Ask a mathematician

Inspired by Omi no Kami’s ask a linguist:

So I don’t know much about Stats, Physics, or computers. Heck, I don’t even know that much Math.

BUT. I am a PhD student in Math and have been for enough years that I feel qualified opening this thread.

I study Set theory, which is a branch of Logic, though I used to be interested in Combinatorics (who hasn’t?). Any questions? I would understand if not. Math isn’t all that exciting, really.

I don’t know if this is relevant, but I’ve also been a teaching assistant during most of my tenure as a grad student, TA-ing mostly Calculus.

Naturally, people such as Ultrafilter, Mathochist, etc are invited to answer questions, should they see fit.

Is it true that once you get past Calc I that there are no more TAs that speak English?

No, they do teach Calc 2 in Anglophone cultures.
Not just for Frenchies anymore!

Have you seen the movie Proof, and if so then what were your impressions?

Didn’t see the movie. Did see the play. I liked it, though of course the Math doesn’t really play an important role. What was she supposed to have proved? Something about primes <mumble>, <mumble>, if I recall correctly. Oh, and the dorky mathematician archetype does of course exist, but he wouldn’t dress as well as in the production I saw.

What the heck is Ito calculus and what is used for? What’s a layman’s explanation?

How far can you get into math and still have applications to, let’s say, physics?

(I had never heard of it before you asked, but I’ll try to answer anyway :slight_smile: )

From wikipedia (a surprisingly good site for math definitions):

“Itō calculus, named after Kiyoshi Itō, treats mathematical operations on stochastic processes. Its most important concept is the Itō stochastic integral.”

So that may not be very helpful, but follow me a moment. What is meant by the word “Calculus” in Mathematics? The same as in ordinary language, that is, a system or method of calculation. I could say that long division is a calculus. People say that utilitarians perform an “ethical calculus” to make decisions. The college courses usually called calculus refer to the calculus of Reimann integrals, that is, how to do calculations on and with them.

Now, from what I can figure from the wikipedia page, Itō calculus is a system of calculation for stochastic processes. What are stochastic processes?

Again from wikipedia:

"In the mathematics of probability, a stochastic process or random process is a process that can be described by a probability distribution.

The two most common types of stochastic processes are the time series, which has a time interval domain, and the random field, which has a domain over a region of space.

Familiar examples of processes modeled as stochastic time series include stock market and exchange rate fluctuations, signals such as speech, audio and video - medical data such as a patient’s EKG, EEG, blood pressure or temperature; and random movement such as Brownian motion or random walks. Examples of random fields include static images, random terrain (landscapes), or composition variations of an inhomogeneous material."
This seems to answer the “what is it used for”, no?

It’s a little tough to explain, but very roughly speaking, Ito calculus is a set of techniques for dealing with variables whose values change randomly over time. I’m mostly familiar with its use to model stock and bond prices, but I know that it also has applications in cell biology.

It’s not a question of how far you go so much as what you specialize in. You can spend an entire lifetime studying math that’s relevant to physics, or you can go into set theory like Jamaika and never touch physics again. To the best of my knowledge, only the very cutting edge mathematical research doesn’t have applications to some science, and that’s mainly because it hasn’t been around long enough.

Certainly this depends on which field of math you get into. I don’t think Set Theory has any applications in Physics, whereas Mathematical Physics…

There seems to be a common misconception embedded in your question (and if not, I apologise, but let me take this opportunity to address it anyway). Many people assume that the study of math is linear. This is because high schools all have the same linear math syllabus, and for most college students, the only math classes they encounter are called Precalculus, and Calculus I, II, III. (A friend was once asked by a student what the highest calculus he got to was.) On the other hand, I could imagine a reasonable math major syllabus which doesn’t involve any of those classes. (I , for one, never took the following classes: Multivariable Calculus, Differentiable Equations, Linear Algebra. I picked up Linear Algebra along the way, and I first learned Multivariable Calculus when I TA-ed it :eek: )

Oh, and just so you know what I really think:

(From English with an Accent, by Rosina Lippi-Green (p126-7):slight_smile:

"In that study of how expectations built around accent and race affected student perceptions and performance, sixty-two undergraduate native speakers of English participated. Each undergraduate listened to a four minute lecture on an introductory topic, prerecorded on tape. There were two possible lectures, one on a science topic and the other on a humanities topic. While listening, the students saw a projected slide photograph which was meant to represent the instructor speaking. Both of the recordings heard were made by the same speaker (a native speaker of English from central Ohio), but there were two possible projected photographs: half of the students saw a slide of a Caucasian woman lecturer, and the other half saw a woman similarly dressed and of the same size and hair style, but who was Asian. Both were photographed in the same setting and in the same pose, and in fact no difference was registered between the Caucasian and Asian photographs in terms of physical attractiveness.

