Archive for November 2010
As a newly minted PhD in mathematics, you probably enjoy doing mathematics. For many people this means traditional scholarship and publication. But another natural consequence of loving your discipline is the desire to tell others about it. For some of us, this takes the form of teaching at schools that focus on educating undergraduates. It’s appealing to share the beauty of the subject with talented students who are experiencing it for the first time, and maybe turn some of them on to mathematics.
This article is directed to recent PhDs who are looking for positions at undergraduate-focused schools; it is based on my 17 years of experience in helping select and interview candidates for faculty positions at the Rose-Hulman Institute of Technology. One important thing I’ve observed is that the kind of application that will get you a position at a tier-one research school might not get you in the door at a school that focuses on undergraduates. In a short article, I can’t tell you everything you might need to know, but I can highlight the salient differences between jobs of this type and more research-oriented positions, and ways in which your application should reflect this.
In recent years, as Jim Crowley reports in the accompanying article, newly formed SIAM sections have been located exclusively outside North America. The much more numerous student chapters, by contrast, continue to crop up worldwide, although 9 of the total of 83 active chapters are outside North America.
Brief reports from a few of the nine:
The Colombia chapter at Universidad Nacional de Colombia actually preceded the new SIAM section in Colombia; Gerard Olivar Tost, leader of the effort to form the section, is the faculty adviser.
Representing the Edinburgh chapter (Heriot-Watt University and the University of Edinburgh) at the student breakfast in Pittsburgh during this year’s SIAM Annual Meeting, chapter vice president Bubacarr Bah (pictured) described the group’s inaugural conference, where student talks were interspersed with talks by high-profile speakers from the UK. Bah gave talks both at the student conference (“Random Matrix Theory in Compressed Sensing”) and, as a recipient of a SIAM Student Paper Prize, at the SIAM meeting (“Improved Restricted Isometry Bounds for Gaussian Matrices,” with co-author Jared Tanner, a faculty adviser of the chapter).
In a piece titled “Expand Your Professional-skills Training,” Science magazine offered online career advice to young professionals, identifying the SIAM chapter at Oxford University as an example of “progams that foster initiative.”
Interviewed for the piece, chapter president Hermes Gadelha, a doctoral student in mathematical biology, described the group’s fund-raising efforts. In approaching prospective industrial sponsors, he said, the students have learned to emphasize benefits to the sponsors, including opportunities to gain exposure and be linked to the university. Mainly, he pointed out, sponsors are looking for “the chance to recruit students.” The students’ insights paid off: They recently secured more than $6000 from industry, supplementing contributions from the Mathematical Institute at Oxford and from SIAM.
Gadelha, who plans on an academic career, said that “the chapter is important for my research connections.” As a result of his experience in managing chapter activities, he concluded, he felt “much more prepared for an interview for a job.”
Finally, as predicted by David Keyes, KAUST, the King Abdullah University of Science and Technology, in Saudi Arabia, is the home of a (brand new) SIAM chapter.
Recently, a fresh look at how computer predictions are made has combined with several old philosophical ideas to bring about a revolution in computational science. The resulting panorama of formidable new challenges and research opportunities have to do with what computer models were always intended to do: make predictions of physical reality. Today, however, the phenomena and processes we ask computer models to predict are of enormous importance to critical decisions that affect our welfare and security—concerning, for example, climate change, the performance of energy and defense systems, the biology of diseases, and the outcome of medical procedures. With such high stakes, we must insist that the predictions include concrete, quantifiable measures of uncertainty. In other words, we must know how good the predictions are. The term “predictive simulation” has thus taken on a special meaning: the systematic treatment of model and data uncertainties and their propagation through a computational model to produce predictions of quantities of interest with quantified uncertainty.
By Jim W. Evans
Thin film deposition on semiconductor surfaces underlies microelectronics fabrication technologies. Indeed, it was the promise of the solid-state electronics revolution in the early 1950s that in large part drove the development of modern ultra-high-vacuum (UHV) surface science in the 60s and 70s. Offering additional motivation was the potential of modern surface science to provide a fundamental understanding of catalytic processes on metal surfaces and films. These developments not only enabled the study of surfaces and thin films in well-controlled contaminant-free environments, but also led to a host of experimental probes, including surface-sensitive diffraction for characterizing thin film morphologies in reciprocal space. The 1980s saw additional dramatic advances, with the development of high-resolution scanning probe and electron microscopes capable of providing real-space images of film morphologies down to the nanometer or even atomic scale (for scanning tunneling microscopy).
Communicating Science: Professional, Popular, Literary. By Nicholas Russell, Cambridge University Press, Cambridge, UK, 2010, 348 pages, $99.00 (hardcover), $31.99 (paperback).
A writer of whatever sort produces a piece of text. Who are the target readers? The writer may have some group in mind: family members, people madly in love with the sport of curling, dinosaur buffs, or even the entire “literate public.” Then again, with no specific target in mind, the writer may simply be responding to an inner itch to write.
