Posts Tagged ‘mathematics’
Institute for Computational and Experimental Research in Mathematics Workshop: Heterostructured Nanocrystalline Materials
May 30–June 1, 2012
Providence, Rhode Island
The theme of this workshop (http://icerm.brown.edu/tw12-3-hnm) is the computation, modeling, and mathematical analysis of heterostructured nanocrystalline materials. This includes quantum dots, nanowires, graphene, and grain boundaries. These various phenomena will be discussed in the context of modeling and computation on different scales ranging from density functional theory to continuum mechanics. The workshop will also address various techniques that allow one to combine models on different scales to yield efficient computational methods.
Organizers: Tim Schulze, University of Ten-nessee; Vivek Shenoy, Brown University; and Peter Smereka, University of Michigan.
About ICERM: The Institute for Computational and Experimental Research in Mathematics is a National Science Foundation mathematics institute at Brown University in Providence, Rhode Island. Its mission is to broaden the relationship between mathematics and computation.
For more about this and other programs, organizers, confirmed participants, and speakers, and to submit an application, readers should go to ICERM’s website: http://icerm.brown.edu.
ICERM encourages women and members of underrepresented minorities to apply.
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.
Careers in the Math Sciences
So, you are a mathematician about to start or already in grad school, wondering about your options after you finish. Now is the best time to wonder–you can prepare to make informed decisions long before you get your degree. In this article I give you an idea about working at a National Aeronautics and Space Administration (NASA) research center, through answers to questions students frequently ask. Some of my impressions are specific to NASA Langley Research Center, where I work, but much of the information applies to other national laboratories too. You should look into the specifics of any labs that interest you for details. Finally, a disclaimer: These are my personal opinions, colored by my experience and career choice at NASA. They do not, in any way, represent the official NASA position.
Q: What does NASA do and where does mathematics play a part?
A: NASA, an agency of the U.S. government, focuses on space exploration, scientific discovery, and aeronautics research. Its applied research activities mainly fall into three areas, with considerable interdependence among them: space (e.g., the shuttle and the space station, exploration of the solar system and the universe, astrobiology, bioastronautics); aeronautics (e.g., fundamental aeronautics, next-generation air transportation), and science (e.g., earth and atmospheric sciences, materials). Information about NASA’s programs, projects, and centers can be found at the agency’s website (www.nasa.gov).
As to be expected, mathematics is everywhere. Some areas of aerospace research, such as computational fluid dynamics, structural analysis, and multidisciplinary optimization, are explicitly mathematically intensive, relying on numerical partial differential equations, nonlinear optimization, approximations. Other areas, such as design and transportation systems, make use of expert knowledge and heuristic approaches, relying, for instance, on simplified models, rule-based simulations, evolutionary algorithms, and scenario-based analysis. Arguably, the complexity of “real-life” systems will always defy attempts at complete rigorous mathematical descriptions. However, the growing complexity of modern systems and the need for radically new solutions also mean that evolutionary, experience-based, and heuristic approaches alone are insufficient for designing new systems. This is good news for mathematicians. Optimal or even feasible solutions for complex, massively multidimensional new systems can be counterintuitive and require rigorous mathematical methods to supplement expert decisions.
Q: What can a mathematician do at NASA? What career paths are available?
A: NASA scientists and engineers work in several general settings: research and development, systems analysis, systems engineering. As a rule, every activity, even in fundamental research, has an applied goal consistent with some aspect of NASA’s mission.
Traditionally, the NASA staff is composed mainly of engineers and scientists. As a mathematician, you can follow one of two paths (in addition to administration, which is not considered here). You might become an expert in a specific discipline and devote your career to it, in essence becoming an engineer or a scientist with good mathematical skills. Many exciting technical areas are amenable to such a strategy. Alternatively, you could choose to be a mathematical generalist, continually learning about new areas at sufficient depth to contribute to research in many applications and disciplines. I have chosen the latter and have never yet met an uninteresting problem! My impressions are based on this choice.
Your role as a generalist mathematician (should you choose to accept it) could span the range of problem-solving activities–from interacting with experts in a field in order to formulate problems amenable to solution, to method and theory development, to computational tool development, to actual solutions, to opening new method and application areas, based on your discoveries.
