Groups
Table of Contents
Part 1A Michaelmas
This is the first term of the Mathematical Tripos you should be taking this with the other first term courses at the same time as Cambridge designed it this way for a good reason.
Course
- Lecture notes (official)
- Example sheets
- Exams
- Modern Algebra lecture playlist which uses the text Visual Group Theory that is recommended by the schedule.
- Someone made lectures on YouTube based on the course notes too.
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 which is on library genesis 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'.
Practice
Work book here 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