Finite classical groups
This is the webpage for my course with the London Taught Course Centre. Practical matters:
- Lectures: There are 5 lectures, given every Monday from 30th September until 28th October 2013, 3:30pm – 5:30pm at De Morgan house in London.
- Lecture notes: These will be put online the morning after the lecture is given. Each lecture contains many exercises which students are encouraged to attempt. Answers to starred exercises will be put online after one week.
- Discussion class: I will run an experimental online discussion class for one hour starting at 2pm on Tuesday 15th October. This is optional and will cover some extra material tangential to the course.
- Exam: This has happened. Email me if you want solutions.
Course material follows.
- Useful reading:
- Course description, including a list of background texts;
- Peter Cameron’s notes on Classical Groups;
- Peter Cameron’s notes on Projective and polar spaces.</ul>
- Lecture notes:
- Lecture 0 on Group theory background (this was not covered in class);
- Lecture 1 on Permutation Groups and Fields and Vector Spaces;
- Lecture 2 on Projective space and Linear groups;
- Lecture 3 on Forms and polar spaces and Isometries and Witt’s Lemma;
- Lecture 4 in which we finish off Isometries and Witt’s Lemma, and then cover Polar spaces and Symplectic groups;
- Lecture 5 on Unitary groups and Orthogonal groups. </ul>
- Exercises and discussion class:
- Exercises 0 (including solutions);
- Exercises 1 (including solutions);
- Exercises 2 (including solutions);
- Discussion class questions (including solutions);
- Discussion class slides;
- Discussion class recording (you’ll need JAVA);
- Exercises 3 (including solutions);
- Exercises 4 (including solutions);
- Exercises 5 (solutions will be posted on request). </ul> </ul>