NASA mathematicians have a great degree of flexibility in pursuing new problems and solutions. Depending on your curiosity, persistence, and willingness to learn and establish collaborations with disciplinary experts, you are free to explore both the depth and the breadth of as many disciplines as you wish, as long as you are productive. Despite very busy schedules, all the scientists and engineers I have met at NASA have been willing to help me learn about their fields and have welcomed collaborations on problems of interest.
My work with colleagues in computational fluid dynamics, for instance, has been especially rewarding and fun for me. I am not sure just how much fun it was for this very busy group when, having spent considerable time showing me how to run their CFD codes, they had to contend with my daily visits that always started with, “the grid broke again!” But they were invariably gracious as we unraveled the causes. I have come to appreciate the complexity and beauty of their subject. In turn, I like to think that they have come to appreciate optimization, at the very least as a great diagnostic tool.
Formal opportunities to work in different groups and positions arise often. Staying in a single group also affords tremendous opportunity for variety, if that is what you like. You are free to bring new aspects and areas to your position. In my recent work in transport systems, for example, I had an opportunity to develop research announcements in such areas as complex network topology optimization and predictive modeling for complex systems, leading to new lines of investigation and new collaborations with NASA and external colleagues.
Q: What are the most important areas in need of mathematical attention?
A: In my opinion, predictive modeling (of everything) with quantified uncertainty and confidence is the most important area in need of development. Numerical modeling is ubiquitous, more so all the time. How much are the answers worth? When can computational simulations really replace experiments? Should they?
In some disciplines (e.g., aerodynamics), the models themselves are well developed but require quantification of uncertainty. Other systems defy traditional mathematical modeling. For instance, very large complex systems with autonomous but interacting components (sometimes referred to as “complex adaptive systems”), such as transportation, have not yet been modeled in the sense of “physics-based” modeling. Their boundaries are unclear; they have never been formally designed but rather have evolved over time, subject to demands and constraints.
Consider the actual air transportation system. As it grows in complexity, increasing automation is required. An automated system must be provably safe and sustainable. How can we construct proofs about the safety of such a system? Clearly, rigorous mathematical methods are the only way to prove statements about safety. Active efforts are under way at NASA to develop methods for reasoning about complex systems so that questions about safety, performance, sustainability, and impact can be answered in ever larger contexts (e.g., environmental).
In general, traditional systems analysis and engineering begin with a definition of the boundary of the system under consideration. New methods for predictive modeling of realistic systems with uncertain boundaries are crucial.
Another general problem is the need to anticipate algorithms that will allow us to take advantage of coming breakthroughs in hardware. Arguably, we have not yet taken full advantage of parallel and distributed computing. What would we do with quantum computing if it arrived?
This is just a sample of general methodological problems of interest to NASA and all other national laboratories. You can find details of specific problems at the agency and lab websites.
Q: What are useful skills to develop?
A: Different application areas require different specific technical skills, but good formal mathematical training will ground you in general problem solving and allow you to acquire missing expertise quickly, as long as you remain flexible and curious. Given that you will almost certainly have to learn the application subject matter “on the fly,” training in either pure or applied math will serve you well. You are likely to benefit from courses in such areas as analysis; mathematical modeling, including numerical solution of differential equations; linear and nonlinear optimization; and graph theory. Strong computing skills are a necessity.
Beyond mathematical skills, learning to communicate with scientists and engineers during the process of problem formulation and solution is one of the most useful skills a “generalist” can acquire. This is both a technical and a social skill. Subject matter experts often think in subject-specific terms, while we (mathematicians) think in variables, functions, etc. It is always up to the mathematician to do the translation. Patience and flexibility go a long way. It helps to keep in mind that, as mathematicians, we are often naÃ¯ve about the realities of applications; engineers are justifiably cautious about new “recipes”–after all, they managed to build a lot of good things by themselves. It is worth the time and effort it takes to inject explicit mathematics into applications that have traditionally relied on it implicitly.
The ability to work in different modes is also important: Sometimes you will be a member of teams of various sizes, and sometimes you will work completely independently. In any case, you will do a great deal of writing, and writing well is an invaluable skill.
