Juggling

Old post (written as I finished my dissertation): With apologies to mathematicians who actually juggle, I am wondering about how people maintain multiple mathematical projects. There are a lot of questions I'm interested in. While some stay in my narrow field of mathematics and are continuations of dissertation questions, others veer into related areas, with contributions from as far afield as combinatorics and PDE.

How many projects are you comfortable with at once? Given the time needed for teaching, service, and administrivia, how many problems do you like to have in active rotation? I am reaching for three. I find that I get very wrapped up in one problem at a time and have an extremely hard time pulling my head out of it to look at another, even if they are closely related. My mind always wants to go back to the one it's spent the most time on recently. I have a little file of questions and I've got six at the top, which means I am keeping my eyes open for papers that apply and people who might be able to help out. I read somewhere that Conway liked six. Maybe over time I will be able to switch more easily from one problem to another and make steady progress on several...

Do you like to have different problems in various stages? Some folks seem to like having a problem they're just starting to think about, a problem that they're making active progress on, one they're writing up. Do you aim to have a range like this? Does it work? How do you do it? I guess right now, by default, I have some things I'm wrapping up (dissertation) and some projects I'm starting.

On a related note, I am getting some advice from my advisor (if I understand correctly) that I should not be spending much time starting different things right now --- I ought to concentrate solely on finishing. If anyone has any first-hand advice they'd like to share, I'd be eager to hear it!


New commentary (after time as something approximating a real professor): These days I am fairly comfortable having three or four projects in the air at once. I only manage this because they are closely related. I really have more projects, but I am not making any progress at all on a few of them -- it seems like the ones left behind are mathematically different than the others. I also manage the projects that are progressing through collaboration. That makes it a social affair and something that must be scheduled into my daily calendar. When a student emails to ask about time to meet outside of office hours it is easy to say, "Oh, I guess I could reschedule my research time and talk to you about calculus instead"........ unless you've got a Skype date with someone across the country!

Small weekly goals and discussions help me move forward with multiple projects even if I can't devote hours a day to anything. Just keeping my head in a problem on a daily basis is pretty important. Being an overworked participant in the American liberal arts system has pushed me to learn this.

On that note.... I need to escape my office as I have a whole free hour. Time to do some research!

Changing of the example -- systemic constraints

This post is in response to this post by the famed FSP, whose blog you should check out.

I've mentioned in earlier posts that I do change what I talk about when I teach calculus at the SLAC which currently employs me. My calc classes have fewer than 25 students each, and I do know everyone's name and something about what interests most of them.

Calculus is a subject that seems timeless. For better or worse, I don't keep notes on teaching from year to year: I don't have lecture notes, a ton of worksheets to recycle, problems I particularly liked. I kind of wing it each year (although I do remember tips and tricks from past years). I don't know if I should admit that.

I change the syllabus with the textbook required by the subprogram of the institution for which the calculus class is being taught. For instance, at the big R1 at which I did my graduate work, I taught versions of calc for three different programs. It is easiest for me to go with the textbook rather than being proudly focused on the best teaching/best order/best anything.  

Within that framework I change the focus of the class considerably from class to class based on the interests of the students. Today we worked on optimization. We optimized the happiness of a pig as a function of corncobs eaten; my students this year seem big on economics but like maximizing happiness and minimizing poverty more than maximizing profits. Last year, as I mentioned, it was chemists. We looked at reaction rates and maximized reaction rate or concentration of particular reactants. I am happy to skip from application to application based on student interest -- it keeps me interested as well.

In introductory classes like this that have strong demands for content coverage by other departments it is really hard to radically change the syllabus. If I switched to an inquiry-based learning model the physics department would go nuts. If I changed to an applications-focused model of the course not vetted by the biologists they'd riot. If I started focusing on proofs the chemists might have heart attacks. Non-mathematicians have some strong feelings about what a first-year calculus ought to cover and how (if they feel that mathematics is useful for anyone at all!).

Are you really going to get a SLAC job? Some questions for grad students

Many mathematics graduate students focus on the thesis and don't learn a ton about what to do afterward. What will they do next?

In case you haven't noticed, the job market has been sh*tty for a while. For several years state funding cuts and dramatic losses in private endowments curtailed hiring. Now hiring is rebounding a bit, but people who took any job they could to stay in the game three years ago are looking to move up. Postdocs at research schools are still vulnerable to budget game-playing. The number of tenure-track positions has been declining steadily for years while the armies of contingent labor grow... just want to warn you all not to expect a smooth sail.

If you're geographically limited, the market gets even tougher because your competition pool remains international but you're not looking at as many colleges or universities. Good luck.

Many graduate students (or their silly advisors) look to jobs at small liberal arts colleges (SLACs) as a fallback from the research life that one should of course want. This is quite foolish: jobs at many SLACs are quite competitive. Not only do SLACs want people with a particular outlook and kind of preparation, but they now have a huge pool of very qualified applicants and they can afford to be picky. In general, the more prestigious the graduate school, the less likely a grad student is competitive for a tenure-track SLAC job. Why?

* Did you teach more than two classes a semester and show you could balance teaching with research?
* Did you ever teach your own classes, setting the syllabus, assigning homework, writing exams, and grading some chunk of this?
* Have you shown you looove undergrads through math club activities, outreach, or mentoring?
* Were you involved in innovations in pedagogy? Do you have experience teaching with technology, teaching through group work, teaching through inquiry, running a senior capstone course, teaching a writing course focused on proof? Can you talk about these experiences intelligently?
* Have you done any service work at your university or in the larger mathematical community?

