## A Call for Better Indexes1

Nick Higham (University of Manchester) writes:

An index is an important component of a book. It provides a view with a much smaller granularity than a table of contents, reveals what is not present as well as what is, and by abstracting concepts can lead the reader to unexpected content.

Most academic books in mathematics are typeset in LaTeX, which has an excellent system for indexing. By inserting \index commands in the source code, and running the MakeIndex program as part of the LaTeXing sequence, an author can iteratively build up an index during the late stages of the writing process, safe in the knowledge that the automatically generated page locators will be correct.

One might expect that the quality of indexes would have improved since the pre-LaTeX days when indexes had to be generated by hand. But in my view they have not. Most indexes I see have obvious flaws. (more…)

## Outreach in the Linear Algebra Community

David Bindel (Secretary of the SIAM Activity Group on Linear Algebra) writes:

Since the start of 2012, postings to the SIAG-LA mailing list have been distributed in a SIAG-LA digest at the start of each month. These postings consist primarily of conference announcements and job listings, as is the case on most of the SIAG mailing lists. As a method of communication with SIAG members, this may be adequate, but it is hardly inspiring. In the October 2014 SIAG-LA digest, I wrote to request feedback from SIAG-LA members regarding ways in which SIAG-LA might better facilitate interactions between members or with the larger SIAM community (or beyond).

Beyond being the home of award-winning expository writers, our SIAG has several members who are promoting linear algebra to the world at large through blogs, Twitter, and other social media. And this is true of SIAM more broadly, as well! SIAM is broadly engaged in experimentation with different forms of outreach. SIAG-OPT is resurrecting its Views and News newsletter; SIAG-MA has started a Facebook page; and the SIAG-OPSF newsletter includes not only pointers to recent SIAM journal articles, but also to recent arXiV preprints. SIAM UKIE maintains a bimonthly newsletter. SIAM also solicits material for SIAM Blogs and for SIAM News. (more…)

## Writing for Success: Applying for Funding

Sven Leyffer (Argonne National Laboratory) writes:

The following are some personal observations on how to write successful proposals. These thoughts are the fruit of half a career’s worth of (mostly unsuccessful!) proposals, observations from funding agency panels, and, most important, lessons learned from the panelists at SIAM’s professional development evening at the 2014 annual meeting in Chicago.

After describing the basic ingredients of a good proposal, I elaborate on the nuts and bolts of a proposal, including formatting and deadline aspects. Then I’ve attempted to include social aspects of proposal writing, offering suggestions on writing proposals with others; finally, I list lessons I learned from the SIAM professional development session.

Ingredients of a Good Proposal

Successful proposal writing starts long before you apply for funding. You might begin by writing white papers for program managers, describing new and challenging areas of research; by participating in special workshops organized by funding agencies that help draft the eventual call for proposals; by participating in forward-looking sessions at conferences; and by simply talking to program managers. Program managers have a wealth of experience and are usually happy to share their views, as long as it is not about one of their active calls for proposals. These activities often help shape calls for proposals, and being involved from the start with your ideas means that you already have a good story when it’s time to respond to the call. (more…)

## Book Review Revisited: Overton’s Numerical Computing with IEEE Floating Point Arithmetic

Nick Higham (University of Manchester) writes:

In the June 2002 issue of SIAM Review I reviewed Michael Overton’s 2001 SIAM book Numerical Computing with IEEE Floating Point Arithmetic: Including One Theorem, One Rule of Thumb, and One Hundred and One Exercises. In this post I reproduce the review and then discuss what has changed in the thirteen years since the book was published.

## The Original Review

This very attractively produced hardback book of just over 100 pages describes IEEE standard floating point arithmetic and associated issues such as hardware implementations and language support, together with some basics of numerical analysis. Its main intended audience is computer science and mathematics students, where it can serve as a supplement to more general textbooks, and its motivation (stated in the preface) is that “15 years after its publication, the key ideas of the IEEE standard remain poorly understood by many students and computing professionals”. One could argue that the standard is so well designed that the average user does not need to understand it; many of the weaknesses that plagued earlier floating point arithmetics, such as $$x-y$$ evaluating to zero when $$x$$ and $$y$$ are different floating point numbers, are not present in IEEE arithmetic, and so the unwary programmer is much less likely to be surprised by the results produced. Nevertheless, an appreciation of the standard is useful for anyone involved in scientific computation. A self-contained, accessible and easy to read treatment dedicated to IEEE arithmetic has been lacking, and this book admirably fills the gap. (more…)

## Mathematics for Future Cities

Des Higham (University of Strathclyde) writes:

More than half of us live or work in a city. As our digital footprints become more visible, and machine-to-machine communication more commonplace, cities can become “Living Labs.”  Researchers, governments and commercial organisations interested in issues such as energy, transport, crime, wellbeing, marketing, privacy and ethics are beginning to map out this new territory, and Future Cities/Smart Cities/Digital Cities is high on the agenda of many research funding agencies.

