This term I’m auditing CSC311 Introduction to Machine Learning. I’ve tried learning this topic before, but it wasn’t at the right level for me. This time I’m optimistic because my colleague Sonya Allin is teaching the course, and I feel comfortable bombarding her with naive questions.
As I was sitting in the first class, I had my mathematician hat on and I noticed some things. I’m not saying these are deep, or unknown things, but they were interesting to me. Maybe they’ll be interesting to you too!
Observation 1: When we turn a picture into a vector we seem to lose a lot of geometric data
A standard way of storing a (greyscale) picture as data is to first write it as a matrix of data (an nxn table) where the entries are intensities (on a scale of 0-255). Then it cuts chopped up and reconstituted into a vector.
“O God, I could be bound in a nutshell, and count myself a king of infinite space – were it not that I have bad dreams.”
Hamlet, Act 2, Scene 2. Lines 252-254.
Recently, a colleague asked me:
I know that there are different sizes of infinity, but what I want to know is how many different sizes of infinity there are?
This is a great question! I tried to explain my answer at the time, but it came out garbled and I think I confused him more than I helped. So this post is an effort to remedy that and answer his question.
This term I’m teaching (and coordinating) a 1200 person Integral Calculus course at UTM. Term Test 1 went surprisingly well for students, and Term Test 2 was an unqualified success (very high average, lots of people got 100% on the test).
This lead to the following (paraphrased) question on our course message board:
Is the exam going to be a lot more difficult because the averages on the term tests were so high?
I took the time to think about exactly why I don’t like adjusting the difficulty of exams based on students doing well previously. Here’s the answer I posted on our message board.
Every summer, Canadian undergraduate students in mathematics meet at the Canadian Undergraduate Mathematics Conference (CUMC). Hundreds of students attend, and it gives them a chance to meet other people excited by mathematics. Students are also encouraged to give a short presentation on a math topic that interests them.
In the summer of 2018, while I was a Post Doc at the University of Calgary, we hosted a “mini pre-CUMC conference” for undergrads to give their presentations ahead of time. It was so successful that I ran an expanded version of this at the University of Toronto for CUMC 2019.
I think these events and workshops are important for all students, but in particular it helps break down barriers to entry for marginalized students. With that in mind, I’m sharing my resources, thoughts and experiences about our pre-CUMC conference with the hope that other universities and colleges in Canada will benefit.
In November 2018, 41 of the top researchers in Ramsey theory met at the BIRS in Banff for the Unifying Themes in Ramsey Theory conference. By all measures the conference was a big success. What makes Ramsey theory so special is that it has wide ranging impacts in diverse fields in mathematics. The participants gave talks showing how Ramsey theory has impacted fields like graph theory, topological dynamics, set theory, model theory, operator algebras, logic and statistics.
Since I have a somewhat broad base of knowledge in Ramsey theory, I tried my best to give a short description of each of the speakers in language that makes sense to me. My view is biased, and my intent is always to show off the amazing work everyone is doing. I hope nothing comes across as negative or critical; that is not my intent.
I will be participating as a trainer for Canada’s 2018 IMO Summer Training camp. I’m giving a session on graph theory. As I prepared my notes I found many resources online that already cover some aspects of graph theory. So here are those resources:
This is an in-depth description of the basic combinatorial and geometric techniques in graph theory. It is a very thorough and helpful document with many Olympiad level problems for each topic. (No solutions are given.)