Sure, none of these things are really prerequisites for the tenure-track job -- you'll get to do all of them eventually. You may turn out to be a stellar teacher who can balance teaching, service, a bit of research focusing on undergraduates, and Pi Day baking. That's not the point. The point is that you're competing against people who have done these things. Done them. They had nice postdocs in 2008 because they graduated in 2006, and in 2009 they took so-so tenure-track jobs, and now that the economy is easing they want to move on. It's easier to go with the sure bet and the extensive track record if you're hiring -- and who would blame the hiring committee for that?

Grad students: my list of questions above is not complete. If you want a SLAC job, read that list and add your own questions. A SLAC job is something to prepare for, not something to fall back on.

Teaching three-three

One of my motivations for blogging is that by reading the blogs of others I get a glimpse into what life might be like (for real) for people in very different situations than mine. This post, on teaching three-three, is one of those posts for other people.

Teaching: I teach every day of the week other than Saturday and Sunday. I teach calculus, of course, and another class. Two of these are MWF and one is TTh. At my school, it is expected that I learn every student's name and hopefully something about them as people. It is also expected that I teach excellently, using either lecture or more "reform"-style teaching methods.

Hours with students: It is requested/required that I have between 4 and 5 office hours a week, distributed over four different days. I do that. I also have meetings with students by appointment. Many weeks, I actually do spend up to nine hours with students outside of class. This does not count my independent study students (oh, did I mention that I'm overseeing some independent studies on topics not covered at my small college?) or my undergraduate research students.

In addition to math questions, I do have a few students who seek me out for conversation, relaxation, and life advice. Interestingly, most of them are not math majors :) This also takes some time, but is usually quite rewarding -- I think these are very interesting and talented people, and sometimes we go for coffee or ice cream rather than sitting in my office.

Research: I try to follow the advice of Robert Boice and work in small daily chunks. I have managed to maintain some research projects using this method. I also like to work with collaborators, as it is fun and they can sometimes keep a project going even if I have to stop for a week. I still don't have a lot of papers, though.

Service: Right now, the department is very busy with some administrative adventures. I attend between 2 and 4 hours a week of meetings. In general, the department does not waste much time or spend meeting time on stupid stuff. Meetings do take time though.

Grading: I have an undergraduate grader, but I do need to grade all exams. I love having an undergraduate grader.

Class prep: Fortunately, I have taught calculus for six or seven years before this. I think about how to present concepts for these classes -- these people -- but I do not have to spend much time relearning integration by parts. I spend time assigning homework problems, thinking about what students should get out of the class, thinking about how to deal with the poor preparation some students are coming in with, and figuring out pacing of the classes whether using worksheets or lecturing. I also spend time trying to come up with new examples or activities that relate directly to the interests students in these classes have. Last semester: chemists all over the place. Reaction rates. This semester: economists, dance majors, and social justice advocates. Different activities.

Service: I work on inviting speakers, scheduling and funding mathematical/cultural events, and organizing workshops on technology that the department would be interested in using. I'm also involved in some regional and national activities.

Undergraduate research: have two undergrads working on a project related to my research. Hopefully they spent all spring break revising the paper we are writing together! I have spent up to three hours a week with these students, although our arrangement is quite informal and some weeks we spend no time together at all.

I certainly did spend my 60 hours a week on this job for a long time. Now I'm not quite sure -- is it 55? Sixty certainly made me very tired, and I am not sure it's sustainable. Of course, last year was my first year, and this is only my second. I hear that some of these things get easier to do -- but then you get more responsibilities.

Introduction

Old post #1:

I've decided it's time that the internet get a blog about life in math. Not about math itself -- I'd love to do that someday, but I worry that I would not be able to produce posts regularly. Besides, that's already covered by blogs like the Secret Blogging Seminar, Terry Tao's blog, and a host of other great sites. No, I want to talk about doing math, living in our little mathematical subculture, dealing with our wonderful fellow mathematicians... all the things blogging scientists talk about without the lab and reagent chatter. Life in mathematics is different than life in the bio-sciences, engineering, or even physics. Maybe it deserves its own forum.

If you have topics for discussion just email me!

I am just finishing up my dissertation and starting a postdoc with a good dose of teaching, and hope to grow an independent research agenda over the next few years. I would like to remain pseudonymous while I feel things out. Since this is not a math research blog but a "soft questions" blog, that ought to be ok. (I borrowed the name from the tag on mathoverflow.net.)

Update: I've been in that postdoc now for a while. The rest is still accurate. Next post: a candid look at teaching three-three for graduate students who might be interested.

Soft Question 1: what do I like?

I am sitting in a local cafe, in which I wrote four posts for this blog last summer. I never did publish them. I was flush with possibility and eagerness -- big ideas. Some of these great ideas came to pass and others didn't. It's interesting to look back at the ideas and the feelings from a new perspective, the perspective of the person who didn't get the tenure-track position this year.

Some background: I'm picky. I'm in a discipline straddling the liberal arts and the sciences. I am passionate about research, and when I'm interested in students, I'm passionate about them as well. I love bringing the experience of research to undergraduates and others. I get bored talking about the same old thing, telling the same old story. I am surprised to learn how attracted to the new and shiny I am: I like to dress in muted colors with no prints and I'm rather conservative in my behavior. I thought I wouldn't mind teaching intro classes but unless I make them new through my students they kill my soul. My strengths are my weaknesses, and vice versa.

Finished lunch; reading career sites and articles on leaving academia. Brushing up on my programming skills. This is a flow activity: I get pulled into it and don't mind seeing the hours pass.

Time to bike to the university soon for a seminar and chat with colleagues. Soft question 1: what do I like? Solving problems (not puzzles -- I hate those stupid trick math problems). Soft question 2: what am I going to do about it?