Tag Archives: research

The semester in review

Plot of the vector field f(x,y) = (-y,x).

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I’ve made it to the end of another semester. Classes ended on Friday, and we have final exams this coming week. It’s been a long and full semester, as you can see by the relative lack of posting going on here since around October. How did things go?

Well, first of all I had a record course load this time around — four different courses, one of which was the MATLAB course that was brand new and outside my main discipline; plus an independent study that was more like an undergraduate research project, and so it required almost as much prep time from me as a regular course.

The Functions and Models class (formerly known as Pre-calculus) has been one of my favorites to teach here, and this class was no exception. We do precalculus a bit differently here, focusing on using functions as data modeling tools, so the main meat of the course is simply looking at data and asking, Are the data linear? If not, are they best fit by a logarithmic, exponential, or power function? Or a polynomial? And what should be the degree of that polynomial? And so on. I enjoy this class because it’s primed for the kind of studio teaching that I’ve come to enjoy. I just bring in some data I’ve found, or which the students have collected, and we play with the data. And these are mainly students who, by virtue of having placed below calculus on our placement exam, have been used to a dry, lecture-oriented math environment, and it’s very cool to see them light up and have fun with math for a change. It was a small class (seven students) and we had fun and learned a lot.

The Calculus class was challenging, as you can tell from my boxplots posts (first post, second post). The grades in the class were nowhere near where I wanted them to be, nor for the students (I hope). I think every instructor is going to have a class every now and then where this happens, and the challenge is to find the lesson to learn and then learn them. If you read those two boxplots posts, you can see some of the lessons and information that I’ve gleaned, and in the fall when I teach two sections of this course there could be some significant changes with respect to getting more active work into the class and more passive work outside the class.

Linear Algebra was a delight. This year we increased the credit load of this class from three hours to four, and the extra hour a week has really transformed what we can do with the course. I had a big class of 15 students (that’s big for us), many of whom are as sharp as you’ll find among undergraduates, and all of whom possess a keen sense of humor and a strong work ethic that makes learning a difficult subject quite doable. I’ll be posting later about their application projects and poster session, which were both terrific.

Computer Tools for Problem Solving (aka the MATLAB course) was a tale of two halves of the semester. The first half of the semester was quite a struggle — against a relatively low comfort level around technology with the students and against the students’ expectations for my teaching. But I tried to listen to the students, giving them weekly questionnaires about how the class is going, and engaging in an ongoing dialogue about what we could be doing better. We made some changes to the course on the fly that didn’t dumb the course down but which made the learning objectives and expectations a lot clearer, and they responded extremely well. By the end of the course, I daresay they were having fun with MATLAB. And more importantly, I was receiving reports from my colleagues that those students were using MATLAB spontaneously to do tasks in those courses. That was the main goal of the course for me — get students to the point where they are comfortable and fluent enough with MATLAB that they’ll pull it up and use it effectively without being told to do so. There are some changes I need to make to next year’s offering of the course, but I’m glad to see that the students were able to come out of the course doing what I wanted them to do.

The independent study on finite fields and applications was quite a trip. Andrew Newman, the young man doing the study with me, is one of the brightest young mathematicians with whom I’ve worked in my whole career, and he took on the project with both hands from the very beginning. The idea was to read through parts of Mullen and Mummert to get basic background in finite field theory; then narrow down his reading to a particular application; then dive in deep to that application. Washington’s book on elliptic curves ended up being the primary text, though, and Andrew ended up studying elliptic curve cryptography and the Diffie-Hellman decision problem. Every independent study has a creative project requirement attached, and his was to implement the decision problem in Sage. He’s currently writing up a paper on his research and we hope to get it published in Mathematics Exchange. (Disclaimer: I’m on the editorial board of Math Exchange.) In the middle of the semester, Andrew found out that he’d been accepted into the summer REU on mathematical cryptology at Northern Kentucky University/University of Cincinnati, and he’ll be heading out there in a few weeks to study (probably) multivariate public-key systems for the summer. I’m extremely proud of Andrew and what he’s been able to do this semester — he certainly knows a lot more about finite fields and elliptic curve crypto than I do now.

