ICERMania   

2computers

Chris Rasmussen, Alejandra Alvarado, Angelos Koutsianas, and Mckenzie West working hard at ICERM in January.  As Mckenzie demonstrates, sometimes it just takes two computers to get a job done.

*What do you with six mathematicians, spread across the world, who all want to solve the same problem but have never all been in the same room?  If that problem involves computational or experimental mathematics, one great answer is Collaborate@ICERM.

ICERM is the Institute for Computational and Experimental Research in Mathematics, associated with Brown University in Providence, RI.  It is the newest of the eight NSF-funded Mathematical Institutes, and like many of the others it runs semester-length thematic programs and large workshops throughout the year.  However, ICERM also has a program for small groups to apply for funding to meet at the Institute to collaborate on projects that are in line with the Institute’s mission, which is “to support and broaden the relationship between mathematics and computation and, specifically, to expand the use of computational and experimental methods in mathematics, to support theoretical advances related to computation, and to address problems posed by the existence and use of the computer through mathematical tools, research and innovation.”  Collaborate@ICERM takes applications from groups of 3–6 people to meet at ICERM during the summer or over winter break.  The American Institute of Mathematics has a similar program in SQuaREs.

Christelle Vincent and Mckenzie West fixing something major during a collaboration at ICERM.

Christelle Vincent and Mckenzie West fixing something major during a collaboration at ICERM.

My collaborator Chris Rasmussen and I found ourselves in the above-described situation.[ii]  We had started working on a project in 2012, one component of which forced us to write code to solve the equation x+y=1, where x and y are S-units in a number field K.  In simple terms, S is a set that contains some primes of K, and the S-units are just the elements of K generated by these primes, their inverses, and the units of the field.  So the {2,3}-units of the rational numbers are just the set of positive and negative fractions that only involve powers of 2 and 3.  In this world, (1/3, 2/3) is a solution to the equation.  By Alan Baker’s work, it turns out that there are only finitely many solutions for any given K and S, and their size can be bounded, a fact that leads to may interesting finiteness results in number theory.  Often, enumerative problems rely on actually finding all of the solutions for a given number field, a problem referred to as “solving the S-unit equation”.  This is a difficult computational problem, involving work of Baker and Wustholz, Smart, De Weger, and many others.  In our project, Chris and I wrote code in SageMath (also known as Sage) to solve the S-unit equation in the fields we needed, which meant that we didn’t need to implement all parts of the general method.  We wanted to generalize our code and incorporate it into future distributions of Sage so that others did not have to repeat our suffering.  I led a group at a Sage Days workshop in 2014 to start this implementation.  The group, Alejandra Alvarado, Christelle Vincent, McKenzie West and I, made some progress, but didn’t get to the most difficult parts of the generalization.  We planned to work on it after the workshop but made no progress–it was nobody’s primary focus and we were all spread out across the country.  In spring 2016, Chris and I heard about the Collaborate@ICERM program and put in an application.  We had just heard that our proposal was accepted when Christelle came into contact with Angelos Koutsianas, a recent PhD from Warwick who had also needed to solve some special cases of the S-unit equation for his thesis project.  He also had Sage code that did a big part, but not all, of the general method.  Talking to Angelos, we realized that between the two projects there was a complete implementation—we just needed to bring it all together!  We were luckily able to add Angelos to the ICERM group, and he was luckily available for the week we’d chosen in January.

Christelle Vincent, Angelos Koutsianas, me, Chris Ramsussen, Mckenzie West, and Alejandra Alvarado

Christelle Vincent, Angelos Koutsianas, me, Chris Ramsussen, Mckenzie West, and Alejandra Alvarado

So that’s how it happened that the six of us came to Providence in early January, all having worked on this same difficult problem but never having been in the same room before.  First of all, it was a joy to meet Angelos, who had been working mostly on his own on essentially the same problem as Chris and I, and so had dealt with many of the same confusions and difficulties that we had faced.  How great to meet someone who has shared the same extremely obscure forms of suffering!  We often found ourselves laughing out loud at a shared aggravation with a strangely phrased passage of a source paper.  And it was wonderful to work with everybody else again—I love this group!  We all bring different skills to the work, and everybody has something very important to contribute.  This project would not have been as successful if any one of us had been missing.  And, given that we came from Oregon, Illinois, Vermont, Connecticut, Pennsylvania, and the Netherlands/Greece, this never would have happened without the support of ICERM.

