Groups
Table of Contents
Part 1A Michaelmas
This is the first term of the Mathematical Tripos.
Course
- Lecture notes (official 2019)
- Example sheets
- Someone made lectures on YouTube based on the course notes.
Books marked with † in the schedule are particularly well suited to the course and here that book is Algebra and Geometry by Alan F. Beardon so that is the book I will work through here. There is old notes for the book here too back when Groups and Vectors and Matrices were one large course called 'Algebra & Geometry Part 1 and 2'.
Strategy
- Modern Algebra lecture playlist which uses the text Visual Group Theory that is recommended by the schedule.
- Work book An Inquiry-Based Approach to Abstract Algebra by Dana Ernst.
Sample lecture
Here is the first Cambridge lecture on groups. Symmetry of an object is defined as 'something we can do to it that preserves it's structure and leaves it looking the same'.
An equilateral triangle has the following symmetries:
- 'do nothing symmetry' (identity)
- 3 reflections by an axis through each inside angle
- 2 rotations
TODO