Finally, a sense of accountability is essential. Deadlines are more firm in some areas than in others, but in any area, you are accountable for your promises. This does not imply that you will go to jail for not proving a theorem on time! But it does mean that you will need to periodically assess your progress and justify your results. It may also mean abandoning a research direction that has not yielded results after a certain amount of time and, perhaps, revisiting it in the future.
Q: How is working in a national lab different from working in industry and academia?
A: In comparing national labs and academia, it is tempting to pass along comments from colleagues in research universities: In academia you are free to pursue any problem you wish, whereas at a national lab your work will be guided by the mission of the lab. As a corollary, one of the main criteria for quality work at a university is acceptance by your peers, while at a lab it is some measure of the applicability of your research to a real problem. Teaching and advising students are academic activities.
Strictly speaking, much of this is true: For instance, the likelihood that a person at an aerospace research center will work on a problem in agriculture is not high. The distinctions, however, can be tenuous and depend greatly on individual career paths.
In principle, at a university you can work on anything you wish, although fiscal realities mean that you will likely be working in areas of interest to funding agencies. Conversely, even though at NASA you will work on problems that support the agency’s mission, you are, as a rule, free to pursue new areas of research and even, if you are persistent enough, to open new active areas of research; you do have to demonstrate the relevance of the work to the ultimate mission. NASA researchers have many opportunities to teach and mentor students; with rare exceptions, I have worked with one or two students every year. There are also opportunities to collaborate with external researchers. And, depending on the research area, publishing can be as important as at a university.
Moves in new research directions have originated in a number of ways for me. A new direction might start with a colleague’s request for help, bringing with it a new awareness of an interesting area. This is how I became involved in modeling of transport systems. A move might also start with a personal interest, not even related to work. My “outside” interest in biology and medicine led me to a recent involvement in the NASA Human Research Program. Pointers from management or project requests for expertise can bring you into new areas as well. In all cases, your work has to be funded, which means that eventually you will have to convince a specific funding organization of the relevance of your research.
And this brings me to the one unwelcome similarity: If you think that working at a national lab will excuse you from proposal writing, you are mistaken! You will likely be submitting as many proposals as your colleagues at research universities.
Distinctions include the increased accountability at national labs (e.g., the potential need to abandon unproductive lines of inquiry mentioned earlier) and a number of controls on information dissemination. For instance, you will need to have your papers reviewed before sending them to a journal.
It is difficult to comment on specific differences between working at national labs and in industry, because there is such a broad range of possibilities in industry, from small technical consulting firms to high-tech giants, each with its own conditions and culture. The general difference lies in the basic goals: National labs are concerned with matters of public interest, while commercial interests are paramount in industry.
Q: Do I need to be a U.S. citizen and do I need a security clearance?*
A: Some DOE labs, including Livermore, Los Alamos, and Sandia, do require citizenship. Most DOE labs, however, including Argonne, Oak Ridge, Berkeley, Pacific Northwest, Brookhaven, and Idaho, do not. Prospective employees should check on the individual policies of labs of interest to them. The majority of work at NASA is not classified and does not require a security clearance. If you are not a U.S. citizen, you may still be able to collaborate with NASA via one of the affiliated research institutes (e.g., the National Institute of Aerospace, www.nianet.org). Other laboratories may have similar affiliated organizations. (*Revised from the print edition; see below.)
Q: Where can I find more information?
A: The main NASA website (www.nasa.gov) contains a wealth of information about current research directions and programs, as well as pointers to the NASA centers. The NASA Technical Report Server (ntrs.nasa.gov) gives you access to recent reports. But the best way to get a feel for working at NASA is to take advantage of the student programs. The Langley Aerospace Research Summer Scholars program (http://www.nianet.org/larss/) offers opportunities for both undergraduate and graduate students to spend a summer at NASA Langley working with a researcher. The NASA Graduate Student Researchers Program (http://fellowships.hq.nasa.gov/gsrp/nav/) is an agency-wide fellowship program for graduate study in science, mathematics, and engineering related to NASA research and development. The award recipients are encouraged to spend part of the year at NASA. Once you are looking for a job, you can place your CV at www.usajobs.gov, which advertises jobs in government labs. You can sign up for announcements of NASA Research Opportunities (http://nspires.nasaprs.com/external/) and ask your faculty adviser to sign up as well. Your adviser can respond to calls for proposals and, if appropriate, include you as a member of a team.