How will the text be aired or made public? As a Letter to the Editor, as a reprint in the famous Everyman’s Library, as an article in the International Journal of Entropographics? The writer may post it on the Internet, a medium considered the modern Forum Romanum by some, the Black Hole of Communication by others.
What can the writer do to ensure that the targeted readers will understand what he/she has written? Oversimplify? Painfully spell out the major lines of the argument? Resort to the coded and specialized vocabulary of the targeted group? Provide a plentiful accompaniment of interactive pictorial possibilities? Include an interview of an entropographical maven by a journalist? While the problems of communication may be multiple, they have been no bar to verbosity. Cisco estimates Internet traffic for 2009 at 14 × 1018 bits/month.
Paralleling the sensible, useful, and famous Elements of Style of William Strunk and E.B. White, Nicholas Russell, emeritus reader in science communication at Imperial College London, gives us Seven Commandments, seven “thou shalt nots” to be followed by authors wishing to produce easy scientific reading: Thou shalt not use or create (1) interlocking definitions, (2) technical taxonomies, (3) special expressions, (4) lexical density, (5) syntactic ambiguity, (6) grammatical metaphors, or (7) semantic discontinuity. Because I had only a vague idea of what these expressions mean, I appreciated Russell’s singling them out for detailed elaboration accompanied by examples.
Barry A. Cipra
From climate modeling to materials science, many of the modern applications of mathematics share an analytic challenge that goes back decades, if not centuries: the need to parlay finite data sets into continuous functions with some semblance of smoothness. Atmospheric pressure, for example, needs at least one derivative to fit sensibly into the Navier–Stokes equations. How best to do this—and, in some settings, whether it can be done at all—has been a long-running question. But as Charles Fefferman of Princeton University explained in an invited presentation at this year’s SIAM Annual Meeting in Pittsburgh, there is now a firm theoretical basis for best-possible practice in smooth interpolation. There’s only one catch: The theory, for now, produces algorithms that are wildly impractical.
Read more: 1841
In recent years the Painlevé equations, particularly the six Painlevé transcendents PI, . . . , PVI, have emerged as the core of modern special function theory. Much as the classic special functions of the 18th and 19th centuries—such as the Bessel functions, the Airy function, the Legendre functions, the hypergeometric functions–were recognized and developed in response to problems of the day in electromagnetism, acoustics, hydrodynamics, elasticity and many other areas, the new Painlevé functions started to appear in applications around the middle of the 20th century, as science and engineering continued to expand in new directions. The list of problems now known to be described by the Painlevé equations is large, varied, and rapidly expanding. At one end is the scattering of neutrons off heavy nuclei and at the other, the statistics of the zeros of the Riemann zeta function on the critical line Re (z) = 1/2. And in between, amongst many others, are random matrix theory, the asymptotic theory of orthogonal polynomials, self-similar solutions of integrable equations, such combinatorial problems as Ulam’s longest increasing subsequence problem, tiling problems, multivariate statistics in the important asymptotic regime in which the number of variables and the number of samples are comparable and large, and random growth problems.
Over the years, the properties of the classic special functions–algebraic, analytical, asymptotic, and numerical–have been organized and tabulated in various handbooks, such as the Bateman Project and the National Bureau of Standards Handbook of Mathematical Functions, edited by Abramowitz and Stegun. What is needed now is a comparable organization and tabulation of those properties for the Painlevé functions. We invite interested parties in the scientific community at large to help in the development of such a “Painlevé project.”
Although the Painlevé equations are non-linear, much is already known about their solutions (known collectively as “Painlevé functions”), particularly their algebraic, analytical, and asymptotic properties. This is so because the equations are integrable, in the sense that they have a Lax pair and also a Riemann–Hilbert representation from which the asymptotic behavior of the solutions can be inferred using the nonlinear steepest-descent method. The numerical analysis of the equations is less developed and presents novel challenges: In particular, in contrast to the classic special functions, where the linearity of the equations greatly simplifies the situation, each problem for the nonlinear Painlevé equations arises essentially anew.
As a first step in the Painlevé Project, we have established an e-site, maintained at the National Institute of Standards and Technology, to which interested readers are invited to send: (1) pointers to new work on the theory of the Painlevé equations–algebraic, analytical, asymptotic, or numerical; (2) pointers to new applications of the Painlevé equations; (3) suggestions for possible new applications of the Painlevé equations; and (4) requests for specific information about the Painlevé equations.
The e-site will work as follows: (1) You must be a “subscriber” to post messages to the e-site. To become a subscriber, send e-mail to firstname.lastname@example.org. (2) To post a message after becoming a subscriber, send e-mail to PainleveProject@nist.gov. The message will be forwarded to every subscriber. (3) The complete archive of posted messages can be found at http://cio.nist.gov/esd/emaildir/lists/painleveproject/threads.html. Access to this archive is not limited to subscribers. (4) For the complete list of subscribers, see http://cio.nist.gov/esd/emaildir/lists/painleveproject/subscribers.html. Again, the list can be viewed by anyone.
