Math and Computers

What kinds of software do you use? Why?

Mathematica: I just renewed my license for Mathematica through the college I've been working at. It's the best option for creating figures for multivariable and single-variable calc exams, multiplying matrices in a pinch, integrating things to check my answers. I've also done some checks of calculations in research with Mathematica because of the easy entry of polynomials and functions on polynomials.

GAP (Groups, algorithms, programming): Haven't used this in years. Do I vaguely remember that some of my groupy and number-theory-y friends used this?


Magma: I used this years ago in graduate school because they had a license and I was doing some number theory. It is not free. The people I know who do a lot with computer algebra systems all use other programs, so I have not felt the need to buy it. Why is that, though? There seem to be many citations of the program in areas I'm interested in. Is there some geographic clustering of users?

Sage: I know many people who use Sage! It is trying to become the great repository of everything. It's open source and user supported. One of my summer goals is to learn more about Sage and write a few packages that I'd find useful... Even if you don't want to download Sage, you can try it online through their web interface.

Macaulay2: While Macaulay2 is narrower in scope than Sage, it's the program I use the most. I found it to have a steeper learning curve for programming than some languages and I don't know enough about computer science to know why. After a week of working with it I could write crappy programs in M2. After some time brushing up on my general programming skills I could write somewhat better programs. The documentation can be a bit spotty but the folks who are community experts in M2 are very nice and helpful.

Pari/GP: Available as a C library or a computer algebra system and designed for fast computations in number theory. I used it way back when I was still studying number theory but haven't touched it in years. I have a fond memory of it, I suppose.

CoCoA is also a program for computations in commutative algebra, etc., and I found it very very easy to learn to use. I was going to say that I don't think it's actively maintained anymore -- but I guess I'm wrong! A new version was put out just this April! Maybe I will check it out again.

My computer usage goes in waves. I can spend weeks or months never using a computer to do a calculation beyond division (I'm not great at mental division). Then I can decide that I want to do a cohomological computation using the computer and spend a week and a half figuring out how to make it work and checking a bunch of examples. I am no computer expert, just someone who wants to automate certain calculations. I use these calculations for both hypothesis generation and hypothesis testing.

Motivation

To do list:

• email editor about that article I submitted a loooooong time ago
• get two articles out the door involving recent work (small things, but still)
• work on material for meeting tomorrow with collaborators
• finish writing proof for other project
• start reading up on my new area of interest

What do I want to do? Only the last one. New and shiny!!

I don't know why I don't want to do the first two; usually I'm all about the editing.

In the past I have bribed myself into tasks like this with pastries. If I am trying to cut sugar and white flour out of my diet for digestive and health reasons, this pastry does not fit. Cocktails? No... too expensive (and not good for 9 am start). Difficult decisions here!

Freedom

Sitting in a cafe listening to Euro-trance, getting that last bit of grading done... one assignment to go. Let things go later than I usually do in order to decompress and give a bit of grace to one troubled black sheep of a student who might maybe not fail this class now that he got his last assignment in. I am a sucker.

It is so odd to sleep enough, wake up in the morning without the kick of adrenaline that usually greeted me during the school year. I don't know why I get so physical about my job or why I store up stress in my body. I have read a lot about cognitive behavioral therapy and can talk myself out of all kinds of fears (putting my head underwater, eating wierdo foods, trying scary physical adventures) but I can't talk myself out of making my stress incarnate. I also can't quite talk myself out of the stress. I think I am just an introvert on a very physical level: I am so happy being alone about 8 hours a day! Add in four hours of talking over dinner or math tea or Skype and I'm peachy.

So now it's summer. I started this blog because I was stressed out about the job search and my apparent imminent unemployment. I've strung together a few things for next year but am still occupied with the task of moving out of my office and saying goodbye to current colleagues. I have worked with a great department and will miss my colleagues. Right now I'm close enough to the 60-hour workweeks and emotional stress of trying to connect honestly and deeply with students that I don't miss that yet.

(Caretakers are the folks who are most likely to get burned out by their jobs. How do nurses or ministers do it year-round? At least for nurses, there is not less paperwork than I have!)

Since I haven't been done for very long I have not demanded much of myself in terms of research. I have slept a lot, got some paper revisions back to a journal. I need to do some more paperwork for the college before I can consider myself done and return some books. I am starting work with a summer research student (am I a fool?) this coming week. I need to set summer priorities and schedules. Two projects close to completion need to get out the door. I suppose that will be my first main priority..... so much to do!