Q: Anything else?
A: Finally, because you are reading this, I assume that you are a student member of SIAM and have attended SIAM conferences. This is an excellent way to meet researchers from national labs and find out about research and work opportunities. I encourage you to remain a member of SIAM and also recommend that you attend conferences and read papers from conferences of other professional societies, where researchers from the labs you are interested in are likely to publish.
Natalia Alexandrov is a research scientist in the Aeronautics Systems Analysis Branch, Systems Analysis and Concepts Directorate, of the NASA Langley Research Center. Her doctorate is from the Department of Computational and Applied Mathematics at Rice University. She is a member of the SIAM Committee on Membership and an Associate Fellow of the American Institute for Aeronautics and Astronautics. Readers can contact her at firstname.lastname@example.org.
Career Clarification (from November 2010 issue)
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, page 4, print edition) 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.
Susan Minkoff (email@example.com), of the University of Maryland Baltimore County, is the editor of the Careers in the Math Sciences column.
Following on its 2004 document offering recommendations to mathematics journals for best practices as they relate to the changing environment of peer-reviewed journals and the communication of research in the digital age, the International Mathematical Union (IMU) Committee on Electronic Information and Communication (CEIC) recently released an updated document endorsed by the IMU General Assembly, held August 16-17, 2010, in Bangalore, India. Based on experiences drawn from existing journals, the document outlines current best practices for journal management within the framework of currently available technology. The focus is on ensuring fundamental principles such as transparency and integrity, even as practices are continually revised and updated to keep up with emerging technological developments.
A full text of the document can be accessed below at the IMU website:
Professor Emmanuel Candès from Stanford University and Professor Terence Tao from University of California, Los Angeles (UCLA) were the 2010 recipients of the George Pólya Prize, which was awarded at the Prizes and Awards Luncheon at the SIAM Annual Meeting held July 12-16 in Pittsburgh, Pennsylvania.
The award recognizes their role in developing the theory of compressed sensing and matrix completion, which enables efficient reconstruction of sparse, high-dimensional data based on very few measurements. According to the selection committee, the algorithms and analysis are not only beautiful mathematics, worthy of study for their own sake, but they also lead to remarkable solutions of practical engineering problems.
Candès is Professor of Mathematics and Statistics at Stanford University and the Ronald and Maxine Linde Professor of Applied and Computational Mathematics at California Institute of Technology (on leave). He completed his PhD in 1998 under the supervision of Professor David Donoho at Stanford University. A past recipient of SIAM’s James H. Wilkinson Prize in Numerical Analysis and Scientific Computing, he serves on the editorial board of the SIAM Journal on Imaging Science.
Tao has been a professor of mathematics at the University of California, Los Angeles (UCLA) since 1999 and was appointed to UCLA’s James and Carol Collins Chair in the College of Letters and Science in 2007. He completed his PhD under Professor Elias M. Stein at Princeton University in 1996. In August 2006, he won the prestigious Fields Medal, often touted as the “Nobel Prize in mathematics.”
George Pólya was one of the most influential mathematicians of the 20th century. Given every two years in honor of Pólya, this SIAM prize recognizes alternately a notable application of combinatorial theory and a notable contribution to one of the other areas in Pólya’s extensive repertoire: approximation theory, complex analysis, number theory, orthogonal polynomials, probability theory, and mathematical discovery and learning. First established in 1969, it was extended in scope in 1992 following a generous contribution from the estate of Stella V. Pólya. Candès and Tao received an engraved medal each and shared a cash award of $20,000.
The Society for Industrial and Applied Mathematics (SIAM) is an international community of over 13,000 individual members, including applied and computational mathematicians, computer scientists, and other scientists and engineers. SIAM advances the fields of applied mathematics and computational science by publishing a series of premier journals and a variety of books, sponsoring a wide selection of conferences, and through various other programs. More information about SIAM is available at www.siam.org. Journalists are free to use this text so long as they acknowledge SIAM.
