Course plan and lecture notes The following is a preliminary course plan and is subject to change. Changes will be recorded here. Day Book chapters Lecture notes Monday 09.01 Chapters 11.1-11.2 1.PIDs and UFDs Friday 13.01 Chapters 11.3-11.4 2.Euclidean domains and polynomial rings Monday 16.01 Chapter 15.1 3.Polynomial rings over fields and irreducibility in ℤ[x] Friday 20.01 Chapter 15.2 4.Field extensions and root adjunction Monday 23.01 Chapter 15.3 + Problem Set 1 5(a).Algebraic extensions of fields + Problem Set 1 solutions Friday 27.01 Chapters 15.3-15.4 5(b).Algebraic extensions of fields + 6(a).The algebraic closure of a field Monday 30.01 Chapter 15.4 6(b).The algebraic closure of a field Friday 03.02 Chapter 16.1 7.Splitting fields Monday 06.02 Chapter 16.2 8.Normal extensions Friday 10.02 Chapter 16.3 + Problem Set 2 9(a).Root multiplicity + Problem Set 2 solutions Monday 13.02 Chapters 16.3-16.4 9(b).Root multiplicity + 10(a).Finite fields Friday 17.02 Chapter 16.4 10(b).Finite fields Monday 20.02 Chapter 16.4 10(c).Finite fields Friday 24.02 Chapter 16.5 11.Separable extensions Monday 27.02 Chapter 16.5 + Problem Set 3 Problem Set 3 solutions Friday 03.03 Chapter 17.1 12(a).Galois groups Monday 06.03 Chapter 17.1 12(b).Galois groups Friday 10.03 Chapter 17.1 12(c).Galois groups Monday 13.03 Chapters 17.2-18.1 13.Fundamental theorem of Galois theory + 14(a).Roots of unity and cyclotomic polynomials Friday 17.03 Chapter 18.1 14(b).Roots of unity and cyclotomic polynomials Monday 20.03 Chapter 18.1 + Problem Set 4 14(c).Roots of unity and cyclotomic polynomials + Problem Set 4 solutions Friday 24.03 Chapters 18.1-18.2 14(d).Roots of unity and cyclotomic polynomials + 15.Cyclic extensions Monday 27.03 Chapter 18.3 16(a).Polynomials solvable by radicals Friday 31.03 No lecture No lecture Friday 14.04 Chapter 18.3 16(b).Polynomials solvable by radicals Monday 17.04 Chapter 18.3 + Problem Set 5 16(c).Polynomials solvable by radicals + Problem Set 5 solutions Friday 21.04 Chapter 18.5 17(a).Constructions with ruler and compass Monday 24.04 Chapter 18.5 + Games 17(b).Constructions with ruler and compass Friday 28.04 No lecture No lecture Friday 05.05 Repetition + Problem Set 6 Exam June 2016 sample solution + Problem Set 6 solutions