In order to tie together the ideas contained in a couple of recent posts (this one and this one), I offer the following:

This diagram, like that contained in the last post, represents what mathematicians call a finite state automaton. Such a creature is little more than a very simple computer, capable of generating and recognizing strings that fall into a class called a regular language.

To be more precise, imagine that you're plopped into the diagram above in one of the ten states (the little yellow boxes with labels on them). You're then asked to move about the diagram by following the red edges in the direction indicated by the arrows, and every time you take an arrow from state s to state s' you write down the letter s', and if s' is one of the consonant states, you can write down any consonant you'd like. The only catch is that you can only follow an arrow heading out of the state in which you find yourself at the current point in time.

For instance, if we're plopped down on the state labeled "consonant_{5}," we can either begin by writing down a consonant (following the red arrow back to "consonant_{5}") or by writing down an a and heading over to the state labeled "a." From there we must either write a consonant (and thereafter any number of consonants for a while) and head to "consonant_{1}," or go directly to "e" by writing an e.

Any piece of writing we can compose in this fashion without causing our walk from state to state to "block" and come to a screeching halt is said to be accepted by this finite state automaton. I'll leave it as an exercise to the reader (I love that phrase!) to check that this automaton accepts precisely the poems generated by the permutation method I described in this post, in which your permutation is (a,e,i,o,u) and your sequence is {1,1,1,...}: you have to use the vowels a, e, i, o, and u in strict rotation, but consonants can be thrown in willy-nilly. (And yes, "willy-nilly" is a technical term [just kidding].)

How does this relate to Hamlet's soliloquy, the subject of my last post? The diagram in that post shows another finite state automaton, and this one is the minimal automaton of the same sort that accepts Hamlet's famous "To be or not to be" speech. By "minimal" I mean that this automaton has only those transitions from state to state that one needs in order to generate that soliloquy: any more edges would give you more flexibility than you'd need, and moreover you'd be able to generate more than you'd like. For instance, as one of Erdrick's students astutely noticed, in Hamlet's automaton you can only reach "z" by coming from "u," and from "z" you can only travel back to "z" or to "l," suggesting that the only z-word you're allowed to build is "puzzle." This is indeed the case, and this limitation puts a strong constraint on the sorts of written work you can produce using this automaton, and as I'm fond of pointing out, poetic constraint is a heckuva lot of fun.

Indeed, there are dozens of poetic possibilities from this point, and I've already started writing a paper that describes a number of them. I'll mention a few interesting constraints, and I hope my readers will help me to explore these and share with me the results of their explorations:

1. Given the minimal automaton for one piece of writing (maybe one that already exists, like Hamlet's soliloquy), generate poems that are "entailed" by that piece of writing, in that they too are accepted by the first piece's automaton.

2. Write the shortest possible piece of semantically and syntactically meaningful prose or poetry whose minimal automaton is the "complete" automaton consisting of all 26 potential states and all 26^{2} transition arrows. I envision lines like "'To Iraq!' Zelda cried."

3. Find the longest possible semantically and syntactically meaningful piece of writing that is completely determined by its minimal automaton, in that the only meaningful (in whatever way you choose to define it) pieces accepted by that automaton are "subpieces" of the original one. For example, even the simple sentence "Me too!" gives rise to an automaton (below) which accepts not only "me" and "too," but also "met" and "to":

4. As my colleague Erdrick has pointed out in private correspondence, maybe you want to introduce whitespace states? Such a modification might be either enabling or disabling, depending on how it's handled...

In any case, there'll be much more to come about this in future posts as I develop the technique, write the paper I referred to above, and actually write some damned poems that fit some of the above constraints. If you'd like to play around a bit, I'd love to see what you come up with. Just remember that you saw it here first!

## Monday, June 29, 2009

### Loose ends

Posted by DocTurtle at 3:57 PM 0 reflections

Labels: graph theory, poetry, theory

## Sunday, June 28, 2009

## Saturday, June 27, 2009

### Fractal Fest '09

I know it's been a while since I checked in...suffice it to say that the REU's been keeping me busy (no surprise there). That, combined with trying to wrap up the proposal to get continued funding for the program (this year's the last supported year) and trying to think of something meaningful to say about writing programs in times of economic hardship, has kept me away.

