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Story From Vivian Kuperberg

On Mar 24, 2021, at 3:49 PM, Vivian Kuperberg wrote:

Hi Dick,

In the end I've decided I just don't want to film a video. But, here's a written testimony.

Good luck with the project! I enjoyed the open house last weekend.

Best, Vivian

I worked at the Math Support Center starting in my sophomore year (2014-2015), and then as a head tutor from 2015 to 2017. As is the case for many undergraduate math tutors everywhere, it was my first major teaching experience. I learned so much about teaching from the students and other tutors there, and I use that knowledge to this day to inform my class design and office hours as a graduate student. At one point at an orientation session my senior year, I explained to new tutors that I think of tutoring and homework help as akin to spotting someone while they are lifting weights. A spotter can spot someone who is lifting much heavier weights than the spotter can handle, because a lifter who is lifting 200 pounds is doing so because they have already lifted, say, 195 pounds, so the spotter is responsible at most for the last five pounds. Similarly, the students are the ones who have been attending lecture and attempting the homework, so as a tutor I am doing my job best when I am only helping with the smallest possible amount of understanding. I was really happy with this metaphor at the time (and I still use it!) but it's worth noting that it was really a product of the environment at the MSC. I remember talking to other tutors about how many students you'd be able to help if you restricted yourself to saying only things like "Have you read the chapter?", "How do you think this relates to the material you've seen?" and "What do you think we should try next?". At some point I decided that although the tutoring center largely just promises to help students in large lower-level courses like linear algebra and calculus, I was equipped with my understanding of math and these strategies, and therefore I should be able to help any student with questions about any undergraduate course.

It's worth noting that the MSC was also a fun place to hang out, with plenty of gadgets and games curated largely by Dick, but with help from the rest of us tutors. At various times the MSC serves as a type of headquarters for mathematical activities in the Cornell math department. For example, when Math Club hosted game nights, we used board games from the MSC. My first year at the MSC, it also served briefly as a T-shirt distribution center. I had been chatting with Dick about a T-shirt I'd designed, and he suggested I could design a Cornell/MSC-themed shirt. Over winter break, I came up with a design that played off of the idea that many of the letters of "Cornell" are common math symbols when written in the blackboard bold font. For example, C represents the complex numbers, R represents the reals, and N represents the natural numbers. In the spring, I contacted a T-shirt company and put up posters around the department. We got 50 shirt orders in the first batch; assuming there might be more interest once the shirts had arrived, I ordered 75 shirts. We sold the shirts for $7 each, which was just enough for us to break even on costs from just the original 50 orders. In fact all 75 shirts sold, and we used the profits to buy a set of Zome for the center. As time went on, some math department faculty started asking about the shirts. In the end, the department took over production, and the shirt became an official Cornell math department T-shirt. I believe that every undergraduate receives a free shirt when they declare a math major. As a side bonus, the Zome was a great investment, which added to the center's collection of math games.

I ended up designing another shirt for the MSC, but never implemented it (although I have a nice drawing of it on my website). This was a set of 4 mutually orthogonal 5x5 latin squares, realized as generalizations of "SET" cards. To unpack that a bit, an n x n latin square is an n x n grid where each small square contains one of n symbols, and where each row and column contains each of the symbols exactly once. So, a filled sudoku grid is a 9x9 latin square, since each row and column contains each digit from 1 to 9 exactly once. In the game of SET, there are cards of three different colors (red, green, and purple), so you could form a 3x3 latin square by making a grid of SET cards, where each row and column has exactly one card of each color. Now, two latin squares with two different sets of symbols are "mutually orthogonal" if any pair of symbols occurs exactly once in the grid. Going back to the cards: SET cards also have one, two, or three symbols on them. So we can make a numbers-latin square, a 3x3 grid where each row and column contains a 1 card, a 2 card, and a 3 card. But we can overlay this with our colors grid, so that if we look at the colors it's a latin square AND if we look at the numbers it's a latin square. The mutual orthogonal constraint says that there's exactly one card in the whole grid with a specified number and color (for example, exactly one card with one red symbol, and exactly one card with two green symbols, and so on).

SET cards have four properties in total: color, number, shape, and shading. So we can imagine setting up not just two mutually orthogonal latin squares, but four of them. This is mathematically possible, but not for 3x3 latin squares. For 5x5 latin squares, however, we can have 4 mutually orthogonal latin squares. So, to extend the SET cards to the 5x5 squares, we need each color to have 5 options, not just 3. For example, these "generalized" SET cards can be red, green, purple, yellow, or blue, instead of just red, green, and purple. This is exactly the design I've drawn; a 5x5 grid of generalizations of "SET" cards, so that any two characteristics form mutually orthogonal latin squares.

-- Dick Furnas - 2021-05-08

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