The page below contains the information about the project as it looked like before you submitted it. For the refereeing process, please see here.
Summary
You are required to complete a project as part of your evaluation in MAT 347. The project consists on writing a paper that solves the problem "Classify all groups of order N up to isomorphism" for a specific value of N, which will be different for each student. Your paper should contain:
a list of groups of order N,
a proof that every group of order N is isomorphic to one in your list, and
a proof that the groups on your list are not isomorphic to each other.
I want to give you a taste of what research is like. Research problems are neither short, nor easy. They require understanding things very deeply, seeing the "big picture", putting together lots of different things, and a dose of original ingenuity. They take you through a roller coaster of excitement, fear, frustration, anticipation, doubt, and finally climax, satisfaction, and pride. It is quite different from anything I could ask you to do in the artificial setting of an exam with a short amount of time.
Students who completed this project the last two times I taught this course reported that it was time-intensive but very rewarding. Many described it as their favourite part of the course and one of their best learning experiences in a math course at U of T.
Timeline
You will want to solve HW7 and HW8 before starting the project.
HW 7 is due on November 14
HW 8 is due on November 28
If you are eager to start on the project, you can finish your homework much earlier and dive in.
Nov 16 - Deadline to sign up for the project. Please complete this survey to do so.
Nov 19 - You will get your assigned order.
Dec 8 - Last day I am available for consultations.
I strongly encourage you to make an appointment to discuss your progress with me at some point.
Dec 22 - The project is due. Send it as a pdf file to me by email. In the subject of the email, write "MAT 347 Project", followed by your name and Student Number.
Important notes:
This late date is so that you can arrange your time as it best suits you. You could perfectly well be done in early December. If you have lots of exams and due dates in late December, you should do so!
Since I know that invariably I will get requests for late submissions, I am setting this policy. If you turn in your project late by n days, for positive n, rounded up to the closest integer, then you will be penalized with an (n^2)% of your mark in the project.
After the projects are submitted, I will send you the classification written by a different student. Then I will ask you to referee it. This accounts for 10% of your project grade, and everybody who makes a good attempt at it will get these points. Deadline to submit your referee report TBA.
How much detail to provide?
Your audience is another student in the course who has not done this particular classification. Will she or he understand you?
In general, try to make your paper self-contained. You may assume general, basic results about group theory without proof. If a theorem or result is proven in the book, or if it was an assigned homework problem, you are welcome to cite it and use it without proof,p although if it is obscure or very particular, you may want to prove it anyway.
Resources and collaboration
You are welcome to discuss with other students in the course about your work in the "research phase". However, the write-up has to be entirely your work. In particular, you are not allowed to share your drafts or have other people read or write them for you before you submit them.
You are welcome, and encouraged, to meet with Alfonso or Jonathan to discuss your progress or ask questions.
Apart from your peers, the book, Alfonso, and Jonathan, no other resources are allowed.
How to prepare
To solve your problem, you will need a good understanding of group actions, the Sylow Theorems,
the classification of finite abelian groups, direct products, semidirect products, presentations by
generators and relations, and the automorphism group of a group. Follow the lectures and the book,
and do all the homework problems, including the ones not to be handed in.
Read the extra examples in the book.
The problem I will give you for your project is hard; you should try to do first all the problems in increasing order of difficulty that I will do as examples in class and that I assign.
As an example of a problem of similar difficulty, here is the classification of groups of order 60. I suggest you postpone reading this until you have studied the material and worked on the easier problems.
If you are stuck, section 6.2 in the book contains a larger collections of tricks and examples.
I am also available to meet with you to discuss your progress or give hints. However, remember that I am not available to meet after December 8.
Remember to leave enough time to write out your paper. In case you have not done this before, writing math papers is more time consuming that it seems.