I simply had to say a little something about this afternoon's first "math in public places" event, the Fractal Making Festival sponsored by Algebra al Fresco. With roughly 25 students and passersby lending their help, we were able to build a Level-2 Menger sponge out of business cards in about four hours. The actual construction of the cubes and the Level-1 sponges took about three hours, and the assembly of the Level-2 from the Level-1s took another hour of careful surgery.

The finished product is pretty sweet, I have to say; it's sitting in the back seat of our car right now, awaiting transport to the Math Department sometime early next week.

Check it out, pictures below!

This first was from early on, when things were just getting underway:

Not more than an hour or so in, we really started to build up a backlog of little Level-0s, as you can see here:

Pretty soon two of us dedicated ourselves to the sole task of assembling the Level-1s, and a third joined us an hour later, just to keep up with the Level-0s coming our way.

We had help from folks of all ages:

Progress was made. Soon we turned to putting together the Level-1s, and the Level-2 was born, a little bit...

...at a time...

In the end:

We had a bit of fun transporting it down Haywood Street to the parking garage where I'd left the car. The table on which we'd set it while it was under construction made a handy palanquin:

Oohs and aahs accompanied this procession (at least, I like to think they did). In any case we got a good number of stares of curiosity.

Next on the Algebra al Fresco agenda? Pi recitation? Math poetry slam? Some sort of graph theoretical six degrees of separation sort of game? I'm not sure. Stay tuned: further bulletins as events warrant.

Posted by DocTurtle at 4:25 PM 0 reflections

Labels: Algebra al Fresco, pictures

## Tuesday, June 16, 2009

### Update on my conversation with Sedgwick

After reading my open-letter response to his e-mail regarding Don Tapscott and the ILS Program at UNC Asheville, Sedgwick wrote me again with a link to an on-line version of the Tapscott interview to which he'd referred: http://aolradio.podcast.aol.

Enjoy!

Posted by DocTurtle at 8:31 AM 0 reflections

Labels: ILS program, Learning Circle

## Monday, June 15, 2009

### In our angelic chorus

A new perimathematical constraint for poetry:

1. Select your favorite sequence, {*a _{i}*}. (An infinite one will ensure that you'll never run out of defining digits.)

2. Select a permutation

*p*of the set of vowels.

3. In the poem you construct, the vowels must appear in the order in which they appear in the permutation from Step 2 (repeating the permutation anew once its ends is reached), and the

*i*th block of consecutive occurrences of the same vowel must contain

*a*occurrences of that vowel.

_{i}As default values, one might take the obvious choices {

*a*} = {1,1,1,1,...} and

_{i}*p*= (

*a*,

*e*,

*i*,

*o*,

*u*).

As yet I've only managed to construct a page or two of semipoetic fragments, like "up sharp gelid mounts, arches high" and "dour pages, iron, unanswering."

Perhaps one might try a random permutation, and a defining sequence such as {3,1,4,1,5,9,2,...} or {2,7,1,8,2,8,1,8,2,...}?

More to come!

Posted by DocTurtle at 7:51 PM 0 reflections

Labels: poetry

## Sunday, June 14, 2009

### A little conversation

As I noted in my last post, I recently received a very thoughtful e-mail from an old student of mine, Sedgwick, who will soon be studied public policy in the graduate school at the University of Minnesota. His letter concerned a number of points I'd made in earlier Change of Basis posts, regarding everything from my (recent) initial response to Don Tapscott's Grown up digital to my views on the UNC Asheville Integrative Liberal Studies (ILS) program. I'd like to make of this post an open letter in reply to Sedgwick, playing off of his ideas and elaborating further my own, where appropriate.

(Note: He's given me permission to quote his e-mail freely.)

Let's just go in order. Sedgwick begins:

In regards to your Learning Circle book, it's a small world...a few weeks ago I heard Don Tapscott talk for a while on a weekly technology show. Much like you, I found a few of his observations on leveraging technology in the classroom useful, but not particularly distinct from the suggestions that any 'wired' person could make about improving academia. Given how conservative educational institutions can be in many respects, it is not a particularly challenging feat to poke fun at, say, the traditional lecture format.

