Office hours for support and moments of ‘wow’ earn Miki Havlíčková the appreciation of her math students
Inspiration and beauty may not be words one typically associates with mathematics, but those are just some of the words that students use to describe the experience of being in Miki Havlíčková’s classroom. “Every time I leave class, I feel I’ve gained new insights into the beautiful mathematical objects that are the subjects of the class,” said one student, adding, “A teacher who can do that is priceless.” Noted another student: “I left the course inspired, something I never expected from an introductory mathematics course.” Students also hailed their teacher for the extra time she devotes to them in her office hours. In turn, Havlíčková — the winner of the Richard H. Brodhead ’68 Prize for Teaching Excellence by a Non-Ladder Faculty Member — loves to see the diverse ways students incorporate math into their lives, from their art to their poetry to their work beyond Yale.
Courses: “Calculus,” “Introduction to Functions of Several Variables,” and “Galois Theory”
What excites you about teaching undergraduates?
I like teaching Yale undergraduates because they are delightful people. It’s wonderful to work with them. They are smart, interesting, and they have a wide variety of interests. You can learn a lot from them, and you learn about different ways of looking at your own subject. Every class I teach, I can’t wait to see how they are going to think about it, and what they are going to do with it. We had a student writing software for secondary schools; another one is using math in her art project; a third one is running education programs in prisons; a fourth one is writing poetry with math in it. It’s amazing to watch it all happen!
Why is it important for students to study what you teach?
I think studying math is important for two reasons. The straightforward one is that math is used in many disciplines. I see it all the time. We cover something in class and the students come up and talk to me about physics and chemistry and economics, and they say, “You know, Miki, we’ve been using these tools in there for months, and it’s only right now that we actually understand why they work!” That’s a very proud moment for a mathematician. It makes us feel useful.
The second reason is a little more subtle. Studying math teaches you how to think logically. It teaches you how to approach problems, how to look for solutions in a systematic way, how to check whether the solutions make sense, and how to present them in a way that’s organized and clear to other people. Those skills are very important to everyone. It’s easy to miss that you are learning them in your math class, but you are, and they will stay with you long after you forget all about the equations.
If there is one thing you want your students to learn from you, what would that be?
Let me answer that with a story from my class for math majors. We were working on a result, and the proof of it is one of the most amazing pieces of mathematics in the entire semester. So there we are setting up this proof, and we are maybe five lines into it when one of the students in the back gets the idea of what’s coming and says out loud, “Oh, wow, this is so cool!” Everyone starts turning and laughing, and of course I agree with him, so we have a nice little exchange about that, and then we continue with the proof. Three lines later, a student in the front gets the idea of what’s coming, and she says out loud, “Wow, that’s amazing!” At this point, everyone is on the floor laughing. It took a full minute before we could even continue with the proof. And that right there — that’s what it’s about. The feeling people get when they really see what’s happening and how it works, and they think it’s amazing and have a great time doing it — that’s what I hope will stay with them.
What do your students teach you?
My students teach me about people. To teach a class like calculus well, you have to know the math, of course, but you also need to know about people: how they think, how they learn, what they might find interesting, what would motivate them. There’s not a lot of time spent on that in graduate programs in math, so that’s what I’ve been learning since, and I’m learning it from my students.
What advice would you give a Yale undergraduate about his or her time here?
Take time to get to know the people at Yale. They are smart and interesting, and it’s worth spending time with them. You never know what you will learn just by sitting down for lunch with your classmates or talking to your teachers. Go to office hours, get to know your instructors, see how they think and what they are like in real life. Being here is a wonderful opportunity to meet fascinating people, and my advice would be to take advantage of that.