In between all the teaching, here are some other things I was able to do:

  • Went to the ICTCM in Chicago and presented a couple of papers. Here’s the Prezi for the MATLAB course presentation. Both of those papers are currently being written up for publication in the conference proceedings.
  • Helped with hosting the Indiana MAA spring meetings at our place, and I finished up my three-year term as Student Activities Coordinator by putting together this year’s Indiana College Mathematics Competition.
  • Did a little consulting work, which I can’t really talk about thanks to the NDA I signed.
  • I got a new Macbook Pro thanks to my college’s generous technology grant system. Of course Apple refreshed the Macbook Pro lineup mere weeks later, but them’s the breaks.
  • I’m sure there’s more, but I’ve got finals on the brain right now.

In another post I’ll talk about what’s coming up for me this summer and look ahead to the fall.

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Filed under Abstract algebra, Calculus, Inverted classroom, Life in academia, Linear algebra, Math, MATLAB, Personal, Teaching, Vocation

Monday GTD moment: Scholarship and GTD

This is the third installment of Monday GTD Moment, where I take a post to blog about Getting Things Done and how it applies in an academic setting. If you’re unfamiliar with GTD, here’s a good overview, and make sure to read David Allen’s book that started it all.

Last week I wrote about grading and GTD. I noted that grading is kind of a poor fit in traditional GTD. A prof can grade anywhere, so the idea of contexts fits awkwardly; and grading “tasks” are usually projects, although we think of them as tasks and although the next actions contained in those projects are usually nothing more than smaller projects. GTD wasn’t really made for the academic profession, and so the staple activities of academics don’t often fit well.

Another area similar to grading in its relatively poor fit within the canonical GTD philosophy is research, or more generally scholarship. By “scholarship” I am including not only the usual pure research that most profs do (at least while they are getting their terminal degrees) but also any significant creative activity based on one’s expertise that contributes to a discipline or the application of a discipline. This is Boyer’s model of scholarship, and it is finding increasing purchase at colleges and universities all over. So, for example, an applied mathematician who contributes her skill by consulting “on the side” for some external project is scholarship; so would be research that she does on the teaching of applied mathematics or using her expertise to  do a math workshop with a bunch of elementary school kids.

Scholarship is hard for many reasons, perhaps the main one being that original creative work is amorphous. When I was working on my dissertation, the hardest aspect of that work was that at any given point in the process, although I could always measure how much work I’d done, I had no way to tell how much more work I needed to do, what course of action was really the best next action, or even if my previous work was going to remain or be wiped out by the discovery of a mistake or a more elegant and general theorem. It wasn’t like reading a book, where you knew not only how far you’d read but also how far you had left to go and which page was next, and you had a reasonable assurance that the pages you’d read wouldn’t disappear from the book once you’d read them.

Even now, I have all these scholarly projects I want to finish (or start), and I struggle to GTD-ize them. For example, I’m currently working through this book on probability as a self-study course. Some parts of this project are pretty linear and predictable and therefore have clearly-defined next actions —  “Read and work through examples in section 1.2”, for instance. But then the nonlinearity hits. I will eventually read through all of Chapter 1 and will need to work through the exercises. Do I do them all in order, or do I skip around? Would it be fair to lump exercises 1-5 together as a single task, or is that another project? Is even a single exercise a task, or a project, and how can you know in advance? Academic or intellectual work is a black box — you have no idea how long it’s going to take, what resources you will need, whether it is properly thought of as a task or a project, or indeed even if David Allen’s idea of a “task” (a single physical action) is even appropriate at any level.

Scholarship is highly nonlinear, which makes it much different from the business tasks for which GTD was originally created. But it’s what also makes scholarship fun and rewarding, and it’s why most of us eggheads went and got PhD’s in the first place. So, what’s a scholarship-enthused, GTD-powered prof to do in order to bring this important aspect of his work under the GTD framework? Here are some thoughts.