We're in complete agreement: I've yet to find anything truly revolutionary in Tapscott's book. Of course, I'm not reading it in order to find therein a recipe for a 21st-century classroom, but certainly I expect various prescriptions and proscriptions to appear. Let's continue with Sedgwick's letter:

That said, as the conversation progressed, Tapscott proposed some solutions which I found...interesting. For example, UNCA is rather keen on the need for interdisciplinary thinking and the liberal arts, but Tapscott's solution to an increasingly complex world is to dump the liberal arts altogether and start giving college students specialized training at the undegraduate level (e.g. law school and med school training from freshman year onwards). However, these suggestions are just for professions requiring some specific training, as Tapscott suggests that instead of 'wasting' four years at university, high school students should instead focus on some marketable technical skill or 'passion' and go 'do their own thing,' for lack of a better term. As Tapscott's hypothesis goes, once kids catch on to the fact that anyone can be as successful as Bill Gates or Steve Jobs by striking out on their own, universities will fade away by mid-century. While I can see how Tapscott is attempting to speak to people who perhaps did not get much out of college, proposing that the solution lies in obviating academia altogether just seems too flippant a suggestion to take seriously. Anyway, not to prejudge your book discussion, but did I want to concur that Tapscott's analyses seemed rather aloof from reality, and that he

did get me a bit miffed.

I find it very hard to reply to this portion of Sedgwick's letter, as I can't be sure of the sort of universities Tapscott has in mind. In some ways, the institutions Tapscott's speaking of already exist: technical and trade schools, and a number of community colleges, for instance, already place their emphasis on technical skills and specialized training, asking students to complete only a bare minimum of coursework in "irrelevant" areas. Likewise, students at more research-oriented universities (including "institutes of technology) often pursue courses of study designed to prepare them for graduate study in one or two particular areas, to the detriment of their engagement with other fields. Furthest from the form suggested above are the liberal arts institutions, in which students are required to engage a broad course of study that incorporates classes from highly divergent disciplines, and to synthesize what they've learned into a coherent whole.

I can't know to which sort of institution Tapscott (through Sedgwick) is referring, but in its broadest sense the claim that universities will "fade away by mid-century" seems prideful and cocky. Of course, to insist that the university system as we know it is timeless and eternal and will persist unchangingly as long as the human race lives upon the surface of the Earth is an equally hubristic claim, but I would be very surprised if the evolution of the university follows any course other than gradual change, morphing smoothly from one sort of institution into another, different but only subtly distinguishable from the last, morphing subtly again, and again, and again, its eventual manifestation starkly different from its present form, but only noticeably so by direct juxtaposition.

Let me offer a defense of the liberal arts institution in particular.

What seems to be missing from Tapscott's presumed argument (not having seen the program to which Sedgwick refers, I can't claim to place this argument squarely in Tapscott's mouth) is a certain measure of humanity; for the proponent of the above argument education seems to be cast as little more than a means to an end, and that end is a purely chthonic one, concerned only with the attainment of a job and the wealth that attends to that job. (Come to think of it...I've seen very little mention of art and literature so far in Tapscott's book...) Little regard is given to other learning goals achieved through a liberal education, including an appreciation for art both for the sake of art and for the unique knowledge it can offer us, an understanding of the interaction between all areas of intellectual inquiry (whether they're catalogued under the "natural sciences," the "social sciences," or the "humanities"), and an understanding of the humanist thread that binds together all of our race's endeavors.

Must a medical doctor be able to quote Chaucer in order to perform a successful heart transplant? Assuredly, no. But should we insist that she know a bit about the history of medicine, and the place medicine occupied in that history alongside the various other disciplines from which it grew and with which it intertwined?

Will the learning goals above be met in the universities of 2050 as they're met in universities now? Almost certainly not: just as our universities today in no way look like Harvard of 1900, Oxford of 1500, or Plato's Academy over two thousand years ago, the schools in which the adolescents of today instruct the adolescents of tomorrow will be profoundly different institutions. But I doubt they'll look anything like the schools proposed in the argument put forth in Sedgwick's letter.

