In Praise of Teamwork

Left to Right: John Jones, Rachel Davis, and Christelle Vincent work on the LMFDB.

Left to Right: John Jones, Rachel Davis, and Christelle Vincent work on the LMFDB.

Part of what makes math blogging so interesting is that it helps to build connections between the people creating math and those consuming math. The evolution in math blogging and blossoming of math on twitter has done a great deal to dispel the crazy myth of math as a solitary pursuit, or worse yet, of mathematicians as weirdo loners. Mathematicians, just like other scientists (or humans for that matter), like to work together.

This sort of working-togetherness and community mathematics can come in many shapes: collaborative research, math blogging, and open source software initiatives, to name a few. I was first inspired to think about this by a wonderful portrait of Terrence Tao in The New York Times this week, calling attention to some of Tao’s exceptional work in collaborative math and mathemematical outreach.

But then those feelings were further amplified when this week found me at the LMFDB workshop in Corvallis, Oregon where I am sitting directly at the heart-center of an incredibly cool community math project. So, being here as I am on the front lines, I wanted to share a bit about the process. I’ve written about the LMFDB before, but to recap, it’s an online database of L-functions and “friends.” The database is open source, edited mostly through github and the kind and selfless hearts of so many contributors.

So here we are, 33 mathematicians, 33 laptops, 7 days and an unlimited desire to classify and sort things. On the first day, David Farmer, one of the LMFDB founding fathers asked that we begin by sorting ourselves according to what we felt we could contribute. He then recommended that we start by “pair programming.” Yes, this is when you sit next to someone and write code together on one laptop. Farmer said, “you might think this would cut productivity in half, but on the contrary, it doubles it since fewer errors are made.” So you see: teamwork.

This is how we spend our days, small groups clustered around tables pair programming whatever pieces of the LMFDB has sparked our interest. Some people are adding new sections to the database, perhaps a whole new wing dedicated to modular forms of half integral weight. Other people are working on the exposition of the database, writing concise descriptions of the objects for non-experts nested in knowls on the page. Some people are skimming the database for typos and html errors to make the whole thing more good-looking — seriously, nobody wants to get the L-functions from an ugly website, right?

After spending the entire day making changes and building new things and all the while programming in pairs, we have an end-of-day report. This is when the collaboration really kicks off. Each small group gives a brief recap of what they’ve done, and it is submitted to the jury of 33 for approval. Everything that goes into this database has passed before the community and been the subject of some intense and thoughtful scrutiny, from small changes (like, maybe these query boxes should be left aligned?) to huge ones (like, do you think we should change our entire labeling scheme?) gets a full-blown conversation. So you see: community.

I think the LMFDB project is an interesting example of extreme community collaboration in mathematics, but it is certainly not unique; this sort of community exists around lots of open source software initiatives. And of course this type of intense collaboration can also exist around the good old fashioned doing of mathematics.

Ok, I know what you’re thinking, “why are you telling me all this on a blog about math blogs?” Because, dear reader, I think this is the point of it all. Blogging abut math, and blogging about math blogs, or even blogging about blogging about math blogs (like I’m doing right this second), is all about brining the community together. So while writing about the LMFDB conference is not directly writing about a math blog, it feels like a friend of math blogging. And I think it’s important to remember why we blog about math.

Posted in Number Theory, people in math, Uncategorized | Tagged , , | Leave a comment

PCMI Blog Roundup

Earlier this month, I had the opportunity to give a cross-program talk at PCMI, the Park City Mathematics Institute. I talked about how doing math online can help us reach others in the math community, building bridges between teachers, researchers, and recreational math enthusiasts and reach those who think math isn’t for them. I talked about both social media and blogs as places where online math happens and some suggestions for how to talk about math so other people will listen.

PCMI'ers march in the Park City July 4th (Dimension) Parade. Image: Wendy Menard.

PCMI’ers march in the Park City July 4th (Dimension) Parade. Image: Wendy Menard.