1. Use the review process — all six levels — to craft a coherent and realistic scholarship plan. The heart of GTD is the weekly review, but don’t forget the other kinds of review that Allen talks about in the book. Specifically, Allen gives a six-level model for review in terms of altitude: 50000+, 40000, 30000, 20000, 10000 feet and “runway”. The weekly review often tends to stay on the runway — which, if your work looks like mine, resembles the runways at O’Hare around Christmas — but those higher-level reviews are important. Scholarly directions change rapidly and often at the discretion of the individual. In the business world, you don’t often get the opportunity to change the fundamental direction of your work on your own initiative. But in academia, every day has the potential for such change. If I decided tomorrow to stop studying cryptology and start doing mathematical finance, I could do that. That ability is liberating but also a recipe for stagnation. It’s important to see your scholarship, regularly, not only in terms of current projects and areas of responsibility but also in terms of where you want it all to head in the next year, the next two years, and so on. The tenure and promotion process at an institution, if that process is well-designed, will help profs to think in these terms, but only once a year or (post-tenure) every five years. GTD, done with these higher altitudes in mind, would say to think about the big picture a lot more regularly so that your overall plan is more coherent.

2. As much as possible, concretize your research agenda. Since scholarship is amorphous, once you get down to the level of 10000 feet and lower, some superimposition of structure on scholarship is necessary. It doesn’t always fit well, like a nice suit on an unruly young boy. But it’s still important to break the scholarship plan you’ve created down into manageable projects with a list of concrete next actions. Having “Write a paper” as a project will lead nowhere; most scholarly activities are projects within projects, and at bottom you find one project that can finally be broken down into discrete next actions, each of which has a well-defined context. The challenge is to get to that point. (This is a major similarity with grading.)

3. Don’t be bothered if the plan changes. The nature of research puts all scholarship-oriented action lists into an automatic state of flux. That nice, tidy list of actions under the “Prove the twin prime conjecture” project stands a good chance of being brutally rearranged if, say, you discover a journal article that shows your main theorem so far (which you thought you proved 3-4 next actions ago) to be false, or somebody proves it first, or if you get an unexpected opportunity to work on something else which requires dropping or postponing the project. We all know that research and scholarship are highly volatile areas. But one of the strengths of GTD as a workflow management system is that GTD assumes that tactical decisions will change fluidly and constantly, and that’s OK. The system doesn’t fall apart if things change; you just adjust your next actions and move on.

4. Subdivide your Read/Review folder and make it more like an inbox. Read/Review means something very different to an academic than it does to a business person. The entire life of an academic could be summed up by the term “Read/Review”. So I think Allen’s conception of the Read/Review file needs to be expanded for academics. In my system, I’ve got three Read/Review folders for physical stuff and three for electronic stuff — the three folders in each medium being Teaching/Service (articles about the profession, articles about GTD, articles about pedagogy, etc.), Research (traditional research papers from journals), and Popular (math-related but not from journals; sometimes ed tech items make it in here). I treat these folders like inboxes in the sense that I make them part of my weekly review. Sometimes I gather articles that look good at the time, and I do intend to read them, but they get crowded out by something more urgent. I find that I need to go through Read/Review at least 2-3 times a week to process stuff. Expanding on the Read/Review idea helps keep fresh ideas coming onto your radar screen and into your brain.

5. Stick to your guns with GTD on everything else besides scholarship. Being a prof involves wearing lots of hats — we teach, we serve on committees, we grade, we mentor and advise students and colleagues, and many other things. In order to have the time and flexibility to carry out these amorphous, nonlinear scholarship projects, we have to exercise discipline in getting things done that are “morphous” and linear — stuff like grading, prepping courses, working on committee proposals, and so on. If a person can use GTD to get those tasks and projects under strict discipline and control, then there will (for the most part) be time and space in our schedules to do scholarship. But if the manageable stuff is running all over us, then we can forget about research, unless you are one of the tiny minority of professors who do research and basically nothing else.

I think there’s a great deal of connection between being happy in your academic work and being balanced. The more we enable ourselves not only to be excellent teachers but also active scholars, the more we benefit and so do our students and institutions. I think GTD can help in that regard.

Have a productive week!

[Photo by Jay Lichtman; artwork by ynot2006]

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Filed under GTD, Higher ed, Life in academia, Profhacks, Scholarship, Study hacks, Tenure

Letting teaching and research feed each other

Good article here at the Chronicle on balancing teaching with research, from a neuroscience professor who makes it work for him.