Speaking of which, let's get back to that letter. At this point, Sedgwick offers a few bullet points in order to summarize his response to an earlier post I wrote on the ILS program at UNC Asheville, in which I was quite critical of the cluster component of ILS. Here's the first:

Get data on the real-world benefits of UNCA's ILS program. Over the years, I saw both ILS and the Humanities requirements take a lot of flack from my peers, but given the (admittedly few) conversations I've had with people after the fact, it seems they ended up enjoying the breadth offered by a cluster. Now that graduates from the ILS program are beginning to enter the real world, perhaps some alumni surveys are in order about how that breadth helped them. I think that by combining the existing data about the comparatively better performance of liberal arts graduates with data specific to UNCA, one could make a compelling argument for attracting serious students to campus.

I won't say so much about this suggestion, besides pointing out that I'd be more interested in getting data on the long-term perception of the other components of the ILS program (the intensives, for instance). The idea has its merits, and honestly I can't be sure that UNC Asheville's not already performing or planning to perform surveys as described above; it wouldn't be a difficult matter to ask a few questions about the ILS program on an alumni survey (much like the ones I recently filled out for Vanderbilt).

Sedgwick's next bullet point:

Better integrate the cluster system into the curriculum itself. While I appreciate the ILS program's relative boldness amongst generic college curricula, I think part of the criticism by students is that it appears 'bolted on' to the normal college requirements. Although I was a GenEd student, it seemed from the outside that many cluster classes appeared to be just 'normal' departmental classes. Perhaps cluster coordinators could work on 'harmonizing' some of the classes to lessen the appearance of patchwork? Actually, I bet this is already happening to a good extent, and that given the budget cutbacks, additional tailoring would be be difficult if not impossible.

(Note: "GenEd" was the general education system in place before the phasing in of ILS; it differed from ILS in a number of aspects, but its ultimate purpose was more or less the same. Sedgwick was likely in the last class of students to whom the old system applied.) I fully agree with Sedgwick's perception of students' complaints about clusters, and I agree that the way to adjust the clusters in order to effectively respond to those complaints is to do as he suggests, harmonizing the classes in some meaningful fashion.

However, I'm not so sanguine about the extent to which this is being done: to my knowledge only a small percentage of the clusters' faculty meet regularly to coordinate their coursework. Sadly, there's little little incentive for faculty to put much effort into aligning their cluster courses with their fellows in whatever clusters they occupy: there's generally no release time, there's no monetary reimbursement. The only real motivation is intrinsic: the knowledge that you're providing an optimal experience to the students in your cluster. Would that this were enough incentive, but considering that even moderately diligent faculty members already spend dozens of hours a week in teaching, grading, class preparation, committee work, research, work for professional organizations, et cetera...it's unrealistic to expect most faculty to devote any more unreimbursed time on cluster coordination than is absolutely necessary.

And, as Sedgwick suggests, budget cuts don't help.

The last bullet point:

Tweak the cluster system to make its relevance more apparent. As a merely personal example, I feel that, for all the knowledge I acquired at UNCA, I graduated without much in the way of marketable skills. All the jobs I've applied for in the past year were entry-level. Now I may be an outlier in that my degree was relatively specific and there are few environment-related organizations where I live, but I think the point remains that a certain proportion of graduates wish they had the opportunity to develop one or more specific skills as part of their liberal arts curriculum. Perhaps the cluster system could require the development of two distinct skills? In particular, I think of your effort to combine math and writing, but any combination could leave graduates with both a personalized and marketable skillset. I think UNCA, as a small and tightly-knit campus, is well suited toward this type of skill cross-pollination. Given how often people change careers nowadays, I think UNCA could market the 'have your bases covered' need very effectively. Of course, skill meshing isn't just about career resiliency but also the potential development of new approaches that can revolutionize existing careers or create new ones.

Agreed! Ideally.

