Most Popular Posts of 2015

WordPress provides detailed statistics on views of posts. These are the five most-viewed posts published on thus blog in 2015.

  1. The Rise of Mixed Precision Arithmetic (October).
  2. Programming Languages: An Applied Mathematics View (September).
  3. The Princeton Companion to Applied Mathematics (July).
  4. Top Tips for New LaTeX Users (September).
  5. Numerical Methods That (Usually) Work (May).

WordPress has also prepared a 2015 annual report for this blog, which can be found here.

Mathematics at the Victoria University of Manchester


The Victoria University of Manchester (VUM) merged with the University of Manchester Institute of Science and Technology (UMIST) in 2004 to form The University of Manchester. The two former Departments of Mathematics joined together to form the School of Mathematics. In 2007 the School moved into a new building at the heart of the campus: the Alan Turing Building. The School is one of the largest integrated schools of mathematics in the UK, with around 75 permanent lecturing staff and over 1000 undergraduates.

As the School moves ahead it is important to keep an eye on the past, and to maintain valuable historical information about the predecessor departments. I know from emails I receive and contact with alumni (most recently at a reception in London last summer) that former students and staff like to look at photos and documents relating to their time here.

I have previously made available various documents and photos concerning the VUM Mathematics Tower on Oxford Road.

Now I have scanned five documents that provided information for prospective and current VUM mathematics undergraduates.


Applied Mathematics Workflow

Image courtesy of Stuart Miles at

This blog, which is almost three years old, is titled “Applied mathematics, software and workflow”. Workflow refers to everything involved in a research activity except the actual research. It’s about how to do many different things: edit and typeset a document, store and access your bibliographic references, carry out reproducible numerical experiments, produce figures, back up your files, collaborate with others, and so on. These tasks all need to be done multiple times, so small gains in efficiency can have a big payoff in the long run.

My article Workflow in the The Princeton Companion to Applied Mathematics gives a brief overview of the subject and can be downloaded in pre-publication form as an EPrint.

Workflow is not just about efficiency, though, or about producing the best possible end result. It’s also about enjoying carrying out the various tasks. Don Knuth put it perfectly when he said, in The Art of Computer Programming (Volume 2, Seminumerical Algorithms),

The enjoyment of one’s tools is an essential ingredient of successful work.

A search of this blog shows that I have barely used the term “workflow” so far. But a number of posts relate to this topic, namely

In the future I will write further posts about workflow as I continue to refine my own.

What is Applied Mathematics For?

Those of us working in applied mathematics are well aware that our field has many important uses in the real world. But if we are put on the spot during a conversation and asked to give some examples it can be difficult to conjure up a convincing list.

One response is to point people to The Princeton Companion to Applied Mathematics. Its 186 articles contains a large number of examples of how applied mathematics is put to work in fields such as sport, engineering, economics, physics, biology, computer science, and finance.

Another way to convince people of the value of applied mathematics is to get them to watch the 1-minute SIAM video below. It was constructed from interviews conducted at a variety of SIAM conferences and comprises snippets of 25 mathematicians saying what they use mathematics for.

Well done to Karthika Swamy Cohen and Michelle Montgomery at SIAM, Adam Bauser and his team at Bauser Media Group, and Sonja Stark at PilotGirl Productions, for producing this great advertisement for applied mathematics!

Knuth on Knowing Your Audience

Donald Knuth has a great ability to summarize things in pithy, quotable nuggets. A good example is the following sentence from his 2001 book Things a Computer Scientist Rarely Talks About:

The amount of terror that lives in a speaker’s stomach when giving a lecture is proportional to the square of the amount he doesn’t know about his audience.

Knuth’s point is about preparation, and it brings to mind the words of Benjamin Franklin, “By failing to prepare, you are preparing to fail”.

It’s essential to find out as much as possible about your audience, not just so that you feel more confident, but also so that what you deliver is appropriate for that audience.

As academics we are used to giving seminars and conference talks for which we know that the audience will be made up of peers, and we usually just need to ascertain where to aim the talk on the axes general researcher–specialist and graduate student–experienced researcher.

For any other talk it is important to go to some effort to find out who will be in the audience, perhaps asking for a list of attendees if the event requires registration. For an after-dinner talk you may want to know whether certain key people who you are thinking of mentioning will be in the audience. For a talk to a general audience you will want to assess the base level of technical knowledge that can be assumed.

Keep these thoughts in mind when that sought-after invitation to give a “TED talk” arrives in your mailbox.

©Guy Venables. Used with permission.

A New Source of Data Errors: Scanning and Photocopying

In numerical analysis courses we discuss condition numbers as a means for measuring the sensitivity of the solution of a problem to perturbations in the data. Traditionally, we say there are three main sources of data errors:

  1. Rounding errors in storing the data on the computer. For example, the Hilbert matrix with (i,j) entry 1/(i+j-1) cannot be stored exactly in floating point arithmetic.
  2. Measurement errors. If the data comes from physical measurements or experiments then it will have inherent uncertainties, which could be quite large (perhaps of relative size 10^{-3}).
  3. Errors from an earlier computation. If the data for the given problem is the solution to another problem it will inherit errors from the previous problem.

Recently I learned of a fourth source of error: scanning and photocopying.

Traditionally, photocopiers were based on xerography, whereby electrostatic charges on a light sensitive photoreceptor are used to attract toner particles and then transfer them onto paper to form an image. Nowadays, photocopiers are more likely to comprise a combined scanner and printer, as for example in consumer all-in-one devices.

Last year, German computer scientist David Kriesel discovered that the Xerox WorkCentre 7535 and 7556 machines can jumble up different areas in a scan. In particular, he found an example where many occurrences of the digit “6” are replaced by “8” during the scanning process. See his blog post.

It seems that the Xerox scanners in question use the JBIG2 compression algorithm (a specialized version of JPEG), which segments the image into patches and uses pattern matching, and that the default parameters used were not a good choice because they can lead to these serious errors. Xerox subsequently released software patches.

One would not imagine that scanning on today’s high resolution machines could change whole blocks of pixels. Given the wide range of uses of scanners, including transmission of exam marks, financial information, and engineering specifications, as well as the ubiquitous digitizing of historic documents including journal articles, this is very disturbing.

The problem of mangled scans may not be limited to Xerox machines, as other reports show (see this post and this post).

The motto of the story is: run sanity checks on your scanned data and do not assume that scans (or the results of optical character recognition on them) are accurate!