So this whole blog post is in some ways a giant thank you to ICERM.  They did everything possible to support us, beginning with an application process in which we were helped directly both by the previous director Jill Pipher and the current director Brendan Hassett.  The staff at ICERM are extremely helpful and the facilities are world-class. ICERM gave us offices and let us use the entire space for the week our collaboration, as well as installing Sage on the computers for us.  ICERM has great technological resources at its disposal, as befits an institute focused on computation and experimentation.  They arranged for us to go out to a “conference dinner”.  On top of it all, the place is beautiful.  ICERM takes up the top two floors of a building beside the river in downtown Providence.  Three walls of the lecture hall and some walls in other parts of the facility are enormous floor to ceiling windows looking out over the town.  I gave an introductory talk to the group in this lecture hall and it felt like I was in a movie or something.

Chris giving a talk in the amazing lecture hall.  This photo does not do it justice, but at least you can see the crazy glass wall whiteboards.

Chris giving a talk in the amazing lecture hall. This photo does not do it justice, but at least you can see the crazy glass wall whiteboards.

Workshop dinner!

Workshop dinner!

In the end we didn’t need advanced computing resources as much as we just needed to be in the same room.  After we all got reacquainted with the project, we brainstormed tasks and made a wall of post-it notes to organize our efforts.  Then everybody chose projects from the wall and we got started.  Of course things didn’t go entirely as planned—several days of work in translating some code into a lower-level language in hopes of speeding it up actually ended up slowing it down (!!).  There were annoying bugs, like an inexplicable clash of data types that had to be fixed in every tiny part of the code.  We worked hard all week, hoping to have a complete working function by 4:30 on Friday, when our friend and expert in the field Bjorn Poonen was planning to stop by and see our progress.  When Bjorn arrived we were really close, but hadn’t quite assembled everything.  We were tired and hungry and bummed that we didn’t have anything to show, but victory was too close to give up, so we went back to work.  Two hours later we were done.  We chose a field, and a set of primes, hit enter, and it worked! Bjorn had been hanging out working on an index for his book, so we even got to show off our function. Victory!  Celebration!!  Then we all headed out for pretzels and beer.

Mckenzie West, Christelle Vincent, Bjorn Poonen, Alejandra Alvarado, and Angelos Koutsianas

Mckenzie West, Christelle Vincent, Bjorn Poonen, Alejandra Alvarado, and Angelos Koutsianas.  Thanks for cheering us on, Bjorn!

This collaboration was a tremendously positive experience for me, and we produced something that will be useful for a lot of other people.  A victory all around.  However, it did bring up the question of how much the rest of the mathematical world (like, say, a tenure committee) will care that we created this implementation.  We are very proud of our work, and I will list the code as a product on my CV, but will it “count” in the same way that a paper would?  I have talked to several computational mathematicians who have been frustrated that their computational and implementation work is not measurable in the same way that other mathematical work might be.  Our group decided to look into journals that publish articles on interesting and substantial implementations.  There seem to be a few possibilities, but it is hard to find a good fit for work like this.  (Which brings me to something I plan to write about next time—what journals are out there for work that is a little different from the norm, or that are especially friendly for early career people?)  Whether we find a venue to publish the code or not, we should be submitting it soon for review to be eventually incorporated into SageMath.  So I’ll just make a pitch right here—check upcoming Sage releases for the awesome function solve_S_unit_equation(K, S)!!  Um, just don’t make S too big, or you might be waiting a while.  I mean it works, but come on, we’re not miracle workers.