There's nothing in this last point that I can find fault with, and it could be that UNC Asheville's ILS program is on a trajectory that will eventually take it to this ideal. As yet, however, it is merely an ideal, and will remain so until the faculty who will implement the program are granted release time or remuneration they'll need to motivate them to design the program and put it into action.

Might we move further beyond cluster courses, implementing team-taught courses in which two or more faculty provide truly integrative real-time instruction on a daily basis? This sort of instruction exists elsewhere...hell, if I received this sort of instruction as an undergraduate at a much larger institution nearly fifteen years ago, what's to stop UNC Asheville from moving in that direction? It's hardly lethargy or laziness (see my comments about being overworked above), and though one might try to finger financing for this fault, why not spend the money currently spent on implementing cluster courses on the faculty development and resources that would be needed to support team-taught courses?

It might simply be that at UNC Asheville, as at many other institutions, it's unstated disciplinary territoriality and parochialism that's to blame for the reluctance to implement such innovative course offerings.

There's much more to be said at a later time. For now, I've been typing too long, and my eyes are demanding that I take a break and enjoy the rest of my Sunday evening.

My sincerest thanks go out to Sedgwick for allowing me to share his e-mail on this blog. I hope he's provided my readers with some rich food for thought, and I hope he'll find my responses to his letter to be worthwhile ones.

Posted by DocTurtle at 6:03 PM 0 reflections

Labels: ILS program, Learning Circle

## Friday, June 12, 2009

### Three great gifts

Week One has ended!

And we've not lost a one.

This afternoon's session on fractal dimension, led ably by my colleague Nostradamus (my partner in crime this summer), marked the end of the week's action for the REU. While they're still a bit reluctant to speak up in front of one another, they're definitely growing more at ease with working together, as evidenced by their professions to collaboration behind the scenes (from Nils and Ole) and the ease with which they cooperate in class (two pairs worked together to complete this morning's LaTeX exercise).

Speaking of LaTeX (and other mathematical technologies), all eight students now have installed on their computers some sort of LaTeX editor and compiler, and all eight have installed some version of Mathematica.

The students are beginning to show the first signs of focus as they near their initial selection of topics: Billie indicated specific interest in the "use it or lose it" tree construction, as did Daria. Nigel likes the look of the same algorithm, though like Daria he'd like to hear more about Cayley graphs before deciding on what to do. Several students asked more about graceful labelings and generalizations of chromatic polynomials, too.

All in all it's been a good first week. I've certainly learned from it that there's no single snapshot of a successful first week's work: while I've made no small point of this group's relative reticence, in their own way they've been no less successful in their mathematical efforts than last year's bunch, say, a band of brothers and sisters to whom I was often tempted during lectures to say, "shaddup already!"

If any of this year's REU students are reading this, please know that we're only remarking on your quietness because we find it a striking counterpoint to the previous years' groups. There's absolutely nothing wrong with your reservedness: it says nothing about your intelligence, your work ethic, or your eventual success as mathematicians. It's just very different from what we're accustomed to.

As yet I've said nothing in this post about the three gifts to which I've alluded in the post's title. It's time to remedy that.

All three of these gifts promise to expand my both my own understanding of the mathematical world and my ability to convey that understanding to others.

The first gift comes to me from Daria. When I fetched her from the airport on Sunday morning she and I got into a conversation about ethnomathematics, which readers of this blog might know is one of my less minor interests, especially given my rather unorthodox (among the research mathematical community) view that mathematics is not universal but is indeed a cultural artifact, a socially-constructed system that varies from one people to another. Somehow it came up early in one of our first conversations that Daria had recently taken a course in ethnomathematics, and in fact would soon have with her the textbooks she'd used for the course. I asked her if I could borrow them when they arrived, and yesterday she brought them to me. I have no doubt they'll prove a fascinating foundation for my own study of ethnomathematics, and a good basis for the course on the subject that I hope soon to develop for UNC Asheville students.

Both books, Ethnomathematics: a multicultural view of mathematical ideas (CRC Press: Boca Raton, 1998), and Mathematics elsewhere: an exploration of ideas across cultures (Princeton University Press: Princeton, 2002), are by Marcia Ascher of Ithaca College. In a heedless display of randomosity I began reading the second-written one first just a half-hour ago. It promises to be an interesting read. Having read little more than the introduction at this point, I already suspect I'll find a kindred epistemological spirit in Ascher.