But I feel free, like I have room to move. Thank goodness.

Conversations

During finals I noticed again a phenomenon that prompts some new ideas (for me) about gender and math. The final exam is a multi-hour affair and students are allowed to ask questions during the final. I often talk with them out in the hallway about problems. At my SLAC students ask many many questions during exams; this was not true at the big R1 I was at for graduate school.


At the SLAC I have often ended up with a young woman frustrated and sometimes near tears who is asking questions about, say, optimization. They are not usually asking about a typographical error or the meaning of the question. Often the student is stuck and "knows what to do" but can't figure out how to do it. I've had so many of these conversations by now that I have a set of stock phrases. Conversations go like this:

Student: "I'm really stuck on this question about optimization."

me: "Talk me through your work so far."

Student: "Well, I have, like, an equation... for... volume..."

me: "Yes?"

Student: "Oh, I forgot (blank) in the formula..." (writing)

me: "Ok? What's next?" (regardless of correctness)

Student: "And then I was trying to put in my constraint... but then I got stuck differentiating..."

me: "Where did you get stuck?"

Student: "Right here.... oh, I see, I need to simplify..." (writes down correct derivative)

me: "Ok? What's next?"

Student: "And then I have to (set derivative function to zero, solve for critical points, use one of various tests to show it's max or min, find dimensions of whatever)."

And then the student writes down the entire correct solution. I didn't say anything but "Yes?", "Ok?", "What's your next step?", "Write things down!", or "Keep talking!"

I hardly ever have this conversation with male students, but with female students it happens at least once per final (sometimes more). I asked one student this year about what was happening in her head as she talked through it, and she said, "It just makes more sense if I can talk out loud about it!"

I am by no means an essentialist: I think most notions of what is "essentially female" or "essentially male" are bullshit. (There are some clear physical differences like the ability to bear children, but even notions of men being stronger than women are obscured by a culture that prizes slender women with little muscle tone. Look at the survey results.) Our cultural baggage obscures any subtle underlying genetic whatever, and epigenetics is changing our whole notion of how genetics impacts life anyway. Given all that, by college we've got to work with what our culture has wrought. My female students seem to really need that processing of mathematics through conversation. I enjoy it myself and am really benefiting from my conversations. I did not have so many of these conversations in graduate school because of a need to not look stupid in front of R1 professors so they would not think poorly of me. Now I figure I've succeeded (gotten a PhD) and failed (gone to a teaching school) and so it doesn't matter anymore!

We got the f(*&ing guns...

Another big secret: I don't give a s$&^ about grades!

I suppose I'd better explain for those sensitive and responsible undergraduates out there. It is the end of the semester and I am putting up grades. I am dealing with late homework (didn't you read that syllabus that says no late homework, and why do you think you're exempt?). I am fielding all the inquiries about last-minute saves. People care so, so much about that grade. But doing all the homework after the semester is over is pointless, don't you think?


Well, no, because my students are focused on the letter that turns up at the end of each line on the main section of the transcript. That's natural, because college selects for people with that focus: such people are more successful in the college application process. It's fostered in high school and emphasized by parents. Why would freshmen think at all differently?

I think differently. Let's use the dreaded sports analogy. To me, your grade is a measure of one aspect of your competence just like the number of pull-ups you can do right this instant is a measure of one aspect of your competence. Maybe you're weak, maybe you're strong, maybe you've got a broken arm, whatever. It's not a moral judgement, it's a measure. You can do some pull-ups or you can't.

You may decide that it's important for you to be able to do more: you're after general fitness or you feel it's a badge of honor or you want to improve your gymnastics or pass some PT exam or you want to be able to save yourself at that pivotal moment when you've just slipped off the edge of a skyscraper in your epic battle with evil but you've caught the edge with your fingers and could pull yourself up... if you had the strength. Or maybe you're just interested in challenging yourself.

So you start training your pull-ups. And then, after some work, you can do more.

No one argues they should pass the PT exam because they worked really hard. They just work to get the number.

Pretty simple. And that's what your calculus grade reflects as well: how well you can do calculus and convey your understanding of it at certain moments in time. I repeat: it's not a moral judgement. It's also not a measure of how much I like you or your future success. It's pretty irrelevant, in fact, to both of those.

