Top Five Tips on Book Writing

I’ve written four books, and am currently writing and editing a fifth (The Princeton Companion to Applied Mathematics). I am also an editor of two SIAM book series and chair the SIAM Book Committee. Based on this experience here are my top five tips about writing an (academic) book. These cover high level issues. In a subsequent post I will give some more specific tips relating to writing and typesetting a book or thesis.

Book publishers ask prospective authors to complete a proposal form, one part of which asks who is the audience for the book. This is a crucial question that should be answered before a book is written, as the answer will influence the book in many ways.

As an example, you might be contemplating writing a book about the numerical solution of a certain class of equations and intend to include computer code. Your audience might be

• readers in mathematics or a related subject who wish to learn about numerical methods for solving the equations and are most concerned with the theory or algorithms,
• readers whose primary interest is in solving the equations and who wish to have lots of sample code that they can run,
• readers in the previous class who also need to learn the language in which the examples are written.

The choice of content, and how the book is presented, will depend very much on which audience you are writing for.

2. Revise, Revise, Revise

Just like a paper, a book draft needs to go through multiple revisions, and you must not be afraid to make major changes at any stage. You may receive constructive criticisms from reviewers of your book proposal, but reviewers may not have time to read the complete manuscript carefully and you should not assume that they have found all errors, typos, and areas for improvement.

3. Take Time to Choose Your Publisher

Given the huge effort that goes into writing a book you should take the time to find the right publisher. Discuss your book with several publishers and compare what they can offer in the way of

• format (hardback, paperback, electronic) and, if more than one format, the timescale in which each is made available,
• if the publisher has branches in more than one country, how price and publication schedule will differ between the countries,
• whether you are allowed to make a PDF version of the book freely available on your website, if this interests you,
• willingness to allow you to choose the book design (page size, font, cover, etc.),
• use of colour (which increases the cost),
• royalties (including a possible advance),
• pricing,
• the publisher’s policy on translations,
• copy editing (see the next section),
• time from delivering a completed manuscript to publication,
• marketing (will the book be advertised at all, and if so how?), and
• how long your book is guaranteed to stay in print.

It is perfectly acceptable to submit a proposal to several publishers and see what they are willing to offer. However, it is only fair and proper to make clear to a publisher that you are talking to other publishers and, once you have set the wheels of a publisher’s review process in motion, to wait for an offer before making a decision to go with another publisher.

I am always surprised when I hear of authors who approach only one publisher, or who go with the first publisher to express an interest in the book. As in many contexts, it is best to make an informed choice from among the available options.

4. Ensure Your Book is Copy Edited

If you are an inexperienced writer, or your first language is not English, the benefits of copy editing are obvious. But even an experienced author finds it virtually impossible to think about all the little details that a copy editor will check for, such as correctness and consistency of spelling, notation, punctuation (notably the serial comma), citations, and references. For example, I sometimes mix US and UK spellings and don’t want to have to worry about finding and correcting my occasional lapses. A good copy editor will also suggest minor improvements of the text that might escape even the best writers.

Unfortunately, not all publishers copy edit all books nowadays. Notable exceptions that always do copy edit (and, as I know from experience, work to the highest standards in every respect) are Princeton University Press and SIAM.

If your publisher has a Style Manual it obviously makes sense to follow its guidelines in order to minimize changes at the copy editing stage. Here is a link to the SIAM Style Manual.

5. Think Twice Before Co-Authoring a Book

It might seem an attractive proposition to share authorship of a book: surely having $n$ co-authors reduces the work by a factor $1/n$? Unfortunately it often does not work out like that, despite best intentions. In fact, $n$ co-authors can easily take $n$ times as long to write a book as any one of them would. One of the biggest difficulties is timescale: one author may be willing and able to finish a book in a year but another may need twice that period to make their contribution. Indeed it is rare for the co-authors to be matched in the amount of effort they can put into the book; this is clearly problematic if initial expectations are not realized. Other potential problems are potentially differing opinions on content, notation, level, length, and almost anything else associated with a book.

Successful authorship teams often have a track record of co-authoring papers together. Although it is no guarantee that a much larger book project will run smoothly, experience with writing papers together will at least have given a good indication of where disagreements are likely to lie.