Glasgow recently became the UK’s flagship Smart Demonstrator City, receiving £24M of government cash to “allow public, private and academic sectors to combine expertise and use cutting-edge technology to enhance day-to-day life in the city”. Within this project, the University of Strathclyde’s Institute for Future Cities will develop a City Observatory, where data streams will be collected, analysed, acted upon and made openly available. A temporary pop-up version of the City Observatory, opened to coincide with the 2014 Commonwealth Games, has attracted 8,000 visitors in two months. Members of the public have been particularly keen to interact with a set of maps (or a three-dimensional tensor for those of us with a linear algebra view of the world) that overlays city features such as house prices, drug misuse and population density. Refer to the figure below. (more…)

## Teaching Numerical Methods for Partial Differential Equations

Lou Rossi, Section Editor of SIAM Review gives an overview of the Education paper in the latest issue:

Most instructors manage two opposing currents in classroom dynamics. The first is a desire to describe the subject in its broadest sense including all the subtleties and nuances. It gives the students a road map to the field, and if they can appreciate it at the time, it provides structure to a course that might otherwise appear to be a loosely connected series of topics. The second is the desire to ground the subject with concrete examples that students can grasp at the finest level.  The examples link prerequisite knowledge with one of the new subjects and provide students with a foundation upon which to construct a deeper understanding. Few courses draw together so many disparate topics as numerical methods for partial differential equations (PDEs).  When first exposed to finite differences for numerical PDEs, students will readily notice the regular structures in matrices, but few texts address these structures systematically and connect them directly to the analytical properties of the solution. There are many good examples, but it’s hard to see the broader landscape. In this Education section article, “Functions of Difference Matrices Are Toeplitz Plus Hankel,” authors Gil Strang and Shev MacNamara fill in some of the big picture by presenting some new results and observations about the structure of difference matrices for approximating solutions to PDEs. (more…)

## Q&A with Tim Kelley, SIAM Review Editor-in-Chief

SIAM Publications Manager Mitch Chernoff interviews Tim Kelley, SIAM Review Editor-in-Chief:

SIREV is SIAM’s flagship journal, dating from 1959. The current format dates to a widely embraced redesign first seen in 1999’s Volume 41.  Where does SIREV go from here?

SIREV’s challenge is to keep pace with the community. We review the editorial board each year for coverage and diversity. The journal experiments all the time. The Research Spotlights section is an example of that experimentation. I have high expectations for Research Spotlights.

I’m also very pleased with the progress the Education section has made since 1999. Education has published some very significant reports on issues such as CSE program development. I hope that those of us in academia can use these reports to convince our management about the importance of applied and computational mathematics in the curriculum. (more…)

## The Mathematics and History of the Trapezoidal Rule

Desmond Higham, Section Editor of SIAM Review, recaps the Survey and Review paper in the September 2014 issue of  SIREV:

The Survey and Review article in the September issue is “The Exponentially Convergent Trapezoidal Rule,” by Nick Trefethen and André Weideman. It deals with a fundamental and classical issue in numerical analysis—approximating an integral. By focusing on one deceptively simple method, the authors are able to combine a lively, historical overview with an insightful, up-to-date coverage of recent results. We learn about the work of Euler, Gauss, Maclaurin, and Poisson, and some of the 20th century pioneers of numerical analysis. We also learn about high-precision computation, treatment of singularities, choice of contours to integrate along, Gauss and Clenshaw–Curtis quadrature,  Padé approximation, and a “quadrature formula that doesn’t even integrate constants right” (see footnote number 15 in paper).

The first half of the article looks at the mathematics behind the well-known geometric convergence of the trapezoidal rule. Here the two fundamental routes to a proof are (a) exploiting Taylor series and aliasing, and (b) introducing a function that has simple poles at the summation points in order to apply residue calculus. The second half deals with applications where the trapezoidal rule has proved useful, including contour integration, rational approximation, problems with endpoint singularities, inverse Laplace transforms, integral equations, zero finding, special functions, and the numerical solution of parabolic PDEs. (more…)

## OSTP Research Priorities

SIAM Executive Director Jim Crowley writes:

The Office of Science and Technology Policy (OSTP) is the agency headed by the U.S. President’s science advisor. Among its duties is to lead interagency efforts to develop and implement sound science and technology policies and budgets. One way it does this is by issuing budget guidance to science agencies as they form their budgets, offering a set of Administration priorities for those agencies.

The 18 July 2014 budget memorandum from current director John Holdren contained seven R&D priorities – one of special note to the SIAM community. The seven were:

1. Advanced manufacturing and industries of the future.
2. Clean energy.
3. Earth observations.
4. Global climate change.
5. Information technology and high-performance computing.
6. Innovation in life sciences, biology, and neuroscience.
7. National and homeland security.

While the SIAM community can contribute to nearly all of these – the item on national and homeland security specifically mentions hypersonics, for example – it is the item on IT and HPC that most directly relates to the research of many SIAM members. (more…)

## Putting a Value on Expository Writing

SIAM Executive Director Jim Crowley writes:

Why don’t applied mathematicians write more expository articles? How can SIAM promote good expository writing and encourage more members of the community to write such articles?

Part of the reason, of course, is that technical articles, written for experts and published in scholarly journals, are the gold standard for professional applied mathematicians. We write for the few people who work in our own research areas, or perhaps for scientists in the main application areas for our work. But we tend not to spend a lot of time writing for a more general audience – even if that audience is only as broad as the SIAM membership.

Even review articles, written for a large audience, are not the norm in our field. Certainly SIAM Review publishes review articles, but such articles seem to be more highly regarded (and hence rewarded) in other disciplines. You need only look at the list of titles in Annual Reviews to get the sense that perhaps mathematicians do not place such a high value on writing such reviews; or else one would expect an AR to have a publication in mathematics. (more…)