Week 5 email
Hey everyone!
Tl;dr:
- SUMO ramble
- Game Theory Study Group - Session 2
- Rewiring session
- Weekly problem
It is an uncontested truth that parents love all their children equally. In similar fashion, none doubt that I hold all SUMS events in equal regard. However, if I - hypothetically - had to have a favourite, it would have to be SUMO.
I attended SUMO last year on zero hours of sleep, and it was glorious. Folk slowly trickling into Parliament Hall from all the different universities. The buzz of discussion, the writing of solutions, invigilated snack breaks in the sun. It was a lovely event, and I strongly encourage you consider signing up, even if your Pi Ball plans include being hungover.
https://sums-sta.github.io/sumo/registrations/
Without further ado, here’s our normal list.
Game Theory Study Group - Session 2
Our Game Theory study group continues. Each week we will do a set amount of reading and meet to discuss the previous week’s content. Most sessions will begin with a short presentation from a member of the study group on the reading (we volunteer to present).
The book is ‘Game Theory: A Playful Introduction’ by Deborah A. Kent and Matthew Jared DeVos.
In this session, we will hope to review chapter 2 of the book, covering normal-play games. Ben will present a brief overview of the content, and then we will engage in some discussion and get to play some games. If you didn’t manage to attend last week’s session, you should still be able to follow along and join in the fun!
Where: Tutorial room 1B
When: Monday, 16:00
Facebook link: https://fb.me/e/41p3Af2mx
Week 5 Rewiring session
In order to avoid overdoing even weeks, we’re moving rewiring sessions to odd weeks, starting now.
Rewiring sessions are designed to encourage and promote the spirit of mathematical playfulness and curiosity. We meet and attendees suggest questions or ideas to play around with. These can be anything and often take the form of investigating some previously studied area without looking at preexisting literature.
Where: Tutorial Room 1D
When: Friday, 16:00
Facebook link: https://fb.me/e/3oWwy3zcU
That’s it for this week.
Sincerely,
Dan Roebuck
President of SUMS
This weeks problem is another from SUMO last year. Here it is:
Problem 4. Let $G$ be a group with identity $e$ and $\phi:G\rightarrow G$ a function such that
\[\phi(g_1)\phi(g_2)\phi(g_3)=\phi(h_1)\phi(h_2)\phi(h_3)\]whenever $g_1g_2g_3=e=h_1h_2h_3$. Prove that there exists an element $a\in G$ such that $\psi(x)=a\phi(x)$ is a homomorphism (i.e. $\psi(xy)=\psi(x)\psi(y)$ for all $x,y\in G$).