Posted in books, writing | | 1 Comment

The Spotlight Factor

In my Handbook of Writing for the Mathematical Sciences I described the spotlight factor, originally introduced by Tompa in 1989. The spotlight factor is defined for the first author of a paper in which there are $n$ authors listed alphabetically, and it is assumed that the paper is from a community where it is the custom to order authors alphabetically.

The spotlight factor is the probability that if $n-1$ coauthors are chosen independently at random they will all have surnames later in the alphabet than the first author. This definition is not precise, since it is not clear what is the sample space of all possible names, so it is better to regard the spotlight factor as being defined by the formula given by Tompa, which is implemented in the MATLAB function below.

The smallest spotlight factor I have found is the value 0.0244 for Zielinski, for the paper

Pawel Zielinski and Krystyna Zietak, The Polar Decomposition—Properties, Applications and Algorithms, Applied Mathematics, Ann. Pol. Math. Soc. 38, 23-49, 1995

This beats the best factor of 0.0251 reported by Tompa in a 1990 follow-up paper.

Can you do better?

Here is a MATLAB M-file to compute the spotlight factor, preceded by an example of its usage:

>> spotlight('zielinski',1)
ans =
2.4414e-02

function s = spotlight(x, k)
%SPOTLIGHT   Tompa's spotlight factor of authorship.
%   SPOTLIGHT(X, K) is the spotlight factor for the author whose
%   last name is specified in the string X, with K coauthors.
%   Mixed upper and lower case can be used.
%   Smaller spotlight factors correspond to rarer events.

%   Reference:
%   Martin Tompa, Figures of Merit, SIGACT News 20 (1), 62-71, 1989

if ~ischar(x), error('First argument must be a string.'), end
if nargin < 2, error('Must give two arguments.'), end

x = double(upper(x)) - double('A') + 1;
x( find(x < 0 | x > 26) ) = 0;  % Handle punctuation and spaces.

s = 0;

% Ideally use Horner's rule, but the following is clearer.

for i=1:length(x)
t = x(i);
s = s + t/27^i;
end

s = (1 - s)^k;

Posted in writing | Tagged | 3 Comments

The Life of James Joseph Sylvester

Following my previous post about the James Joseph Sylvester Bicentenary and my article Sylvester’s Influence on Applied Mathematics I now give a brief, very selective, overview of Sylvester’s life. Some of this material was used in an after-dinner speech that I gave at the Householder Symposium XIX on Numerical Linear Algebra at Spa, Belgium on June 11, 2014.

I’ve drawn on many sources for this post, but the most important is the 2006 biography by Karen Parshall, James Joseph Sylvester. Jewish Mathematician in a Victorian World. That title brings out two key points: that Sylvester was Jewish, which hindered his career, as we will see, and that he lived much of his life in Victorian England, when almost everything that today we take for granted when doing our research did not exist.

Thumbnail Sketch of The Man

Sylvester was born in London in 1814. He was short, mercurial, absent-minded, temperamental, fluent in French, German, Italian, Latin and Greek, and loved poetry but was not very good at it. He was a man of remarkable tenacity, as his career on both sides of the Atlantic shows.

Career Outline

I’ll give a brief outline of Sylvester’s unusual career, with its many ups and downs, then go on to discuss some specific events in his life.

First Spell in UK

• Sylvester was a student at University College London (UCL) under De Morgan, age 14. He was withdrawn by his family after attempting to stab a fellow pupil.
• He was a student at Cambridge, but was not able to take the degree because he was Jewish.
• He held the chair of natural philosophy at University College London (UCL) for three years.

First Sojourn in USA

Sylvester became Professor of Mathematics at the University of Virginia in 1841. He left after four months after an altercation with an unruly student, because he was felt that the faculty did not back him up in a subsequent inquiry.

While in New York he applied for a position at Columbia University. According to R. L. Cooke (quoted in James Joseph Sylvester. Life and Work in Letters)

After leaving Virginia he sought a position at Columbia University, with a recommendation from one of America’s leading scientists, Joseph Henry. In a wonderful irony … the selection committee informed him that his rejection was in no way connected with the fact that he was British, only the fact that he was Jewish.

Rest of Career (age 29–).

• Sylvester Worked for the next decade as an actuary for the Equity and Law Life Assurance Society in London and trained for the Bar. He founded the Institute of Actuaries. This is when he met Cayley, who became his best friend. For this ten-year period he was doing mathematics in his spare time.
• He was appointed Chair at the Royal Military Academy, Woolwich and spent 15 years there.
• He was appointed Chair at the newly founded Johns Hopkins University, Baltimore, at the age of 61. He negotiated a salary of $5000 payable in gold, plus an annual housing allowance of$1000 also payable in gold.
• His final position was as the Savilian Professor of Geometry at New College, Oxford in 1883, which he took up at the age of 69.

The Neologist

Sylvester introduced many terms that are still in use today, including matrix (1850), canonical form (1851), Hessian (1851), and Jacobian (1852). Another notable example is the term latent root, which Sylvester introduced in 1883, with two charming similes:

“It will be convenient to introduce here a notion (which plays a conspicuous part in my new theory of multiple algebra), namely that of the latent roots of a matrix—latent in a somewhat similar sense as vapour may be said to be latent in water or smoke in a tobacco-leaf.”

The term has fallen out of use in linear algebra and matrix theory, but it can still be found in use through “the latent root criterion” in, for example (to pick two articles found with a Google search) Differentiating with brand personality in economy hotel segment in Journal of Vacation Marketing (2014) and GHOSTS: A travel barrier to tourism recovery in Annals of tourism research (2011).

Editor

Sylvester did a great deal of editorial work. He was an editor of the Quarterly Journal of Mathematics for 23 years. He founded the American Journal of Mathematics in 1878 when he was at Johns Hopkins University. This was the first mathematics research journal in the USA, and indeed Sylvester set up the first mathematics research department in the country. As Editor-in-Chief he experienced some of the problems that subsequent journal editors have suffered from.

• He had to work very hard to secure high quality contributions, e.g., from his friend Cayley and from students and colleagues at Johns Hopkins, in addition to his own papers.
• He solicited Alfred Kempe’s proof of the four color theorem. After Sylvester had accepted the paper his managing editor, William Story, realized there was a gap in the reasoning, due to overlooked cases, and wrote a note the accompany the paper in which he unsuccessfully tried to patch the proof. This all happened while Sylvester was in England and he was very unhappy with the incident.

Author

Even though Sylvester was an editor himself, he was also the author from hell! He was notorious for what his biographer Parshall calls “an impatience with bibliographic research”—something that led him into disputes with other mathematicians.

MacFarlane states that

Sylvester never wrote a paper without foot-notes, appendices, supplements; and the alterations and corrections in his proofs were such that the printers found their task well-nigh impossible. … Sylvester read only what had an immediate bearing on his own researches, and did little, if any, work as a referee.

The title of one particular paper illustrates this point:

J. J. Sylvester, Explanation of the Coincidence of a Theorem Given by Mr
Sylvester in the December Number of This Journal, With One Stated by
Professor Donkin in the June Number of the Same, Philosophical Magazine
(Fourth Series) 1, 44-46, 1851

Secular Equation Paper

Out of Sylvester’s hundreds of papers, one in particular stands out as notable to me: “On the Equation to the Secular Inequalities in the Planetary Theory”, Philosophical Magazine 16, 267-269, 1883, for the following reasons.

• The title has virtually nothing to do with the paper.
• This is the paper in which Sylvester defines the term latent roots—but as if a totally new concept, even though the concept of matrix eigenvalue was already known.
• He states a theorem about a sum of products of latent roots of a product $AB$ being expressible in terms of sums of products of minors of $A$ and $B$.
• He gives the first general definition of function of a matrix (later refined by Buchheim).
• He discusses the special case of $p$th roots.

The paper is short (3 pages), no proper introduction is given to these concepts, and no proofs are given. In short, a brilliant but infuriating paper!

Baltimore Summer

In these days of ubiquitous air conditioning it is interesting to note one of the things that made it difficult for Sylvester to do research. Parshall writes, of Sylvester in Baltimore,

“He could not concentrate on his research on matrices in the debilitating summer heat and humidity”.

Teaching

Sylvester’s enthusiasm for matrices is illustrated by his attempt to teach the theory of substitutions out of a new book by Netto. Sylvester

“lectured about three times, following the text closely and stopping sharp at the end of the hour. Then he began to think about matrices again. I must give one lecture a week on those,’ he said. He could not confine himself to the hour, nor to the one lecture a week. Two weeks were passed, and Netto was forgotten entirely and never mentioned again.” (Parshall, p. 271, quoting Ellery W. Davis).

Compare this with the following quote about E. T. Bell (famous for his book Men of Mathematics, 1937), from Constance Reid’s book about Bell:

Bell’s method of teaching was to read a sentence aloud and announce that he didn’t believe it. By the time we students convinced him that it was true,’ concedes Highberg, we pretty well understood it ourselves.’

Inaugural Lecture at Oxford, 12 December 1885

There are many ways in which we are more fortunate today than mathematicians of Sylvester’s time. But there were some advantages to those times. From his inaugural lecture, published as On the Method of Reciprocants as Containing an Exhaustive Theory of the Singularities of Curves (Nature, 1886)

It is now two years and seven days since a message by the Atlantic cable containing the single word “elected” reached me in Baltimore informing me that I had been appointed Savilian Professor of Geometry in Oxford, so that for three weeks I was in the unique position of filling the post and drawing the pay of Professor of Mathematics in each of two Universities:

Obstinacy

Emile Picard recounted how Sylvester, on a visit to Paris, asked him if in six weeks he could learn the theory of elliptic functions. Picard said yes, so Sylvester asked if a young geometer could be assigned to give him lessons several times per week. This began, but from the second lesson reciprocants and matrices started to compete with elliptic functions and in the ensuing several lessons Sylvester taught the young geometer about his latest research and they remained on that topic.

What Can We Learn from Sylvester’s Life?

If I had to draw two pieces of advice from Sylvester’s life story I would choose the following.

• You are never too old to take on a major challenge (he took up the chair at Johns Hopkins University at the age of 61).
• If you want to be remembered, define some new terms and have some theorems named after you!

Typewriter Art

In 1981 my mother showed me a magazine (Woman’s Realm) that had instructions for producing on a typewriter a portrait of Prince Charles. The instructions had been designed by Bob Neill, who had worked out how represent a photograph of Prince Charles as a 100-by-79 grid of characters, choosing the density of each character appropriately and exploiting the facility of a typewriter to issue a carriage return without line feed and thereby overwrite one character with another. The instructions looked like

(6) 26G 16@ 1& 36G
(6a) 22sp 2. 1: 95 1& 15 1& 3S 2& 3: 1.

which say that on the 6th line you should type the letter G 26 times followed by 16 @ symbols, etc., then overwrite the line with 22 spaces, 2 full stops, etc.

This is an example of ASCII art, though ASCII art does not usually involve overwriting characters.

At the time I had a Commodore Pet microcomputer and it struck me that the painstaking process of typing the image would be better turned into a computer program. Once written and debugged the program could be used to print multiple copies of the image. By switching the data set the program could be used to print other photos. So I wrote a program in Commodore Basic that printed the image to a Commodore 4022 dot matrix printer.

I sent the program to Bob. He liked it and printed the program in an appendix to his 1982 book Bob Neill’s Book of Typewriter Art (With Special Computer Programme). That book contains instructions for typing 20 different images, including other members of the royal family, Elvis Presley and Telly Savalas (the actor who played Kojak in the TV series of the same name, which was popular at the time), and various animals,. Bob Neill’s Second Book of Typewriter Art was published in 1984, which reprinted my original program. It included further celebrities such as Adam Ant, Benny from Crossroads, “J.R.” from Dallas and Barry Manilow

I recently came across some articles describing Bob’s work, including one by his daughter, Barbara, one by Lori Emerson that includes a PDF scan of the first book, and an article The Lost Ancestors of ASCII Art. The latter pointed me to a recently published book Typewriter Art: A Modern Anthology. This resurgence of interest in typewriter art prompted me to look again at my code.

I had revisited my original 1982 Basic code later in the 1980s, converting it to GW-Basic so it would run on IBM PCs with Epson printers. I had also added the data for The Tabby Cat from Bob’s second book. Here is an extract from the code, complete with GOTOs and GOSUBs (GW-Basic had few structured programming features).