PCMI is really several programs in one. There is a research program with a graduate summer school, a secondary school teachers program, a program for faculty at undergraduate teaching-focused institutions, and an undergraduate summer school. (There might be more, but I think those are the groups I’ve encountered. It is large. It contains multitudes.) When I attended in the past, the instinct was for people to associate with others in their group, but some gentle nudges towards cross-program socialization led to some interesting and fruitful conversations. I think it’s easy to have tunnel vision as a participant in any of the programs, so those nudges really help people make connections and think about the broader math community they belong to. Incidentally, these are two of the things I find most gratifying about doing math online. Programs like PCMI are rare and short; the Internet, for better or worse, is always there. I’d never cross paths with math teachers who live thousands of miles away if I didn’t do it online.

With all that online math talk, I thought it would be nice to share some of the blogs written by this year’s PCMI participants. It turns out the teacher program is one step ahead of me: they keep a list of participants’ blogs here. So I’ll just include a few blogs by the people I met either in person or online during my brief trip up into the mountains.

I was happy to see that my AMS blogging pal Adriana Salerno, who writes PhD Plus Epsilon, was at PCMI this year. She was even kind enough to include my talk in her week one roundup post. While I didn’t get to meet him, I also heard about Dagan Karp, AMS blogger, Harvey Mudd math professor, and leader of the Undergraduate Faculty Program at PCMI.

I got to meet one of my online math pals, Ashli, known to me on Twitter as @mythagon and the author of Learning to Fold. I had lunch with her, Wendy Menard, who writes Her Mathness, and Dylan Kane of Five Twelve Thirteen. Both Menard and Kane blogged about the PCMI teacher program this year. Kane posted about a short talk he gave on the #MTBoS (math twitter blog-o-sphere), a cool online conglomeration of people blogging and tweeting about math and teaching. Later, I met Anne Paoletti Bayna on Twitter, where she shared her math Tumblr, paomaths. Menard and Bayna both blogged/tumbl’d about making conic sections with piles of salt. I’ve never done that before, but there’s a PCMI page about it (pdf). I’ll have to try it.

I really wish I had been able to stay and talk more with other math bloggers at PCMI (and of course see Henry Segerman’s talk on 3D printed geometry the day after mine). If I missed any PCMI blogs, please leave a note in the comments or find me on Twitter. I’d love to connect online, even if we didn’t get to meet face-to-face.

Posted in Math Communication, Math Education | Tagged , , | Leave a comment

Talking ‘Art of Mathematics’ With Its Creators

Left to Right: Volker Ecke, Anna Haensch and Christine von Renesse.

Left to Right: Volker Ecke, Anna Haensch and Christine von Renesse.

This week I was at the Inquiry Based Learning (IBL) Workshop in San Luis Obispo and I had the rare and wonderful occasion to sit down for dinner with a great team of bloggers and get to know them a bit better. That team was Volker Ecke and Christine von Renesse, two of the masterminds behind Discovering the Art of Mathematics (DAoM), an enormous blog, video, and teacher resource network for inquiry based teaching.

Since not everyone just came form an IBL workshop, I’ll give a quick’n’ dirty rundown of what it entails. The general idea is that an IBL classroom is genuinely student-centered, that is to say, the students do almost all of the speaking during class time. Moreover, the students determine the pace and content of each lecture, by uncovering course material through inquiry. This means that eventually, students have the sensation (and ideally the reality!) that they have discovered the entire curriculum on their own. That’s my take-away, but for a better description, check out this from DAoM.

Often, educators reach a point in their evolution where they realize that the traditional lecture format is not getting them the results they desire. For Ecke this realization came early in his career, “When I realized that lecture wasn’t going to work, I thought, well, how else can I structure my class? And IBL was just that!” For von Renesse, who grew up in Germany, teaching in this style came naturally. “I was dying to teach the I was used to in Germany, so I knew I wanted to teach IBL from my background,” she says.

