Joshua Tan (@duckguins) AY25/26 Sem 1

About the Instructor

Prof Francesca was a really engaging professor, who played a little more of a facilitator role during some of the lessons. She was generally quite supportive and aware that some segments of the class might be from backgrounds outside math, and makes it clear in the introduction that the class will not be math-intensive. As a more introverted student, I really appreciated how she counted contribution into a discussion google document as a form of class participation. She also takes the time to wander around the class during discussions and to check on how different groups of students are progressing. For the more math-loving, she does take the time to explain more difficult concepts in a simple way after class (though she has a strict policy that all math covered in the student presentations should fit a generalist audience). I had a blast learning about her research interest in group theory from one of her post-class talks. And about how to pick really good oranges (after someone brought an orange to class).

Content (Structure/Organization)

I think the course curriculum was generally well-structured, and the workload was rather manageable. The course is structured into a first half covering Euclid's Elements (you can skim the free English-Koine parallel text online for a taste) and on how to do geometric proofs step-by-step, and a second half covering art history and the construction of one-, two- and three-point perspectives. As someone not from a math-intensive background, the section on writing proofs was a little hard to grasp initially, and a conversation in class initially read something like:

Prof: How do you know this is an equilateral triangle?

Student: Each angle is 60 degrees.

Prof: Yes, but how do you know that each angle is 60 degrees?

Student: Because....I have a protractor...?

Prof: You don't have a protractor in this case. 

Student: Um....because all the sides are equal?

Prof: Ok but how do you know all the sides are equal?

Student: ....because I have a ruler?

Prof: You don't have a ruler either.

Student: ....I have to use one of the postulates don't I.

Prof: Yes, which one?

 .......

Eventually you do get the hang of proving things from first principles (the postulates and common notions), and I found the process quite fun.

The section on art history has a mostly Eurocentric lens (think Michaelangelo and Brunelleschi), which is great because that opens up the option of covering non-European art in the final project.

Manageability of Workload

Most of the work was concentrated on making a group presentation (each group of students takes the lead in introducing the class to a topic for each lesson), a mini-project on drawing something in perspective, and a final project on something pertaining to art history (and a dash of mathematics). The final project might take a while to complete, but there is quite a bit of freedom regarding the format (some of us opted for in-class presentations, I did a website on geometric patterns in mosques)

Ease/Difficulty of Attaining Grades

I got a B+ for the mod and I'd assume that the professor isn't too harsh in handing out grades, though I suppose you'd probably have a good chance at an A if your final project is something particularly exciting (one young man in the class did a presentation on the application of geometry in fencing - that was pretty awesome)

Learning Value/Recommendation

Generally this was a really useful course in easing into math. I feel the art history section adds a bit more concrete application and cultural relevance to all the math we covered, and the course really helped make such a technical subject a lot more approachable. Some of my classmates were really into math so it was an interesting experience to learn about things like hyperbolic geometry from them.

Additional Comments

You'd probably have an advantage if you've had some background in art or math (as per the course title); but even if you don't, an open mind is more than enough preparation.