For instance, "we now know that there is no single, universal path -- following set stages -- that cultures or mathematical ideas follow" (p. 2). Take that, proponents of mathematical universalism. As I'm fond of saying (and have said elsewhere in this blog), mathematical language is hardly more universal than the English language, and the mathematics of an alien race would likely be as indescribable and indiscernible to us as their courtship rituals.

Or take this line: "most practitioners of modern mathematics value their ideas because they believe them to be context-free; others value their ideas as inseparable from the cultural milieu that gives them meaning" (p. 4). Indeed, it's a blight on modern mathematics that so many modern mathematicians might laud math's seeming baselessness and independence from any fixed ground. This view could hardly be farther from the truth, as math is a highly predicated belief system, the truths it embodies obtaining only when certain cultural norms about truth and knowability are applied. How is it that a mathematician unwilling to state her or his hypotheses, elements necessary for the application of any reasonable theorem, would be laughed from the lecture hall, while it can be commonly supposed among mathematicians that the very science of mathematics does not rest on similar epistemological hypotheses?

I'll be sure to blog about these books as I make my way through them this summer.

A second gift, one of recognition and promise for future collaboration, comes to me from a heretofore unknown colleague in South Carolina. Lately my work on the intersections between poetry and mathematics has been getting the attention of more and more poets. Io, a poet and teacher from South Carolia, came across a copy of my paper on using poetry to teach mathematics (the one to appear in WAC Journal), and told me of her interest in the subject. She confessed that abstract algebra had been one of her favorite classes in college, and that she had great interest in understanding more fully the similarities between math and poetry.

Already, in just a short exchange of e-mails, I can tell I've found another likely friend and colleague. I hope to continue my correspondence with this woman as I further develop my own understanding of the ways poetry and math interact.

Side note: next year marks the 50th anniversary of the founding of Oulipo. Perhaps some sort of public and poetical and perimathematical celebration is in order? That's something to think about.

The third gift comes to me from an old student, Sedgwick, who graduated about a year ago with a degree in environmental studies. Sedgwick was one of the star students in the second section of my Spring 2008 Calc II course, a close-knit class that was a lot of fun to work with. He's still, a year after graduation, a regular reader of my blog (shout-out, Sedge!), and after reading a relatively recent post (this one, I believe) on the effectiveness of various components of the Integrative Liberal Studies program at UNC Asheville, and an even more recent post on Don Tapscott's Grown up digital, he wanted to offer a former student's perspective on the ILS Program, and did so extensively in an e-mail he wrote to me about a week ago.

His e-mail is, as is all of his work, thorough, well-thought out, and well-organized. This guy's always been a top-notch thinker. He makes many excellent points about various components of the ILS system. I asked Sedgwick's permission to excerpt his e-mail to me and to form a response to it in the form of an open letter consisting of a blog post here. Having been granted his leave to do that, do that I shall, in a post I hope to write this weekend.

For now, though, the dinner bell is readied to ring, and after a long, long week or work with a new crop of talented young researchers, I'd like nothing better than a few hours off. (If only I could get this damned channel assignment problem out of my head!)

To be continued...

Posted by DocTurtle at 6:35 PM 0 reflections

Labels: ethnomathematics, poetry, REU, theory

## Wednesday, June 10, 2009

### Stand and deliver

Day Three has come and gone, and though they're still quite quiet, they've begun to strut their stuff, mathematically speaking.

Yesterday evening I presented them with the most substantial "homework assignment" I'll be giving them during these first couple of weeks of the program (the dreaded list of 34 terms and concepts from graph theory for which they were asked to find definitions and examples they would then take turns presenting to each other in seminar), and they completed it well. They'd divided the work up almost perfectly evenly, each taking about four of five of the terms for her or his own, and working together to produce a single Word document (by Friday it would be LaTeX) containing all of their findings. Impressive! They're the first group we've had who's created, unprompted, their own lexicon at the stage in the game. (Or at any stage, for that matter...)