So Ecke and von Renesse, both professors at Westfield State University, teamed up with fellow faculty members Julian Fleron and Phil Hotchkiss to revamp their existing courses at WSU, and in the process created Discovering the Art of Mathematics.

One of the greatest challenges of IBL, say Ecke and von Renesse, is asking the right questions. “How do you make someone discover what they need to discover,” von Renesse says, “it has a lot to do with personality stuff.” The right questions need to be asked of the right student, Ecke says, “A good question is asking `How do I support a student in their struggle.'” The team offers a traveling workshop in which they coach instructors in good question asking. But if you’re curious to see what it might look like, you can watch Ecke guide students in doing the impossible — solving the Rubiks cube.

Of course it’s also important that students ask plenty of questions. Von Renesse addresses this in the blog post “Curiosity — A Culture of Asking Questions.” She discusses the gentle balance that naturally exists between relaxation, curiosity, and anxiety, and how to maintain that in the classroom. The DAoM video library has plenty of great examples of this, but watching von Renesse wrangle directional derivatives with a group of Calc III students is a beautiful example.

It was such a treat to sit down with these bloggers and learn more about their project and their passion for teaching and learning. I’ve only mentioned a small fraction of what you can find on DAoM, there are also e-books, assessment tools, content ideas, and the list goes on. If you’re planning to dip your toe into IBL this fall, I recommend you stop by for some inspiration!

Posted in Uncategorized | 1 Comment

Specifications Grading Redux

An alternative grading system. Image: Sage Ross, via Flickr, h/t Robert Talbert.

An alternative grading system. Image: Sage Ross, via Flickr, h/t Robert Talbert.

Last December, I wrote about specifications grading, an idea I first saw on Robert Talbert’s blog Casting out Nines (Co9s is ending, so you can find new posts at rtalbert.org) and wanted to try out in my class. Talbert has blogged about his experiences using the system a few times; you can read some of his specs grading posts here and the rest here. You can also listen to a Teaching in Higher Ed podcast of Nilson discussing the system. Now that the semester’s over, I wanted to let you know how it went for me as well.

First, a word about the book, Specifications Grading by Linda Nilson. I decided to read it rather than just base my grading scheme on Talbert’s and others’ blog posts about it. I hoped that it would give me some nuts and bolts advice for how to make it work in my class. It did, but I almost put the book down after reading this on page six:

What the faculty reap for their endless hours of grading are more grading protests and conflicts with students than ever before. Of course, the reasons behind this student behavior lie largely in the values and beliefs of the Millennial generation and their parents, such as their consumer attitude toward higher education, their distaste for academic learning and the life of the mind, their alienation from standard teaching methods, and their sense of entitlement to high grades in light of high tuition costs.

I am a Millennial, albeit on the old side, and this broad generalization about my generation rubbed me the wrong way. Aside from the fact that it offended me personally, I had serious qualms about taking classroom management advice from someone with such a negative, adversarial view of students and other people my age, especially someone who would say we have a “distaste for the life of the mind.” I do see some amount of entitlement and a consumer attitude, but I have had almost no students who were not interested in learning something. I’m also not at all convinced that Millennials have these traits to a larger extent than members of any other generations. I mention all this here because I hope that Nilson and other educators with this viewpoint will reconsider the way they think of their students (and some of their colleagues). 

That said, I do think the book has good advice overall, and I like the idea that employing specs grading will make assessment a less adversarial process. I used specifications grading for my math history class this past semester, and it was a mixed success.

Some background on my class: this course gives students a writing credit, so the majority of assessment was based on written work. I had 43 students registered on the first day of class, a slight increase over last semester, and my attrition rate was significantly lower; by the end of the course, I had about 40% more papers to grade than I did last semester. Some of the problems I had implementing my grading scheme and with the semester in general were related to the unexpectedly large size of the class. A writing class with 40 students in it is, at least for me, nearly untenable.

