MA3D5 Galois Theory
Term I 2018-2019

Module Description

This module, MA3D5 (Galois theory) has the prerequisites MA106 (Linear algebra) and MA249 (Algebra II).

Galois theory is the study of roots of polynomials and the fields that they generate. The theory answers classical questions dating back to the ancient Greeks. It is also a key tool in many areas of modern mathematics such as numerical analysis and dynamics. Finally, it is required knowledge for number theorists.

The material covered in this module is directly relevant to the modules MA3A6 (Algebraic number theory), MA426 (Elliptic curves), and MA4L7 (Algebraic curves).

Schedule

The schedule has a planned list of topics, organized by lecture. We will change the schedule as necessary, as we work through the material. Links to example sheets will be posted week-by-week.

Instructor and TAs

Name Building/Office E-mail Phone Office Hours
Saul Schleimer B2.14 Zeeman s dot schleimer at warwick dot ac dot uk 024 7652 3560 Friday 13:30-14:30
Alessandro Arlandini NA a dot arlandini at warwick dot ac dot uk NA NA
Mattia Sanna NA m dot sanna at warwick dot ac dot uk NA NA
George Turcas NA g dot c dot turcas at warwick dot ac dot uk NA NA

Class meetings

Activity Led by Time Building/Room
Support class George Turcas Monday 10:00-11:00 H0.58 Humanities.
Support class Mattia Sanna Wednesday 13:00-14:00 MS.B3.03 Zeeman.
Lecture Schleimer Thursday 13:00-14:00 H0.51 Humanities.
Support class Alessandro Arlandini Thursday 16:00-17:00 S0.19 Social Sciences.
Lecture Schleimer Friday 9:00-10:00 H0.51 Humanities.
Lecture Schleimer Friday 15:00-16:00 H0.51 Humanities.

Reference materials

We will follow Professor Siksek's lecture notes. The notes refer to many other resources, including Professor Stewart's book. This last is the first place I learned about Galois theory. Another extremely useful resource is Professor Conrad's collection of expository papers. These are very terse, but they often cover exactly the correct point of mathematics you are stuck on...

Links to the Lecture Capture audio files, and to the discussion forum, are on the module's Moodle page.

Example sheets and assessed work

See the schedule for the example sheets.

Assessed work will be 15% of your mark. We will have five homework sets, consisting of three exercises. These will be marked by a TA (out of ten). Your "overall homework mark" will then the smaller of (1) the sum of these five marks or (2) 45. Please let me (Saul) know if any of the problems are unclear or have typos.

Homework solutions must be placed in the dropoff box (near the front office), by 14:00 on the Friday specified on the sheet. No late work will be accepted.

Please write your name, the date, and the module code (MA3D5) at the top of the page. If you collaborate with other students, please include their names. Solutions typeset using LaTeX are preferred. Each problem should require at most one side of one page. If you find you need more space then write out a complete solution and then rewrite with conciseness in mind.

In addition to the example sheets, and the exercises proposed in lecture, there are exercises in Siksek's notes and Stewart's book. You can find the assessed example sheets for Siksek's version of the module at his webpage.

Exam

The exam will be 85% of your mark. The exam will be closed book. Here are the exam papers for this module from the last five years.

Mistakes

Please tell me in person, or via email, about any errors on this website or made in class. I am especially keen to hear about mathematical errors, gaffes, or typos made in lecture or in the example sheets.