What experiences have you had collaborating at an institute?  Are there any other programs that you would suggest for collaborations like this?  Let us know in the comments!


[*] A note on the title: Okay, I guess a second institute-mania post is starting a dangerous trend.  Now I will have to try to visit all the math institutes and come up with some kind of mania theme.  For MSRI I will have to do some crossword style title, and who knows where that will lead…

[ii] Long paragraph about how we got there follows—feel free to skip on if you just want to hear about how awesome ICERM is.

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Evernote: My External Brain

A few notes with the linear algebra tag, as seen on the mobile interface

A few notes with the linear algebra tag

As we slide in to the new year, with resolutions to finally get organized, I wanted to share a quick tool that’s really helped me: Evernote. I know this is going to sound like some kind of paid promotion. I promise you it’s not. I’m just so genuinely thankful that I finally found an easy way to keep track of everything I need.

Evernote is my collection of bookmarks, important documents, and random lists and notes all in one place. It’s where I store papers I’ve been meaning to read or ones to reference, links for things I want to try out in classes, ideas for math tea activities, and all the music and books that people tell me to check out. As a person with a fairly limited long-term memory, Evernote is a lifesaver.

Evernote is an application for both desktop and mobile interfaces. You can type straight into it, send photos to it with your phone camera, forward emails to it, or clip websites into it from a browser extension. It’ll take video and audio notes too. Whenever I bump into something I might want to remember or use later, I dump it into a note.

What sets it apart from just a bookmark list is that every note is tagged and searchable. So when I’m working on getting a course ready, I don’t even have to remember the things I wanted to try out. I can just search for the tag for, say, linear algebra, and everything will pop up.

Notes can be shared with collaborators, which is nice for departments, research groups, or just keeping a shared family grocery list. I’m also a big fan of the scanner feature, that lets me scan documents in straight from my phone. Sometimes when students are presenting work on a document camera, I’ll scan it in to Evernote quickly and email it on to the class so they can have a copy to look at. It even makes scanned documents searchable, but it still seems a little shaky on my handwriting (which is completely understandable).

Other people have developed very specific ways to use Evernote to manage to do lists and create elaborate systems to manage their tasks. But they’re all too fiddly for me. I just keep a running set of tags: each course I might teach has one, as well as all my different research interests, hobbies, and projects. It’s possible to organize your notes into little folders called stacks, but I really don’t bother. The tags are enough for me.

So if you’ve got a neglected bookmarks folder, a stack of old post-it reminders, and a few random notes in your phone that you’d like to consolidate, give it a shot. And if have a tip for how you use Evernote, or if you prefer a different application, let me know in the comments.

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Math-tivism

Getting involved with causes I care about is a more realistic new year's resolution than changing any of my bad habits. Here's a blast from the past from xkcd.com. Wise mouseover text:

Getting involved with causes I care about is a more realistic new year’s resolution than changing any of my bad habits. Here’s a blast from the past from xkcd.com. Wise mouseover text: “If at first you don’t succeed, that’s one data point.”   

Mathematicians have a super power: problem-solving. This power must be good for more than wowing our students with trig substitution. Lately I have run into some inspiring examples of mathematicians working to help address some bigger problems in the larger world. I’m sharing these this week in PhD+Epsilon because I know a lot of early-career mathematicians care about these issues. Also, my experience is that it can be hard to figure out how to engage when you might be consumed by the wonders and horrors job market, isolated and overwhelmed in a new job, or, say, freaking out about creating your third-year review portfolio or tenure dossier. So here are some worthwhile math-centered, mathematician-created initiatives that help solve problems you really care about, and manageable ways you can get involved to contribute or connect with other math people who feel the same.

