## Math 3345: Algebra 2 (Honors) -- Field Extensions and Galois Theory

*2015, Semester 1*

**Lectures:** Tuesday 3-4, Wednesday 10-11, Thursday 2-3 in Moran G008

**Instructor:** Jarod Alper (`jarod.alper@anu.edu.au`)

**Office:** John Dedman Building 1169

**Office hours:** Wednesday 11-12, Thursday 10-11

**Tutorial:** Friday 10-11 in Moran G008

**Tutor:** Hannah Keese (`u5025630@anu.edu.au`)

Course Information

** Final Exam **

** Midterm Exam **

- Thursday, March 26 from 1:45 - 3:25 in Melville Hall.

** Textbook **

** Historical supplements **
- Quick history of polynomials due to Thoms M. Bösel.
- Early history of Galois' theory of equations, James Pierpont, 1897.
- Galois's letter to his friend Auguste Chevallier, written on the eve of his death. English translation
- Biography of del Ferro, from the St. Andrews collection. Scipione del Ferro of Bologna is credited to be first to solve the cubic equation.
- The cubic dispute: Tartaglia versus Cardan, from the St. Andrews collection. This is a short description of the historical dispute between Tartaglia and Cardan concerning credit for the discovery of the cubic. It contains the solution finally written by Taraglia to Cardano in the form of a poem.
- Biography of del Ferro, from the St. Andrews collection. Scipione del Ferro of Bologna is credited to be first to solve the cubic equation.
- Biography of Galois, from the St. Andrews collection,
- Genius and Biographers: The Fictionalization of Evariste Galois by Tony Rothman, American Mathematical Monthly, 89, 84 (1982)
- Gauss’s proofs of the fundamental theorem of algebra by Harel Cain

** Supplemental notes **

** Assignments **
- Homework 1, due Wednesday, Febrary 25.
- Homework 2, due Monday, March 2.
- Homework 3, due Tuesday, March 10.
- Homework 4, due Monday, March 16.
- Homework 5, due Monday, March 23.
- Homework 6, due Wednesday, April 1.
- Homework 7, due Monday, April 20.
- Homework 8, due Wednesday, April 29.
- Homework 9, due Monday, May 11.
- Homework 10, due Monday, May 18.
- Homework 11, due Friday, May 29.

** Tutorial sheets **
- Tutorial 1, Friday, Febrary 20.
- Tutorial 2, Friday, Febrary 27.
- Tutorial 3, Friday, March 6.
- Tutorial 4, Friday, March 13.
- Tutorial 5, Friday, March 20.
- Tutorial 6, Friday, April 24.
- Tutorials 7 and 8, Friday, May 1 and Wednesday, May 6.
- Tutorial 9, Friday, May 15.
- Tutorial 10, Friday, May 22.