syllabus
This is a multi-level tutorial. Everyone should master some core topics in the theory of groups, rings and fields. This will be assessed by an exam at the end of the semester and contribute 50% of your grade. Everyone should also strive to learn new material and push themselves a good amount. This other 50% of the grade will be determined by regular(ish) assignments that usually conclude "...and add some problems you have found for yourself" or something similar. Your grade will also be subject to moving up or down by up to one letter grade based on your attendance, participation and preparation for class sessions.
For Tues 4th Sept
- Make sure you understand
- Proof methods, including induction and contradiction,
- Equivalence relations,
- Modular arithmetic.
- Bring examples of problems you have solved and questions about anywhere you get stuck.
For Fri 7th Sept
- Make sure to understand...
Come to class with a specific example of a group (or family of groups) to explain to everyone else.
For Tue 13th Sept
- Keep reading and bring a theorem (and proof) to share with the class from what you've read so far. Aim for short and snappy and lean towards results about groups in general rather than specific groups (e.g. an element of a group has a unique inverse).
For Fri 23rd Sept
- Read about cosets, normal subgroups and quotient groups (aka factor groups). Come ready to talk about an example or a short proof, or something you had difficulty with.
For Tue 27th Sept
- Read about homomorphism, isomorphisms and the three isomorphism theorems. Come ready to talk about an example or a short proof, or something you had difficulty with.
For Fri 30th Sept
- Complete the assignment that doesn't exist yet, but will be on the assignments link soon.
- In class I'll lay out a rough guide to what you might study next within group theory before we switch to rings.
For Fri 7th Oct
- Get stuck into Ring Theory. Come ready to talk about what you've read.