Either the material is important or not. You're learning how to think, you're learning something to help you in economics or chemistry, you're learning computational skills, you're learning about the history of intellectual achievement in mathematics -- or you are wasting your time.

If you're fully engaging in this process of learning, communicating, and challenging yourself, you'll get something out of it (and often your grade will be alright as well). This is what life is about, challenge and exploration. Whether you're engaging is actually a better measure of your future success than your grade.

If you're ignoring it, I'll only respect you if you're doing something more interesting and not whining about the consequences at the end.

Codes

In the play "Truth Values" the protagonist ends up dressing "inappropriately" in math grad school as a way of... mmm... acting out? Showing independence? Differentiating herself from others?

My husband once went to an AMS regional meeting and pronounced it a markedly unattractive group of people.

In graduate school I generally wore jeans and t-shirts and sweatshirts. Don't want to stand out.

In undergrad that really was driven home for me, as when you wear a dress at an engineering school all the guys ask, "Hey, is it laundry day?"

My current department seems to have a different code. There are a few more people who had a corporate life, even if only briefly, and so there are blazers now and then and business casual pants and the occasional real suit or even a woman who looks like an Ann Taylor ad. No, I'm not monetizing the blog yet... although their triacetate pants really do last forever (I have a pair that is going on ten years old).

MAA conference attendees are less gray than AMS conference attendees: more likely to wear colors or even ruffles. Maybe it's because there are more women and the women don't feel this American pressure to wear drab colors and a backpack. 

In Portugal and France mathematicians are orders of magnitude more fashionable than in the US. Why is that?


I do try to dress like a professor is "supposed to" look in some freshman's warped view of reality, at least at the beginning of the semester. I am small and female and relatively young-looking at this point. Haha. A student in the library was astounded just a few weeks ago that I got the long check-out period for books -- she said she thought I was a student. This means I can't wear that grad-school uniform of jeans, holey sweatshirt, and Chacos. Looking poorer and scruffier than my students... mmm, just can't do it. But it's rather an experiment to figure out what looks adult without looking matronly or frumpy. Why does it matter anyway? There are plenty of normal fashionable things I don't do because it seems like an absolute waste of time (shaping my eyebrows?). Why do I even care if I look matronly? Maybe if I was more immersed in the mathematical tribe rather than living among the art historians and French professors of a SLAC I wouldn't notice so much.

The conference ramble

One wonderful aspect of the week-long math conference in Europe, in particular, is that while Monday, Tuesday, Thursday, and Friday are entire days of lectures, Wednesday often includes the afternoon hike. Germans especially seem to love the hike, and they have convinced me! The afternoon hike gets the whole group out of chairs and into nature. The group rambles along at a relaxed pace (except for the overachievers at the front) chatting about math, not-math, and everything in between.

It's important to give the brain a little break so that it can do its unconscious work of solidifying connections and giving rise to new ideas.

A walk in the woods has also been shown to increase the capacity to focus. It's as effective as drug therapy for some children with ADD/ADHD.

You get to meet people you may not have talked to otherwise as the group stratifies by walking speed and style.

You get to see the place you're visiting in a new way, as well. I went to Boston for the Joint Math Meetings last January. Boston for the first time... and I saw essentially none of it, for there was no conference ramble. Between interviews and talks and panel discussions I never made it farther away from the hotel than the wonderful Indian restaurants two blocks away one direction and the Charles river. I saw MIT from a distance...

By contrast, on a visit to Oberwolfach I got to meet a goat!

"Break"

My summer is indeed busy. I will be home and non-conferencing for 17 non-weekend days between June 1 and August 31. Perhaps that explains the frisson of apprehension that accompanies the excitement.

I get a little oversensitive when talking to non-academics about the summer. Many believe that it is a vacation. It is in some ways -- I am not lecturing or preparing class syllabi (until August if I'm teaching in the fall). I do get some flexibility in location. But there is a fair bit of pressure to write and research and publish -- Lord knows that at a small liberal arts college that stuff doesn't happen during the academic year yet it's a significant portion of what goes into tenure and promotion decisions.

I don't have to worry about that, though, since I don't have a tenure-track job -- isn't that great?! Well, no; I won't get that tenure-track job if I don't do those things. When I'm being an honest Debbie Downer I say things like, "Sure, it's a vacation if I want to end up unemployed next year! Hahahah!" Responses like this start to step outside the bounds of polite conversation. People don't really want to hear about that -- they want to imagine that I'll spend the summer gardening. That justifies the low pay.