“Immediately after listening to the four-minute lecture, each student completed a test of listening comprehension, and then a testing procedure which was designed to test homophily, which in effect asks the respondents to compare the person speaking to themselves and to judge the degree of similarity or difference. This measurement has been found to be very useful in studying communicative breakdown accross cultural boundaries. […] There were other items included in this questionnaire which asked the students to rate accent (speaks with an American accent … speaks with an Asian accent), ethnicity, and quality of teaching.
Depending on the slide projected, the students evaluated the same native speaker of US English as having more or less of a foreign accent. To put it more bluntly, some students who saw an Asian were incapable of hearing objectively. It can be stated with absolute certainty that the prerecorded language they listened to was native, non-foreign-accented English; students looking at an Asian face, however, sometimes convinced themselves that they heard an accent. Here it becomes clear that the students’ negative perceptions are at work.”

The relevant study is:

Rubin, D. L. (1992) “Nonlanguage factors affecting undergraduates’ judgementsof nonnative English-speaking teaching assistants.” Research in Higher Education 33(4):511-531
This doesn’t account for all miscommunication, of course, but I take students’ complaints about foreign professors with a grain of salt.

I’m less concerned with what the TA says to the class verbally, as if necessary he can write it on the board and I can understand it that way (especially in math courses). What worries me is when students ask a question and the TA is unable to answer it because he can’t understand what we are asking.

If I may, I’d also like to ask a more serious question:

What is the hardest concept in mathematics that you’ve had to internalize to get where you are now? Did you have some sort of revelation when you finally comprehended it, or was it more of a gradual enlightenment?

I have been wanting to ask this for a while.

I was once in a PhD program in Behavioral Neuroscience. I busted my ass in animal research. We often had to give injections to dozens of rats on a schedule (like every 3 hours) around the clock 24/7. We also had to do loads of animal surgeries and animal sacrafices. That was just the prelude to the experiments. The experiments required all kinds of behavioral watching and recording every single day.

I assume that you don’t have any lab work. What does research mean for you and what do you do with all that free time?

This doesn’t necessarily have to worry you. You have two ways to respond to a situation like this, IMHO.

  1. The TA can’t speak English
  2. The TA and I are having trouble communicating.

Guess which mindset get more learning done? When I was an undergrad, I had a TA for a Physics lab whose English was terrible. However, instead of throwing up our hands, we (the class) doubled our efforts to communicate, explaining words he didn’t know, repeating things slowly and enunciating carefully, and by the second lab found out that he really was a great TA, and I eventually learned much in that lab.

Of course some people are terrible TAs/teachers/professors/human beings :wink:

Now, I know that some people’s language skills really can be prohibitive to teaching. My above post was meant to assert that communication is a two way street, and that the rumor that foreign TAs in general “don’t speak English” is exaggerated. Heck, my students have complained to me about various professors I have TAed for. Then I went to talk to the professor, and they seemed to speak English just fine.

This is a really cool question. For many mathematicians, things you currently understand are “easy” while things you don’t are “hard.”

But seriously, I think Set Theoretic Forcing fits the bill. I gradually understood more parts of it as time went on. When I was teaching it to someone else years after I first saw it, it was as if light bulbs were going off with each explanation I gave. If you try to explain a mathematical concept to someone else, you will see what I mean. All of a sudden you seem to really grok it.

So was Venn obsessed by Mickey Mouse, or what?

If not, why do all of his diagrams look like the start of a Mickey Mouse front view? Why no square or triangle diagrams?

Yeah, I have a friend in Oceanography that drills stalagmites (stalagtites?) for many hours each weekday. Right now, I am sitting at home in my underwear putzing around the internet. This afternoon, I may go see some cherry trees in bloom. I also read a lot of novels.

I should be thinking about Math, reading Math, and writing Math more often than I do.

Well, Venn did die 5 years before Steamboat Willie.

According to the wikipedia page on Venn Diagrams, he liked symmetrical figures.

That brings me to the flip side of that. In the natual and more biological sciences, you can write a dissertation based on experiments that didn’t really break any significant ground. It isn’t great but at least you put in the effort related above and maybe became a good researcher anyway.

How do you fake it in math? What if you get bogged down in a field where there isn’t anything obvious to do at the moment? What if the remaining problems are so difficult that normal students can’t solve them? What do math graduate students at crappy schools do?