The reality of modern academe is that, no matter what your institutional affiliation, the time you can devote to research is being squeezed by multiple competing demands. No simple solution to that problem exists for any of us. But I have found that rethinking the nature of our professional commitments, such that teaching activities bleed into research ones (and vice versa), can be an effective way to reduce the time crunch. Academics describe their workload of scholarship, teaching, and service as if those were entirely separate entities. In reality, the line between teaching and research is usually much fuzzier.

Read the whole thing, in which Prof. Gendle writes at length about the potentially prosperous symbiosis between teaching and research. He points out three key scholarly skills which teaching reinforces: developing your presentation skills, responding appropriately to odd questions, and making connections across fields. He emphasizes his success in maintaining an active research agenda while keeping a “moderately heavy” teaching load, which for him is 5-6 courses per year. My teaching load is 8 courses (6 preps) per year, and to that situation Prof. Gendle says:

I am fortunate that my teaching load still allows some dedicated time for research. That may not be the case at institutions with teaching loads of seven or more courses in a single academic year. Teaching loads of that magnitude often pass a tipping point for most faculty members (myself included). With that many courses, there simply are not enough hours in the day to conduct classes, grade papers, etc., and still have time left for research.

Gendle is in the psychology department at Elon University, which is well-known for being an undergraduate institution with a reputation for engaging students in meaningful scholarly work.

Do any of you teach at institutions with a 7+ course-per-year teaching load, and still manage an active research program of some sort?

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Filed under Education, Higher ed, Life in academia, Scholarship, Teaching

Spring break report

My busier-than-usual Spring Break is all but over with. Here’s a brief update.

The ICMC went off much better than it looked like it was going to. This was my first of a three-year stint as Student Activities Director for the Indiana section of the MAA, and while my predecessor was really great an answering my questions about how to organize the ICMC, he could only answer the questions I could think of, and the un-thought-of questions were starting to pile up at an exponential pace the week before the contest. But with the generous help of Mike Axtell, who — sadly — is leaving the Indiana section for a new position in Minnesota, all the logistics went off just fine and we had no major incidents. Kudos to the Purdue, Rose-Hulman, and Taylor teams who finished first, second, and third respectively.

That was last weekend. On Tuesday and Wednesday of this week I had a very nice time at Benedictine University near Chicago as the guest speaker to the Math Club and to Manu Kaur‘s topics course in cryptology. I gave a talk to the Math Club on cryptology in general — 50 minutes to cover the whole subject! — and despite some technical difficulties, the talk went reasonably well. There were close to 75-80 people in the audience! Then, the next day, I gave a talk on the Digital Signature Algorithm to the crypto class. In between, I got the rare opportunity to talk shop with Prof. Kaur on cryptography, and I also got a very nice tour of nearby Naperville, which is really quite lovely. (Not what I expected for Chicagoland suburbia.)

Benedictine has a fine department, and I was especially impressed by their students. To have close to 80 students show up in the middle of the day for a Math Club ta,lk at a school of under 3,000 students, is really amazing, and I got some very good questions after the talk. Following the digital signatures talk, one student asked me a really insightful question about Blowfish and SSL encryption; not only was this an undergrad asking the question, he was an undergrad chemistry major. And everywhere you looked, students were working on things — the science labs in particular seemed to be full every moment I was there.

St. Procopius AbbeySpecial treat for me: I got to spend the night in the extraordinary St. Procopius Abbey amongst the Benedictine monks. I’ve been reading Thomas Merton and the like for a long time, and the monastic life has been a guiding force in my Christian experience ever since I became a Christian, but until this week I had never actually gotten to experience monastic life firsthand. The abbey itself is breathtaking, with its Edward Dart-designed architecture combining soaring vertical spaces with hidden rooms for prayer and meditation, with a common thread of simplicity and silence throughout. I’m considering making a longer retreat there sometime soon. Something about the kindness, simplicity, and warmth of the abbey and the monks who live there follows one home from a place like this, and I could certainly use more of that.

So I’m wrapping up break doing the stay-at-home dad thing, having stayed with the girls for the last couple of days and spending the weekend doing the same before getting back to work on Monday. Ironically, this semester I made the conscious choice at the beginning not to emphasize scholarship so much but focus almost all my energies on teaching, but I ended up with one of the busiest semesters I’ve had scholarship-wise in a long time, mostly stuff that I have done or wrapped up this week! Now to finish off those pesky last five weeks of the semester.