Another complication not related to specifications grading was that I had students turn in most of their work on the course website powered by Canvas and used the grading tool there for the first time. I had two problems: Canvas inexplicably lacks a way to save feedback while you’re writing it but before you want to give it to your student, and it logs you out without saving after a certain amount of time. A few times, I was grading during office hours and had a student visit. By the time I was done with the student, the feedback I was working on was gone. The other problem was that some students could not access the feedback on Canvas. This seemed to be a browser issue on their end, not something I could control, but it threw a serious wrench into getting feedback to them in a timely fashion, especially because they sometimes didn’t realize there was supposed to be more feedback.

I used a blended grading scheme, which Nilson calls a synthetic option in the book. The two major projects (a group project and a research paper) were graded using a fairly traditional writing rubric that produced numerical grades. The average of those two grades determined the final grade with additional requirements for each letter grade. These included a certain number of math homework assignments and blog posts that were graded complete or incomplete, as well as turning in paper and project proposals and a paper draft on time.

I allowed resubmissions of one of the homework assignments because a number of students had more trouble than expected on it, but the rest of the homework assignments were one-shot deals. Students could revise blog posts until they were passing. I tried to have a rule that the next revision had to be finished within a week of my giving feedback on the last revision, but I had trouble enforcing that deadline (see below).

I used Nilson’s suggestion of tokens/free passes to turn in assignments late in the hopes that it would cut down on students begging for extensions. I gave each student a total of three for the semester, and there was no bonus for unused tokens. For most assignments, a pass was a one-class extension, and for blog posts, it was a one-week extension. In general, I think the passes helped, but they didn’t eliminate extension discussions altogether. I don’t know if I just didn’t give students enough free passes or if they should have been able to earn more or if I just need to be less of a pushover.

Because I required assignments to be turned in by a certain date for students to get a certain grade in the course, some assignments became high-stakes. If a blog post wasn’t on time, a student couldn’t get an A; if the rough draft of the final paper wasn’t on time, they couldn’t get a B. I am not used to classes like this where a student can’t do more work to make up for a bad week later, and for that reason I sometimes had trouble enforcing deadlines.

I had trouble giving homework assignments an incomplete grade when they weren’t quite up to the level I wanted but reflected a significant amount of effort. Perhaps next time I could borrow Talbert’s idea of Mastery-Progressing-Novice and allow progressing students to resubmit the work. In my case, I would probably use different labels. Something like Passing-Effort-No effort would better reflect the fact that I want students who try the homework in good faith to get a chance to learn from their mistakes.

In reflecting on the deadline and homework complete/incomplete problems I had, I wonder if part of what made them difficult for me is that in traditionally graded courses, you don’t immediately see the consequences of your actions in your final grade. In reality, people who didn’t turn in the first blog post in last semester’s class were unlikely to get an A, but they didn’t immediately know this. Likewise, people who consistently turned in late assignments or homework that was not high quality would get lower final grades, but the effect didn’t happen immediately.

One of the benefits of specs grading that Nilson mentions is that students can to some extent choose what grade they want. Most of my students were shooting for an A, but some only wanted a B or C and chose the assignments they did accordingly. In the future, I like the idea of having students signal to me what grade they would like in the class so I won’t worry about the students who don’t turn in some early assignments.

On the other hand, sometimes a student did all the complete/incomplete work to get a grade that was higher than the grade their paper and project earned; they did all the assignments required to get an A, but their major assignments were B material. Some of these students felt like the rules had been changed on them, and I wish they hadn’t felt that way. One unfortunate aspect of the schedule of the course was that the traditionally graded work came towards the end of the semester, so students were sometimes unsure of where they stood.

I had students turn in rough drafts of their papers about two weeks before the papers were due. I gave a lot of written feedback on the papers, but I did not return them with a rubric that showed what grade they would have gotten if they had been turned in as final versions. I am sure this would have helped my students, and I will try to do that if I teach a course like this again. I also think Talbert is right on the money when he says that giving students more examples of passing and non-passing work would be helpful.

