My professor goes through a proof during lecture that requires the definition of a convex combination.

**Situation A: BSM, Game Theory Classroom:**

He sees our blank stares and says, “What? Weren’t you required to take matrix algebras before you came here? Don’t you know what a convex set is?”

A number of students pull out theirs phones to look the term up as he proceeds with the lecture. We all receive an email later that day with the subject title “READ” and a link to an explanation of convex combinations that everyone *will* know before the next lecture.

**Situation B: Smith College: Optimization Class:**

She sees our blank stares and asks if anyone knows what a convex combination is. I’m the only one who raises her hand (thank you, Game Theory Professor).

The lecture stops and a full-out definition of convex combinations begins, complete with diagrams of geometric convex sets and explanations of the necessary set notations. We don’t finish the planned lecture for the day.

I find the two versions of this situation quite representative of the difference between my Hungarian mathematics experience and my liberal arts mathematics experience. Honestly, I’m not sure which I prefer anymore.

On the one hand, it was very easy to get lost in lecture at BSM (e.g.: you just missed everything that was happening when you looked up the definition of convex combinations on your phone), but my current math lectures are so slow in comparison. People ask SO. MANY. QUESTIONS. Like, people ask questions about other people’s questions.

In Hungary, the professor might *actually *tell you that your question is too basic and needs to be talked about after lecture. And we covered so much more ground because of it. But… we covered so much more ground because you never fully understand everything that was being taught.

I can’t say that one mathematics experience is BETTER than another; they serve different purposes.

Although I’m definitely missing my Hungarian mathematics very much right now.

Also, snow. So much snow. :o

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I had a teacher for several analysis-related courses who was outstanding at beginning every lecture with the definitions of terms he thought most likely to be unfamiliar (generally, the things we’d learned just in the past couple class days). And he’d leave them up on a corner of the board for as long as possible. I admired his skill in anticipating what his students were most likely to find confusing and I’ve tried imitating that when lecturing.

Of course it’s impossible to guess everything that might confuse people, but supposing that someone might not know a ‘Sobolev space’ after seeing it for the first time last Thursday is a fair bet.