lecture
Thursday 02.05 Problem Set 6 Problem Set 6 Solutions
Friday 03.05 Repetition Exam June 2015 sample solution