Another overarching problem was that I don’t think students really bought into the specs grading idea. If I use it again, I might spend some time in class or in assigned reading explicitly talking about how the system works and the advantages it has over traditional points grading. I had a syllabus quiz for my students at the beginning of the semester to make sure they understood how the grading scheme worked, but I think I could have made assessment feel more like a partnership if I had let them know exactly why I thought specs grading would be better for both them and me.

I was curious about how specs grading would affect the final grades in my class. I think they were a bit higher than last semester. Most of this I attribute to students (and myself) having a clearer idea of what work needed to be turned in at what time in order to get the grade they wanted, so there were fewer students who thought they could scramble at the end to make things up. For example, they couldn’t get an A or B without turning in a rough draft of the final paper on time. I required a rough draft last semester as well, but I deducted points from the assignment if they didn’t have one. This semester, I got rough drafts from more students, and I think that improved their final papers substantially. I was somewhat torn by the rough draft requirement; it hurt two students who wrote good papers but hadn’t turned in a draft, but I think it helped more students than it hurt.

If you’ve used specs grading in a math class, I’d be curious to know how it went for you.

Posted in Issues in Higher Education, Math Education | Tagged , , , | 5 Comments

An Ugly Song That Definitely Won’t Get Stuck In Your Head. I Promise.

If you’ve ever had the hook from Call Me Maybe stuck in your head for three days, you know the power of a well-patterend musical hook. It’s these patterns in music that speak to our human brains and often help us differentiate good music from bad, and beautiful from ugly. Patterns, of course, suggest that math is at play, and this is no surprise. The connection between math and music has been well-studied from the geometric ideas of Pythagoras, the symmetries in music, and even music as topology.

What I want to talk about is how to use math to make the ugliest music possible. If patterns register as “beautiful” in our minds, then a completely pattern free tune would be the least beautiful. But to actually compose a totally pattern free piece of music is not an easy feat. Remember, pattern free is distinctly different from random (the latter being relatively easy). An interesting solution to this problem came to us by way of 1950’s work of engineers John P. Costas and Solomon W. Golomb. Costas and Golomb weren’t trying to write ugly music, rather, they were trying to solve a problem in sonar signaling. Turns out the same principles that make an ugly sound also make a great sonar ping. The solution was a combination of the Golomb Ruler, or its multi-dimensional cousin, the Costas array. These tools give a method for generating points that are not random (obviously), but are completely pattern free.

Using these tools, the mathematician Scott Rickard engineered the ugliest song every written. The basic idea is quite clever. Beginning with an 88 by 88 grid, starting in the far left column, he moves along the columns filling in boxes in rows corresponding to powers of 3. So in each column n he marks the 3n-th block. And when the numbers get too big, he reduces them modulo 88. This gives a totally pattern free sequence of points, and hey, also a handy representation of notes on the 88 key piano! He debuts this hideous (yet mathematically clever) opus in TEDx Talk: The Worlds Ugliest Music. You probably won’t be humming the riffs all day, but it’s cool to hear.

The AMS has a great link-roudup of other blogs and videos about math and music, and since it’s still the month of June, find something beautiful to enjoy and have a happy Fête de la Musique!

Posted in Mathematics and the Arts | Tagged , , , , | Leave a comment

Getting Warmer…

I’m currently teaching a summer school for high school students. Our main focus is number theory and its applications to cryptology, but I like to start each morning with some kind of warm-up math puzzle or game. I know plenty of fun math stuff, but I’ve never worked with high schoolers before, so I took to the blogs to find some good activities for that age group. The Internet has almost as many puzzles and games as it has cat pictures, so the sites I’m highlighting here are just the tip of the iceberg.

An element of {cats}∩{math}. Thanks, Internet! Image: Jimmie, via Flickr.