To come away with the top prize at a math modeling contest among 531 teams in 18 states is a feat in itself. But that was just the harbinger of things to come for Andrew Das Sarma, Jacob Hurwitz, David Tolnay, and Scott Yu from Montgomery Blair High School of Silver Spring, Maryland.
Since winning the $20,000 award and the accolades that came with it at Moody’s Mega Math Challenge 2010 earlier this year, the team has been interviewed by Pimm Fox of Bloomberg radio, has presented its findings at Lockheed Martin’s Data Capture Center, and met with U.S. Census Bureau Director Dr. Robert Groves.
And now they’ve had their research published in SIAM’s prestigious undergraduate publication, SIAM Undergraduate Research Online (SIURO). Their paper provides suggestions and recommendations to improve the adjustment of the Census undercount, identifies the most accurate method available to apportion the U.S. House of Representatives, and determines the fairest way to draw Congressional districts.
To minimize error in strategies employed by the Census Bureau to make up for undercounting–the term used to denote the number of people excluded due to delayed or absent responses–the authors deem as effective only two of the three procedures currently used. The authors reason that post-Census sampling, which is undertaken to estimate the excluded number of individuals, is counterproductive, generating more errors than the ones it seeks to remedy in the first place. The other two processes employed by the Bureau, which include estimating values for missing data and analyzing population breakdown through public records, on the other hand, can provide valuable information to account for omitted individuals, the team concludes.
For accurately dividing seats in the House of Representatives based on the count, the paper analyzes the currently used Hill method and five alternative methods that have been used historically: Dean, Webster, Adams, Jefferson, and Hamilton-Vinton. The authors come to the conclusion that the Hamilton-Vinton method is the most appropriate to ensure fair political representation of states. With regard to proper apportionment of federal funds to states based on Census numbers, the paper proposes the impartial division of states according to population density.
The paper, reflecting the Montgomery Blair team’s 14-hour research work conducted during the M3 Challenge, was published with minimal editing for style and grammar in Volume 3 of SIURO. It appeared electronically on August 4, 2010.
A PDF of the paper can be accessed at:
Help us identify one. Or two!
Recognizing exemplary applied mathematics is perhaps as important as studying it. Which is why SIAM created the Fellows program to acknowledge individuals who help advance the field with outstanding research and achievement.
Each year since the program was approved in 2008, SIAM designates as Fellows of the Society certain members who have made noteworthy contributions to the fields of applied mathematics and computational science. Fellowship is an honorific designation, which is conferred on deserving individuals in order to recognize exceptional talent. While such recognition is vital to encourage individual accomplishments, it also aids in promoting applied mathematics in the larger community.
There will be up to 34 Fellows selected for the 2011 Class. Nomination of SIAM Fellows is now an ongoing process, and we would like to encourage people to submit nominations. Criteria for selection of fellows are excellence in research, industrial work (that might or might not involve traditional research), and/or educational or other activities directly related to the goals of SIAM.
Help SIAM identify deserving members by making your nominations. It’s easier than ever! As requested by users and the SIAM Board and Council, we have simplified the process of nomination and you’ll see those changes on the fellows nomination page of our website.
If you have already made your submission, your proposition should not be affected by the new procedure.
Each SIAM member can nominate up to two individuals for fellowship in a given year. Please read the guidelines here: http://www.siam.org/prizes/fellows/nomination.php
Use the Nomination website to submit required information: http://nominatefellows.siam.org/Pages/Home.aspx
All inductees to the 2011 Class of SIAM Fellows will be acknowledged at the SIAM/CAIMS joint awards luncheon held next July at ICIAM 2011 in Vancouver, Canada.
The Society for Industrial and Applied Mathematics (SIAM) is an international community of over 13,000 individual members, including applied and computational mathematicians, computer scientists, and other scientists and engineers. SIAM advances the fields of applied mathematics and computational science by publishing a series of premier journals and a variety of books, sponsoring a wide selection of conferences, and through various other programs. More information about SIAM is available at www.siam.org.