The first few turns taken were orderly ones, each student presenting on several subjects appearing consecutively on the list.

Demeter started things off with a discussion of the many different sorts of sequences of vertices and edges one can consider: walks, paths, trails, circuits, and cycles. Her presentation was straightforward and confident. It was solid, and left little room for questioning.

Dora's presentation on cliques and blocks and related ideas raised a few more questions, which she handled smoothly. I appreciate how hard it is to think on one's feet in any setting, and I can't imagine how much harder it is when the questions you're being asked to answer (on the spot!) involve high-level math you began learning about just two days earlier.

Next it was Daria's turn, and her introduction to independence and domination led to good many more questions, which she too fielded handily.

Nigel's turn came, and he approached his presentation a bit more lightheartedly then his peers had before him. He was particularly adept at using the board and the colored chalk, and he seems very at ease working in front of his peers, providing clear and correct descriptions for each of the terms he'd been assigned. I hope he can build upon that confidence.

After a break for lunch, the rotation became more scattered. Billie's presentation on coloring and all matters chromatic stood at the center of a scattered maelstrom of turn-taking by Omer, Ole, and Nils, who traded off with one another as they discussed everything from graceful labelings to adjacency matrices.

Billie, who comes to us having taken a graph theory course (the only one of the bunch to have done so, I believe), had no trouble at all searching through her old course notes to root out a good working description of the Deletion-Contraction Algorithm. Like Demeter and Nigel before her, she was confident and clear.

To be honest, the tag-teaming trade-offs the guys made made it hard for me to get a good grip on their presentation styles. Even though they spent as much time at the board, cumulatively, as had their colleages, they weren't up before the class for a long enough chunk to get a sense as to how they'll be in sustained presentation.

Ah, but that will come later!

All around, the students did well. There were several minor slips, but that's to be expected. As I'm fond of saying, truthfully, hardly a day goes by without me making a dozen mistakes at the board. Sure, there were a few misstatements and a few definitions that might have been made clearer, but in the end it was good.

One thing I would like to see more of: the students challenging each other and asking questions that serve to further the work their colleagues have done.

And I'd like for the student who's presenting to not look at me when she or he asks "does this make sense?" or "is that right?" Who am I to say? I don't want to be thought the only expert in the room. I realized earlier this evening that in the last couple of days I've made the mistake of sitting at the center of the room's semicircular arc; tomorrow I'll decenter myself by moving to one side. (Funny: it took precisely one day for the students to fix their places in the classroom. From the near side to the far side, they sit thus: Nils, Ole, Dora, Billie, Daria, Demeter, Nigel, Omer; the last two days I've sat between Daria and Demeter.)

I find myself wondering what it is that's interesting them, mathematically...what sort of projects will they opt to undertake this summer? We've now posed maybe a score of open problems (with another score or so lying in wait), but I've no sense as to which ones they're finding appealing. I'm excited to find out.

For now, speak up, my young colleagues! Let us know what's caught your eye.

Posted by DocTurtle at 9:42 PM 0 reflections

Labels: REU

## Tuesday, June 09, 2009

### Credo

I may be a bit of a Pollyanna (given how treacly, or even declassÃ©, the following might seem to some), but...

Credo of a Humanistic Professor

I believe in cooperation.

I believe in friend-making and in bond-building.

I believe in mutual respect and in shared responsibility.

I believe in achievement of understanding, and in always-open lines of communication.

I believe in controlled, consensual risk-taking.

I believe in honest intellectual inquiry.

I believe that little is more important in an academic relationship, up to and including mastery of the material being studied, than ensuring the conditions and goals indicated above.

Posted by DocTurtle at 7:19 AM 0 reflections

Labels: theory

## Monday, June 08, 2009

### Day One, Part Deux

It's been a good day, all in all. First days are always a bit awkward, simply because (a) no one really knows everyone else yet, (b) no one's really got a full sense of what's about to go on, (c) everyone's testing each other out and figuring out what to expect from each other, and (d) there's a lot of tangentially-related bureaucratic crap to cut through before you can get to the fun stuff.