For the first day, I wanted an activity that would get the kids working together a bit and introducing themselves to each other. A bit of searching, I came upon Dan Meyer’spersonality coordinates” activity. Meyer write the must-read math teacher blog dy/dan (which, by the way, I can’t decide how to pronounce, but I suppose that’s the point). His activity had students in a group label themselves on a coordinate axis by how much of two different traits they had. I didn’t use that activity but one I found in the comments: break people up into groups of size 2n and have them come up with yes-or-no questions so that each person in the group has a different set of answers. I only did it with groups of four students, and I had students mix up a couple of times to meet new people and come up with different traits. The next time I use this activity, I will probably ask them to get into groups of eight after playing once or twice in groups of four.

Sam Shah’s blog Continuous Everywhere but Differentiable Nowhere has some nice problems and puzzles, including the sack problem that nerdsniped me a while ago. Math Munch, “a weekly digest of the mathematical internet,” has also been featured on this blog before. It doesn’t just focus on puzzles and games. There’s a strong art component as well, and the curators usually include some web-based interactive activities. Periodically they run interviews with mathematicians, teachers, and artists. I especially enjoyed the Q&A with Carolyn Yackel, who just sounded so enthusiastic about abstract algebra that I wanted to go find some symmetry groups.

A new-to-me blog that’s been a good puzzle source is Math=Love by high school math teacher Sarah Hagan. Don’t tell my students, but I think I’ll be using the 1-4-5 square puzzle challenge next week, and I might talk about happy numbers at some point. Very helpfully, Hagan often includes logistical information about how she made the puzzles or games work in the classroom and ideas to make them go more smoothly in the future. She also shares links to other sites with math games and puzzles Now that I’ve been reading the blog for a few months, I’m a bit embarrassed that I didn’t start reading it earlier. Hagan is very well known in the math teacher blogging world. Aside from the puzzles and games, she shares a lot of helpful tips about running the classroom and reflections on her teaching practices.

Futility Closet isn’t strictly a math blog, but it has tons of fun puzzles. The jeweler’s observation caught my eye recently. Why must every convex polyhedron have at least two faces with the same number of sides? It’s a simple question with a short, clever answer, but I think students will have fun trying to figure it out.

I’ve found some activities in other places as well. Last Thursday, we made a level one Menger sponge using leftover supplies from MegaMenger in October. The students had heard about fractals from a guest speaker earlier in the week, so we talked a little more about how something could have a non-integer dimension and figured out the fractal dimensions of the Cantor set and the Menger sponge. The seven penny game from The Proof and the Pudding by Jim Henle was fun (my review of the book is here), and I’ll be using Matt Parker’s Things to Make and Do in the Fourth Dimension later in the program (see my review here). I might even try to make a domino circuit (pdf), but I’m not sure if I have enough patience or dominoes.

Do you have a favorite source for math puzzles, games, or activities?

Posted in K-12 Mathematics, Math Education, Recreational Mathematics | Tagged , , , , , , | 1 Comment

Happy Deep Fried Torus Day

Last Friday was National Doughnut Day and I hope everyone celebrated accordingly. Aside from being delicious with a cup of coffee, these sweet treats are a great way to think about math. From simple brain teasers to advances in quantum teleportation, this shapely pastry has a lot to offer.

How many doughnuts are in this picture?  What sort of things would you need to know to answer that question?

How many doughnuts are in this picture? What sort of things would you need to know to answer that question?

Let’s start out with something fun. The photo above was popping all over the internet this weekend, and it’s a great way for students to work on their understanding of spatial reasoning and geometry. The math teacher focused site YummyMath guides students through a doughnut inspired estimation exercise, and BedtimeMath gives a series of doughnut questions for all ages. Between doughnut flavors, different toppings, and doughnut holes, there are plenty of questions to be asked!

Of course doughnuts as math objects reached their cultural apex around 2006 with the solution to Poincare’s Conjecture, inspiring the popular joke,

A topologist is a mathematician who can’t tell a coffee cup from a doughnut.

Or its lesser known modification

How many topologists does it take to change a light bulb?
Just one. But what’ll you do with the doughnut?

courtesy of the blog MathJokes4MathyFolks. Even Stephen Colbert got in on the action, smooshing a doughnut on the Colbert Report.