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Filed under Christianity, Crypto, Higher ed, Life in academia, Math, Personal, Student culture, Vocation

Some ruminations on research

4909171_c626708935_m.jpgSo I spent the entire day today up the road at Butler at an NSF workshop for people interested in writing grant proposals. It was very informative, and it was especially helpful to have most of the actual program directors there in person — all of whom were friendly, very down-to-earth and open to talking with faculty grunts like me. (One request for the NSF folks, though: Please, for the love of God, consider the 10/20/30 rule for your presentations. Four straight hours of 40+ slide Power Point presentations done in 20-point font almost (but not quite) drove me crazy. Thanks.)

What I wanted to blog about right now, though, isn’t the NSF stuff per se, but more about the feeling I always seem to take away from conferences or workshops like this where there are a lot of people who actually do research. The feeling is one of being on the outside looking in, of being past my prime.

To understand this, you need some context. It’s been 10 years now since I finished my PhD in mathematics, with a specialty in some very esoteric homology theories that I myself never fully understood, and the use of exotic category theory stuff to make the symbols associated with those homology theories do what I wanted them to do. At the end of the day, I had proven that Quinn homology was isomorphic to G-equivariant homology when G is a discrete group acting cellularly on a simplicial complex. I worked for another year following my dissertation to edit it down into publishable form, and got it published.

But that was the last real mathematical research I have touched since then, with the lone exception of a paper I got published in Cryptologia a couple of years ago. And that paper was so error-riddled in the original draft that it only barely was accepted at all, and  even then it was more of a curiosity than an actual result. But it was research. However, it took me a year to write it, and over a year to edit it since part of the editing process was interrupted by traveling to China to adopt our oldest daughter and stumbling into being a parent.

Getting that paper published, especially since it was in an area (cryptology) in which all my training has been self-teaching and in which I have no formal coursework, makes me believe that I still have the intellectual chops to do mathematical research. But the amount of time it takes to get anything done, and the number of times I’ve sat down to try and learn new things and get out to the frontiers of a subject where the research happens, makes me think that I’m too old or too involved with other things in life or carrying too heavy of a teaching load to make it happen.

Don’t get me wrong — my family is more important to me than research, and teaching is what drove me into being a college professor to begin with. But I also want to be a well-rounded professional, which means that not only am I teaching excellently and leading a fulfilling personal life, I am also learning — consuming and producing new knowledge both for the purposes of the world and my discipline at large but also for my colleagues and students. The more I look back on the last several years, the more I realize that my scholarship and the attempts to satisfy my hunger for learning have not gone anywhere.

And this is no more frustrating than when I am around a bunch of talented researchers, especially scholars who work at liberal arts colleges whose job is primarily teaching but still have the time and space to learn and be experts in their areas. I have been trying to reinvent myself as a scholar over the last few months in a different area — computational linguistics and data analytics — in hopes that I could succeed in scholarship here where I had not succeeded elsewhere. Things went well over the summer. But when the semester started,  everything ground to a halt as every moment of the week was taken up by grading, prepping for the next class, grading some more, etc. Then, today, I was walking from one meeting room to the next when a guy behind me starting talking about his research in computational linguistics. I turned around to introduce myself, thinking perhaps it was somebody from IU’s excellent linguistics department. But it turned out to be… someone from a neighboring liberal arts college. Where they have the same emphasis on teaching as we do. So, how is this guy able to get his research done where I can’t even find the time to open my Jurafsky and Martin?

So I am left with a question, which I wrote in large print at the bottom of my workshop notes today: How does somebody like me — holding a PhD but 10 years removed from any significant research, not anywhere close to the cutting edge of any discipline, and tenured in a position at a small, teaching-oriented liberal arts college — how does somebody like me get to the point where he can do research in his field or a closely related field? Is it possible? If so, how do I get there? If not, how do I come to terms with knowing that my math research days are over, even though intellectually I feel like I am still in the game, and want to be in the game?

[Photo by slight clutter]

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Filed under Life in academia, Math, Personal, Scholarship