The period from 9:00 to 11:30 this morning was spent almost entirely in filling out forms, getting pictures taken, coding in identification numbers, and so forth. The upshot is that the kids now fully exist, according to most of the file systems on campus. Their existence so verified and redundicated (I know that's not a word, but I felt like using it anyway...at this point my brain is more or less tapioca, so I hope you'll cut me some slack), we were finally free to start working on some math.

We got through a couple of pages of set theory and notation (in about half an hour) and two pages of graph theory (in another hour) before it was time for lunch, after which we returned to discuss some high-level open problems in fractal geometry (yet another hour) and some more graph theory (the last hour of the day).

So far? They're a bit shy about presenting in front of one another...but who isn't at first? It's definitely too early to tell how well they'll come together as a team, but as friendly as they all are (I've had lovely conversations with them all as individuals) I can't imagine they won't coalesce into a terrific theorem-proving team.

From the "Oh, and" Department: today was also the first day of my Learning Circle for the summer, on the book Grown up digital: how the Net Generation is changing your world (McGraw Hill: New York, 2009), by Don Tapscott. I'm yet to be impressed with the book (so far, though it makes some insightful and worthwhile claims, it's a rather uncritical gathering of anecdotes, only marginally relevant data, and personal observations), I very much enjoyed the conversation I shared with my colleagues in the Circle, and I had several thoughts I might blog about later...especially regarding the construction of collaborative syllabi and other course documents. I'm looking forward to next week's discussion on the text.

So much to learn, so much to live for!

Posted by DocTurtle at 4:56 PM 0 reflections

Labels: Learning Circle, REU, theory

### Day One

Ugh.

No sleep last night, too excited.

Much to do today, but much of it boring (sorting out housing snafus, filling out paperwork, getting folks into the library system, etc.).

We'll make it through all right.

But if I don't bowl well tonight, Wes'll kill me.

Posted by DocTurtle at 7:24 AM 0 reflections

Labels: REU

## Sunday, June 07, 2009

### First impressions

My first impressions of this year's REU group:

1. They're a bit more timid than last summer's bunch. This isn't a good thing or a bad thing, it's just a thing. It's all good, it just might mean it'll take them a little longer to come out of their shells. (Nothing a bit of bonding over a long-ass list of graph theory definitions can't cure...)

2. They seem highly dedicated. They all talked about how much they love math, and several have mentioned how they become absorbed by problems on which they're working, and several of talked about their futures in math (grad school, teaching, etc.)

3. They strike me as talented, but modest. I already have a feeling they've got a great deal of math smarts collectively, but I don't think we've got any hotshots: almost every one of them mentioned to me within minutes after meeting me that she/he was excited to be here, and they seem to understand their participation in the program as a privilege and as a responsibility rather than as a right.

Tomorrow, we begin. Excitement!

Posted by DocTurtle at 10:04 PM 0 reflections

Labels: REU

### Mission: mathematician

This summer's goal: turn eight math majors into mathematicians.

Posted by DocTurtle at 9:29 AM 1 reflections

Labels: REU

## Friday, June 05, 2009

### Any minute now

The 2009 Summer REU is set to start.

Although I usually count the Sunday night potluck at our place as the "official" kick-off, the first of this summer's students will be arriving any minute now, if her estimate is anywhere near correct (and I think it is).

Monday should be fun. I've adapted several of the handouts from last summer (they all worked out pretty well) to reflect changes in the problems I'll be pitching to the kiddoes by Week 2. There was little change beyond removing a few graph-theoretic definitions that don't seem all that crucial anymore and adding a few missing ones that do. If this year's crew is as outgoing and eager as last year's, the first week's going to be a fun one.

I guessed I'd better get busy with some new pseudonyms, huh? How about these: Demeter, Billie, Daria, Dora, Ole, Omer, Nils, and Nigel?

Those oughta do.

Is everything in place?

Housing? Check.

Checks? Check.

Plans for managing their arrivals? Check.

First week's work? Check.

Whew.

We'll see how this goes.

I'm excited.

Posted by DocTurtle at 3:51 PM 0 reflections

Labels: REU