But beyond the fun questions and smooshing of baked goods, the doughnut — or torus as we call it in the biz — plays a very important role in advanced mathematics and physics. The special shape of the torus means that it has a relatively large amount of surface area relative to its size. Compare the torus, for example, to a sphere or a cube. Tori are also special because when you rotate them around a central axis, every point moves. But wait, doesn’t that work on any 3-dimensional shape? Not so fast, think about the sphere-like planet earth, it rotates around the axis through the north and south pole, but this means that points exactly at the north and south pole don’t actually move. This torus is special in this way. If you rotate it around an axis through the “doughnut hole,” then every point moves.

This observation was critical in a recent development of new techniques in quantum teleportation. If you imagine sending encoded pieces of data from one torus to another, the large surface area means there are many more points on which to place the data bits, and the nice axis of rotation makes these pieces easier to encode. The math blog and community forum Mathesia gives a nice down-to-earth explanation in donuts, math, and superdense teleportation of quantum information.

Ok, now I want a doughnut.

Posted in Events, Math Education | Tagged , , , , | Leave a comment

Botanical Mathematicians

When I clicked on a blog post called “Bamboo Mathematicians,” I assumed it would be about the bamboo multiplication table recently cleaned up and analyzed by researchers at Tsinghua University in Beijing. Those bamboo strips, dating from approximately 305 BCE, contain the oldest known base 10 multiplication table.

A forest of mathematicians. Image: JFXie, via Flickr.

A forest of mathematicians. Image: JFXie, via Flickr.

But the “Bamboo Mathematicians” I clicked on was a post by Carl Zimmer, a science writer who specializes in biology and evolution, about bamboo plants with decades-long flowering cycles. He reports that researchers have developed mathematical models that explain how a bamboo forest ends up synchronizing to these long cycles. The main idea is that if some plants mutate to have a flowering cycle that is an integral multiple of the dominant flowering cycle, they will tend to outcompete the shorter-cycled plants. Over time, this has led to plants with 32-, 60-, and 120-year cycles, all products of small primes.

On the other hand, periodical cicadas favor larger primes: 13 and 17.This year, broods of both 13- and 17-year cicadas are scheduled to appear in the midwest and southeast US. Cicada Mania reports that they have started emerging in Illinois and should be around for about a month. The cicadas and the bamboo have long life cycles for similar reasons: by appearing at once, they flood the market, so to speak—their predators can’t eat all of them, so the species has a better chance of survival. Steve Mould has a nice Numberphile video about this predator satiation strategy. It’s interesting that the cicadas’ survival strategy led to (relatively) large prime numbers while the bamboo ended up with composite numbers with small prime factors. It’s interesting to think about the evolutionary factors that may have contributed to that difference.

Bamboo isn’t the only mathematical plant. Two years ago, there was a flurry of articles claiming that plants do math when they change their starch consumption at night. The Aperiodical mentioned it, and Christina Agapakis had a nice post about it at her blog, Oscillator

The plants in question aren’t spitting out numerical answers to word problems on their leaves, but doing normal plant stuff: using energy stored as starch at different rates depending on environmental conditions. Plants get their energy from sunlight, so at night the rate of starch consumption has to be smooth in order to maintain energy until dawn and prevent a “sugar crash.” The researchers found in a previous study that that plants will consume their starch almost completely every night and that the rate of consumption will stay mostly constant after “sunset,” regardless of whether the lights go out earlier or later than the plant “expects” based on their circadian rhythm. Based on these results, the researchers proposed a mathematical model whereby the plants are “dividing” the level of starch stores by the number of hours until dawn in order to determine the proper rate of consumption.

So plants can multiply, at least by small numbers, and divide! I wonder what other mathematical tasks they’ve been doing in secret.