Depending on the response to this appeal, we plan to set up a wiki for the Painlevé equations and, ultimately, a comprehensive handbook along the lines of the hyperlinked version (http://dlmf.nist.gov) of the new NIST Handbook of Mathematical Functions, edited by Olver, Lozier, Boisvert, and Clark and published by Cambridge University Press. Incidentally, this work contains, for the first time, a chapter on the Painlevé equations.—F. Bornemann, P. Clarkson, P. Deift, A. Edelman, A. Its, and D. Lozier.
Talk of the Society
SIAM has a rich tradition of regional sections, reaching all the way back to the years immediately after its founding. While the sections in the early years tended to be fairly local, those created more recently have been outside North America. It is in this new tradition that the Board of Trustees, at its July 2010 meeting, approved the creation of a new SIAM section in Colombia. The second SIAM section in South America, it complements the active section created in Argentina in 2006. Quiz question: What was SIAM’s first international section? (The Colombia section plans to conduct regular regional conferences within the country. SIAM welcomes its newest section and thanks Gerard Olivar Tost for his efforts in organizing it!
The trend toward increasing numbers of sections outside North America demonstrates the globalization of applied mathematics research. Of course, research in applied mathematics was never confined to North America—many countries around the world, especially Japan and western European countries—have long-established programs in applied and computational mathematics. But in recent years we have seen worldwide growth in research in our discipline. One interesting bit of evidence can be found in the changing distribution of papers in SIAM journals by country or region (classified by corresponding author).
In 1999, the U.S. accounted for about 44% of all SIAM journal papers. While the number of papers from the U.S. grew in the course of the subsequent decade, the percentage fell to 33% in 2009. (These figures do not include TVP, the Russian applied probability journal we publish in translation, or SIAM Review.) During the same period, the percentage of papers from western Europe increased, from 35% to 42%. Other countries, most notably China, while still relatively small in terms of total numbers of SIAM journal papers, show tremendous growth rates and will undoubtedly become major contributors in future years.
SIAM conferences haven’t been left out of this trend toward globalization. A glance at the SIAM conference calendar reveals that our activity groups increasingly opt to hold conferences outside North America. The major international conference in our discipline, of course, is the quadrennial International Congress on Industrial and Applied Mathematics; the next one will be held in Vancouver, BC, Canada, July 18-22, 2011. The program is taking shape, and we encourage the community to participate. (Keep in mind that in favor of ICIAM, we will not have a SIAM Annual Meeting in 2011. On a sad note, I mention the recent death of Jerry Marsden, co-chair (with Ivar Ekeland) of the ICIAM 2011 Scientific Program Committee. His unflagging efforts, along with those of Ekeland and the rest of the committee, have produced an outstanding scientific program.
I draw your attention to one further item from the July meetings of the SIAM Council and Board: The governing bodies approved the creation of a new activity group in uncertainty quantification, or UQ. The group is now in the process of putting together documents describing how it will operate. Briefly, the intention is that activities of SIAG/UQ will complement those of the American Statistical Association and will bring together computational scientists, modelers, and statisticians interested in UQ. SAMSI, the NSF-sponsored Statistical and Applied Mathematical Sciences Institute, also plans a program in this area in 2011. Readers interested in the subject will want to read the insightful article on UQ, V and V, and prediction science in general by Tinsley Oden, Robert Moser, and Omar Ghattas in this issue.
One final item: The Board on Mathematical Sciences and Their Applications has initiated a study, “Math 2025,” in preparation for a report on research opportunities and trends in the mathematical sciences that could prove influential for those making decisions about our field.
Answer to quiz question: The first international section of SIAM, formed in 1974, was the now-inactive Pacific Northwest Section, which included two Canadian provinces—Alberta and British Columbia—along with the states of Idaho, Montana, Oregon, and Washington. In recent years, all the new SIAM sections have been located outside the U.S., beginning with the United Kingdom and Republic of Ireland SIAM Section, which was followed by the East Asia Section and, most recently, the Bulgaria Section and the South American sections in Argentina and Colombia.
The statement “As a rule, you must be a U.S. citizen to work at a national lab” (“A Career in the Math Sciences at a National Lab,” SIAM News, October 2010, ) merits some clarification. Foreign nationals interested in jobs at national labs should be aware that some Department of Energy labs (e.g., Livermore, Los Alamos, and Sandia) require U.S. citizenship. Many other DOE labs—including Argonne, Oak Ridge, Berkeley, Pacific Northwest, Brookhaven, and Idaho—do not. As suggested in the article, readers interested in opportunities at any lab should check that lab’s requirements.