Equal Opportunity for Women and Girls: Girls’ Angle is a non-profit math club with a mission “To foster and nurture girls’ interest in mathematics and empower them to be able to tackle any field no matter the level of mathematical sophistication.” Girls’ Angle began in 2007 when founder Ken Fan began noticing a systemic bias against girls in math education. He says, “the more I thought about it, the more I came to see that the way math is generally taught in the US is biased against girls for a variety of reasons, some more subtle than others. I saw many Math Circles sprouting up, but most were coed, and I didn’t see any program just for girls, run by mathematicians, where girls could keep coming back for more math. So that’s how Girls’ Angle started.” The organization runs a weekly club for Cambridge-area girls, and has hosted over 80 Math Collaborations across a wider geographical region. These are alternatives to math competitions in which groups of girls work together to solve substantial mathematical problems. Girls’ Angle also produces a Bulletin with articles about mathematics for middle school to high school students, girls in particular. I recently had the opportunity to contribute an article to the Girls’ Angle Bulletin, and it was incredibly fun to write for this special audience. The bulletin is seeking articles on real math, aimed at a math-enthusiastic middle/high school audience, written by active researchers and scientists. According to Ken, “All kinds of formats are welcome, including experimental ones, but the 2 things we reject are a patronizing tone and the watering down of the math. (It’s fine to address basic math, so long as it isn’t over-simplified.)” The Bulletin even pays for articles that are used. If you are a woman who will be in the Cambridge area, another way to get involved with Girls’ Angle is to make a Support Network Visit. Support Network visitors are “professional women who use math in their work in some vital way and visit the club to show the girls how and for what they use math.  They serve as role models and give members another reason to study math.”

To learn more, submit an article, or volunteer to make a visit, contact Ken Fan at girlsangle@gmail.com.

Environment and Climate Change: Every time I buy a plane ticket to attend some amazing but far-flung math conference, my conscience cries out that I am doing more than my share to contribute to climate change, and that it’s my fault that polar bears are losing their homes. Thinking about her own sabbatical travel, my former advisor Rachel Pries created Math People for the Planet, a Facebook Group (I’m not on Facebook, but you should join!) for mathematicians to “start a discussion about how the math community can reduce its carbon emissions while maintaining the vibrant discussions at conferences.” The JMM is the perfect place to begin: Anne Ho and Melody Alsaker have put together a simple slide that you can add to your JMM talk to start a conversation about climate change and how mathematicians can help. Rachel also started a Sierra Club Group to pool donations from mathematicians. The money goes to the Sierra Club group on International Climate and Energy http://www.sierraclub.org/international. Donations through Dec 31 are doubled by an anonymous donor. Also at the JMM, check out the MAA Invited Paper Session on Role of Modeling & Understanding Environmental Risks on Wednesday afternoon, which was organized by Ben Fusaro and features many talks on climate change and environmental issues.

Social Justice: I believe that the mathematics classroom can be at the center of the social justice movement. However, figuring out exactly how to bring this together with meaningful, substantive classroom activities can be daunting. Luckily, other people have done a lot of work on this. This is the focus of a special session at the JMM: the MAA Special Session on Intertwining Mathematics with Social Justice in the Classroom, taking place all day on Saturday, January 7. This session was organized by Catherine Buell, Zeynep Teymuroglu, Joanna Wares, and Carl Yerger, and has talks that can help if you are looking to create your own math and social justice course, or simply include social justice topics in the courses you teach already. If you’re not going to the JMM, here are some websites that can get you started from home: Radical Math, Dave Kung’s Social Justice Page, Daryll Yong’s “Social Justice Equity: STEM and Beyond” Reading List.

What other math-centered activism is out there? How can we get connected with others who want to make change in the world? Let me know in the comments!

P.S. I won’t be posting in January, since I’m using up all of my blogging mojo writing about the Joint Mathematics Meetings, January 4-7 in Atlanta GA. Check out the JMM blog, where I will be writing (with some other amazing bloggers!!) about all things JMM, including some of these activities.

P.P.S. Also, can I just share some more math New Year’s resolutions from Math with Bad Drawings?

 

 

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