Posted in Applied Math, Biomath | Tagged , , , , , , | Leave a comment

How To Optimize Summer Travel And Not Get Blown Up

The only thing more fun than traveling to a math conference is optimizing the route you'll take to get to it. Photo Jo@net via Flickr

The only thing more fun than traveling to a math conference is optimizing the route you’ll take to get there. Photo: Jo@net via Flickr

Every year I promise myself that I’ll just stay in one place for the summer, and every year that simply doesn’t happen. Today I’m posting from CIRM in Marseille, France. Next week I’m headed to Hong Kong to visit with a collaborator, and eventually will make my way back to the US for an IBL workshop in San Luis Obispo, CA, a conference to work on the LMFDB in Portland, OR, and MAA MathFest in Washington, D.C.. (I know, so many acronyms, life is tough.) All of this has gotten me thinking about the fun mathematical questions that come up in transportation and travel.

For travel by car, Laura McLay has some great posts on her blog Punk Rock Operations Research. She talks about the some statistics behind traffic jams, and why women are more likely to cause congestion (it’s not because we’re worse drivers, so wipe that smirk off your face). How to use Operations Research to optimize your search for a parking space. And in one post she answers that question we’ve all had at some point: how likely are you to actually blow yourself up pumping gas? (Not very.)

In OR By the Beach, Tallys Yunes blogs about traveling by air, discussing the apparent strategy behind the unrelenting and seemingly arbitrary gate changes at airports. Is there a better way to do this? In a similar turn, Michael Trick’s Operations Research Blog laments the annoying practice of overbooking hotels and discusses a more quantified approach to accommodating guests.

One undeniable downside of so much travel is the resulting carbon footprint. Particia Randall, who blogs for Reflections on Operations Research, writes about optimizing carbon emissions for her corporate clients. And while you are likely not bringing any sort of payload with you to your summer conferences, it is a good way to think about your own carbon footprint.

Do you have some favorite OR or transportation math blogs? Tweet them at me @extremefriday, I’d love to hear what you’ve got.

Posted in Recreational Mathematics | Tagged , , , , , , , | Leave a comment

Money, Money, Money

Ben Bernanke is blogging. (For some reason I find that funny: former Federal Reserve chairmen— they’re just like us!) In March, he started a blog at the Brookings Institution website. Several of the early posts are about explaining (and defending) the Fed’s low interest rates. He includes a response by Larry Summers to a post about “secular stagnation.” I think it would be interesting to see more different viewpoints on the blog.

Money. Image: Nick Eres, via flickr.

Money. Image: Nick Eres, via flickr.

Like many mathematicians, I have some of the tools to understand finance and economics, but I’m naive about both subjects. After reading some of Bernanke’s blog, I wanted to look at some math blogs that focus on finance. I’ve had the Mathematical Investor in my feed for a while. It’s written by David H. Bailey, Jonathan M. Borwein, Marcos Lopez de Prado, and Qiji Jim Zhu and is a result of their “growing concern with the usage of less-than-fully rigorous mathematical and statistical methodologies in the financial/investment world.”

Recent posts have been about the 2010 “flash crash,” conflicted financial advice, and an assessment of 2014 market predictions. The authors are especially concerned about “backtest overfitting,” which is basically the error of making investment decisions that are based too heavily on historical data; one of their posts announces an online tool that demonstrates the problem.

Cathy O’Neil is my other main source of blog posts about finance, and I’m eagerly awaiting Weapons of Math Destruction, her forthcoming book about big data and the dangers it poses to democracy.

I poked around for some other financial math blogs and stumbled on Fermat’s Last Spreadsheet, a blog that hasn’t been updated in a while but has posts on coding, normal subgroups, and poker in addition to the main focus on fixed-income trading. Fermat’s Last Spreadsheet also introduced me to Magic, Maths and Money by Timothy Johnson of Heriot-Watt University. He concentrates on moral/ethical aspects of finance and the recent financial crisis.

Do you have any recommendations for financial math blogs?

Posted in Applied Math | Tagged , , | 1 Comment