MAG
Welcome to metauni Algebraic Geometry. This is a series of online algebraic geometry classes taught at metauni, using Roblox for the 3D virtual environment and voice chat and Discord for community.
We are currently preparing MAG1, a first course in algebraic geometry, which will be free and open to anyone with an Internet connection who is over the age of 13 (Roblox voice chat requires age verification).
Orientation is 07:00-08:00 Thursday 26/5/22 AEST, to join go to metauni.
- When: starting June 16 2022, weekly 1.5 hour lectures on Thursdays 7:00-8:30am AEST, weekly 1 hour exercise sessions on Friday 18:00-19:00 AEST (Friday 10:00 CEST) and Thursday 8:30-9:30am AEST. You should plan to show up to one of the exercise sessions (and both if you like). The class will run for 8 weeks with a two-week pre-course, starting June 2nd at the same time and day as the lectures, for those wanting to brush up on the background material.
- Where: The Rising Sea, a 3D virtual world built in Roblox, which is part of metauni. At metauni we write on blackboards (which retain their contents when you leave) and talk using position-based voice chat (people far away can’t hear you). We also use the metauni Discord. See the instructions for how to set it up.
- Why: to introduce the beauty of algebraic geometry in a hands-on way, emphasising the link between classical ideas and modern computation.
- What: the textbook is D. A. Cox, J. Little, D. O’Shea “Ideals, Varieties, and Algorithms”, referred to below as CLO. You don’t need a copy as we’ll post our own lecture notes based on the book, but it’s a great book and we recommend getting a copy.
The who is a community of volunteers:
- Lecturers: Ken Chan and Dan Murfet, both with PhDs in algebraic geometry.
- Tutors: Edmund Lau, Rohan Hitchcock and Will Troiani (and you?).
- Illustrators: Ethan Curtiss (AstroCode) and Mathias (and you?).
Registration is now open, see below. Subscribe to the mailing list to receive course updates (if you keep an eye on the #mag
channel in the metauni Discord, no need to sign up for this).
Registration
Registration is now open. Here is the registration process:
- Follow Steps 1 and 2 of the instructions to setup your Roblox and Discord accounts.
- Open the metauni Discord server and post in the
#mag-registration
channel with your Roblox username and how you want people to refer to you. This is mainly for your classmates, so you may wish to include a brief description of your interests and reasons for attending the class, and any links to personal webpages or Twitter accounts you want people to see. No pressure though, your Roblox username is enough (for administration purposes we need to know the connection between Discord accounts and Roblox usernames). - Join the metauni Roblox group. This way we can give you permission to write on the blackboards throughout metauni.
If you have any problem with these steps, ask for help on the #mag
channel of the metauni Discord, or email us. Before the beginning of the class we will circulate (on Discord and via email, so you may wish to sign up for the mailing list above if you haven’t already) some orientation videos and announce some drop-in orientation times where you can try out metauni before class begins.
Course content
There will be a two week pre-course
- Pre-course 1: Where do lines meet? (solving linear equations by Gaussian elimination) and where does a parabola meet a line? (proof of the quadratic formula) 2-6-22.
- Pre-course 2: Functions and set theory, long division for integers 9-6-22.
Each lecture will be 1.5hr. In the schedule below, S1.3
refers to Section 1.3 of CLO, (K)
means Ken and (D)
means Dan.
- Lecture 1: What is algebraic geometry?
(D) S1.1, S1.2, S1.3
16-6-22. - Lecture 2: Ideals and polynomial division
(K) S1.4, S1.4
- Lecture 3: Gröbner bases
(D) S2.1, S2.2
- Lecture 4: Division algorithm
(K) S2.3
- Lecture 5: Dickson’s lemma
(D) S2.4
- Lecture 6: Hilbert basis theorem
(K) S2.5
- Lecture 7: Buchberger’s algorithm
(D) S2.6, S2.7
- Lecture 8: Elimination theory
(K) S3.1, S3.2
There will be assigned exercises and students will be encouraged to complete a core subset each week. Solutions will be provided and it is up to students to seek feedback on their solutions from tutors.
Illustrations
In a virtual world we can use the environment to communicate ideas, using code; we call these illustrations.
Exercise sessions
The volunteer tutors will take turns hosting the exercise sessions, in which groups of students will work together at virtual boards, with a roving tutor assisting. Exercises will be assigned beforehand and students will be encouraged to make a start on problems before the exercise sessions.
Pre-requisites
High school algebra plus a little bit of linear algebra (a basic familiarity with matrices). More precisely, you should have experience working with polynomials in small numbers of variables and low degree. You should know
- How to find the roots of a quadratic polynomial,
- How to plot
q(x,y)=0
whereq
is a quadratic polynomial, - How to differentiate a polynomial,
- How to multiply matrices and do row operations.
You should also be comfortable with functions and terms like domain, codomain, image and preimage, injective, surjective, bijective, union, intersection and complement. If you want to brush up, here are some modules from Khan Academy that cover the necessary background:
- Introduction to Algebra
- Polynomial expressions, equations and functions
- Matrices up to “Row-echelon form and Gaussian elimination”
- Basic set operations.
- Functions.
Hardware
At metauni learning is centered on virtual blackboards that we call metaboards. It is therefore recommended that you have access to a tablet with stylus, in order to collaborate on the metaboards with other students. Tablets that plug into your computer via USB can be found for as little as AUD$50. Members of our community have successfully used the following products:
- XP-PEN G640 graphics tablet (~AUD$50)
- XP-PEN Deco 01v2 graphics tablet (~AUD$80)
- Apple iPad with Apple Pencil (~AUD$650)
- Apple iPad Pro with Apple Pencil (~AUD$1650)
In some countries Roblox may not be available through the Store for your device, in which case you should go with the USB tablet plugged into your PC. The USB tablets may not have a built-in screen, but when you hover the pen above a graphics tablet, the mouse onscreen follows your pen.
What doesn’t work:
- Huion H610 Pro V2
- The Wacom Intuos small
What is it like?
Here are some videos of learning at metauni in action: