Date  Topics covered  Due  Video, slides and notes 

Week 1  
Mon Mar 29  Introduction: course summary and policies  
Wed Mar 31  Cubic equations  Reflection 1 
•
video,
slides
• notes on cubics (Smyth) 
Fri Apr 2  Cubic equations continued 
•
HW 1
• HW1 solns 
• video,
slides
• Quick history of polynomials (T. Bösel) • Biography of del Ferro (St. Andrews collection) • Cubic dispute: L. Liberti, St. Andrews collection. 
Week 2  
Mon Apr 5  Review of group actions, structure of roots of polynomials in k[x], symmetric polynomials 
•
video,
slides
• Chapter 14Group Actions (Judson) • notes on roots and symmetric polynomials (Smyth) 

Wed Apr 7  Elementary symmetric functions, Fundamental Theorem on Symmetric Functions, Lagrange's solution to the quartic  Reflection 2 
•
video,
slides
• Lagrange's quartic solution (Smyth) 
Fri Apr 9  Recap Lagrange's solution to quartic, review of groups, rings & fields 
•
HW 2
• HW 2 solns 
• video, slides 
Week 3  
Mon Apr 12  Review of vector spaces and basis, field extensions (degrees and simple field extensions)  Quiz 1 
• video,
slides
• Hungerford 11.111.2 
Wed Apr 14  Simple field extensions, algebraic elements, minimal polynomials  Reflection 3 
• video,
slides
• Hungerford 11.211.3 
Fri Apr 16  Algebraic elements, algebraic field extensions, degrees of field extensions in towers 
•
HW 3
• HW 3 solns 
• video,
slides
• Hungerford 11.111.3 
Week 4  
Mon Apr 19  Finite, algebraic and transcendental field extensions; sums and products of algebraic elements are algebraic  Quiz 2 
• video,
slides
• Hungerford 11.3 
Wed Apr 21  Ruler and compass constructions I  Reflection 4 
• video,
slides
• Hungerford 15 
Fri Apr 23  Ruler and compass constructions II 
• HW 4
• HW 4 solns 
• video,
slides
• Hungerford 15 
Week 5  
Mon Apr 26  Splitting fields  Quiz 3 
• video,
slides
• Hungerford 11.4 
Wed Apr 28  Uniqueness of splitting fields and discussion  Reflection 5 
• video,
slides
• Hungerford 11.4 
Fri Apr 30  Normal field extensions, splitting fields are normal, definition of separable field extensions 
• HW 5
• HW 5 solns 
• video,
slides
• Hungerford 11.411.5 
Week 6  
Mon May 3  Separable field extensions  Quiz 4 
• video,
slides
• Hungerford 11.5 
Wed May 5  Finite fields  Reflection 6 
• video,
slides
• Hungerford 11.6 
Fri May 7  Revisiting normal and separable field extensions; further discussion of finite fields 
•
HW 6
• HW 6 solns 
• video,
slides
• Hungerford 11.411.6 
Week 7  
Mon May 10  First properties of the Galois group  Quiz 5 
• Galois bio (MacTutor) • Mirzakhani bio (MacTutor) • The Beautiful Mathematical Explorations of Maryam Mirzakhani (Quanta magazine) • video, slides • Hungerford 12.1 
Wed May 12  Examples of Galois groups and discussion  Reflection 7 
• video,
slides
• Hungerford 12.1 
Fri May 14  More on Galois groups, statement of the Fundamental Theorem of Galois Theory 
• HW7
• HW 7 solns 
• video,
slides
• Hungerford 12.2 
Week 8  
Mon May 17  Fundamental Theorem of Galois Theory  Quiz 6 
• video,
slides
• Hungerford 12.2 
Wed May 19  Discussion of Galois theory and homework  Reflection 8 
• video,
slides
• Hungerford 12.2 
Fri May 21  Wrapping up the Fundamental Theorem of Galois Theory: For K > E> L, E is normal over K <=> Gal(L/E) is normal in Gal(L/K) 
• HW8 • HW8 solns 
• video,
slides
• Hungerford 12.2 
Week 9  
Mon May 24  Galois's criterion  Quiz 7 
• video,
slides
• Hungerford 12.3 
Wed May 26  Discussion  Reflection 9  • video, slides 
Fri May 28  Galois's criterion 
• HW9 • HW9 solns 
• video,
slides
• Hungerford 12.3 
Week 10  
Mon May 31  No classMemorial Day  
Wed Jun 2  Wrapping up Galois's criterion 
• video,
slides
• Hungerford 12.3 

Fri Jun 4  Discussion  • HW10  not recorded 