 So, summer. Fewer deadlines. More flexibility. The freedom to concentrate on things I choose rather than reacting to crises and requests from higher-ups in the academic tribe. Some pressure to perform. I do need to give myself a real vacation; the unrelenting knowledge that I could be doing something "useful" is not conducive to real creativity. I will certainly get more sleep at home and therefore be smarter. At conferences, I'll get less sleep and immerse myself entirely into mathematical endeavors like Frederick the mouse soaking up colors for winter.

Outlook

As you might be able to tell from my last post, I'm in an emotional hole. Teaching is hard for introverts and managing the unmanageable is hard for people who like to be competent and in control. Buddhist philosophy counsels nonattachment, simply letting go. Taoist philosophy counsels staying true to your own nature and finding a course through the world that is in harmony with one's own nature and one's surroundings. These currently seem like different paths. Am I to simply let go of my frustrations or change my environment?

It's a moot point anyway. Teaching winds up soon and final exams begin. After grades are calculated and turned in (yes, students, simply calculated -- not given), I am (almost) on "summer break." Next fall I am headed to a different institution, and after that, somewhere else. A peripatetic academic lifestyle, not the one I intended. One which I fought against, in fact, but that's the job market these days: travel or unemployment!

This summer, too, I get to do some travel. I have three conferences and some other trips lined up. Given my recent week I was not seeing the joy involved in 36-hour journeys to exotic locales. Talking with my grandparents on Mother's Day brought back some of the wonder -- they seemed pretty excited about my academic travel. I get to go to interesting locations with some funding help from others and talk about things I love! Thank you, grandparents, for restoring some of my perspective and excitement! It won't all be grading this summer.

In fact, I have two research projects with students very close to completion and two research projects with professional mathematicians making great and intriguing progress. When I think about this summer and the chances I'll have to talk with people (and read all those papers I keep intending to read...) I do feel the stirrings of a battered passion. I am really excited to make progress on these questions, the questions that lead me to talk to myself on the walk back home from the coffeeshop and thus make me look like a crazy lady (more neatly dressed than the archetypal homeless crazy cat lady, but only just). I can't wait to spend all day mulling over them and caffeinating, traipsing from tea shop to coffeeshop to collaborator's office to the back porch. I'm going to read so much and write so much and learn so much and ...!

It is nice to have something to look forward to.

Somatizing

Apologies for the blog break to anyone who actually reads regularly. I had to take time for gastrointestinal distress, two days of migraines, one sleepless night, one evening of uncontrolled crying, and the usual teaching/grading/conversing but unfortunately no research.

It is the end of the semester and plenty is going on. We're not done yet. The department had several large events in the last week or two. The event I was most involved with was of course a team effort, but a lot of the responsibility had been put on my desk as the most junior female. Most of my colleagues were quite helpful and came through when I needed help. The senior colleague who'd initiated the event was not helpful. I got yelled at and told my request for help was unimportant, in front of a student. Sigh. This is why I'm pseudonymous -- who else am I going to talk to about this? Nothing much can be done.

It's Friday. Students are restive. They have tons of work to do and they are freaking out. I also have tons of work to do, but I am not freaking out anymore. Grade 200 pieces of homework in an afternoon? Sure, whatever. At this point in the semester it's going to be graded for completion.

I feel like I've been a somewhat crappy professor this semester -- not up to my usual standards. I still got nominated for outstanding professor by a student group I care about. That makes me feel a bit better.

Grading, editing, organizing the gradebooks and Excel files.... that's my coming weekend.

Juggling 2: How do you learn new math?

How do you start on problems that require learning the basics of another mathematical field? All I know how to do is read. I read the papers I'd like to understand, I follow back through the bibliographies, I try to get back to the basics in the field. Sometimes that is not so easy, as there is no basic introduction. Talking to people seems to be a very effective way to learn the basics of another area of mathematics, but this requires finding a person who knows what you want to know and who is willing and able to explain these things.  I have had particular difficulty with this when I've seen some words that make me think that the ideas from another area might help me out but I'm unable to formulate a good question. "Tell me about how combinatorics might help me with my PDE problem" is awfully vague.

Collaborators are also phenomenally useful in this regard: they are usually people who like you and respect you at least a little bit, so you can ask questions without feeling terribly stupid. I have collaborators with complementary expertise and really enjoy learning from them.

Looking forward to summer -- I have an immense pile of reading I'd like to get to.............