10 REM TYPEART.BAS
20 REM Program by Nick Higham 1982 (Commodore Basic),
30 REM and 1988 (GW-Basic/Turbo Basic).  (c) N.J. Higham 1982, 1988.
40 REM Designs by Bob Neill.  (c) A.R. Neill 1982, 1984.
...
530 REM -----------------------------
540 REM ROUTINE TO PRINT OUT DATABASE
550 REM -----------------------------
560 DEV$= "LPT"+PP$+":"
570 OPEN DEV$FOR OUTPUT AS #1 580 PRINT #1, RESET.CODE$
590 WIDTH #1,255 ' this stops basic inserting unwanted carriage returns
600 GOSUB  800
610 L$="" 620 GOSUB 700:IF A$="/" THEN PRINT#1, NORMAL.LFEED$+L$: GOTO 610
630 IF A$="-" THEN PRINT#1, ZERO.LFEED$;L$: GOTO 610 640 A=ASC(A$):IF A>47 AND A<58 THEN A=A-48: GOTO 660
650 L$=L$+A$: GOTO 620 660 GOSUB 700:B=ASC(A$):IF B>47 AND B<58 THEN A=10*A+B-48: GOSUB 700
670 FOR I=1 TO A:L$=L$+A$:NEXT: GOTO 620 680 ' 690 REM -- SUBROUTINE TO TAKE NEXT CHARACTER FROM Z$
700 A$=MID$(Z$,P,1):P=P+1: IF A$<>" "  AND A$<>"" THEN 730 710 IF P>Z THEN GOSUB 800 720 GOTO 700 730 IF A$="]" THEN A$=" " 740 IF A$="#" THEN A$=CHR$(34)
750 IF A$="^" THEN A$=":"
760 IF P>Z THEN GOSUB 800
770 RETURN
780 '
790 REM -- SUBROUTINE TO READ NEXT LUMP OF DATA
800 READ Z$:Z=LEN(Z$):P=1
810 IF Z$="PAUSE" THEN FOR D=1 TO 20000:NEXT: GOTO 800 820 IF Z$="FINISH" THEN PRINT #1, CHR$(12)+RESET.CODE$: CLOSE #1:END
830 RETURN
840 '
850 REM -------------------------------------
860 REM * DATABASE1 - H.R.H. PRINCE CHARLES *
870 REM -------------------------------------
880 '
890 DATA "H.R.H. Prince Charles"
900 DATA  79G/79G/79G/79G
910 DATA  /79G-25]2.2^2&^L2^2&3^2.
920 DATA /26G16@&36G-22]2.^9]&S&3S2&3^.
930 DATA /22G23@34G-20].^10&]3&^6Y2C&^.
...
4710 '
4720 REM -- EXPLANATION OF DATA --
4730 REM / MEANS NEWLINE
4740 REM - MEANS CONTINUATION LINE
4750 REM 29G MEANS PRINT 29 LETTER G'S.
4760 REM @ MEANS PRINT ONE @ CHARACTER.
4770 REM CHARACTERS : " AND 'SPACE'
4780 REM ARE REPRESENTED BY ^ # AND ]
4790 REM IN THE DATA STATEMENTS.
4800 REM ALL OTHER CHARACTERS ARE
4810 REM PRINTED OUT AS THEMSELVES.
`

The full code is available, along with documentation.

Like typewriters, dot matrix printers could carry out a carriage return without line feed. Today’s inkjet and laser printers cannot do that. I pose a challenge:

convert the program to a modern language (MATLAB or Python are natural choices) and modify it to render the images in some appropriate format.

References

• A. R. Neill. Bob Neill’s Book of Typewriter Art (With Special Computer Programme). The Weavers Press, 4 Weavers Cottages, Goudhurst, Kent, 1982, 176 pp. ISBN 0 946017 01 8.
• A. R. Neill. Bob Neill’s Second Book of Typewriter Art. The Weavers Press, 4 Weavers Cottages, Goudhurst, Kent, 1984. ISBN 0 946017 02 6.
Posted in software | Tagged , | 4 Comments

James Joseph Sylvester (1814–1897) Bicentenary

This year (or more precisely September 3, 2014) is the bicentenary of the birth of James Joseph Sylvester, FRS, a prolific 19th century mathematician who led an eventful life, holding positions at five academic institutions, two of them in the USA.

My article Sylvester’s Influence on Applied Mathematics published in the August 2014 issue of Mathematics Today explains how Sylvester’s work continues to have a strong influence on mathematics. A version of the article with an extended bibliography containing additional historical references is available as a MIMS EPrint.

In the article I discuss how

• Many mathematical terms coined by Sylvester are still in use today, such as the words “matrix” and “Jacobian”.
• The Sylvester equation $AX + XB = C$ and the quadratic matrix equation $AX^2 + BX + C = 0$ that he studied have many modern applications and are the subject of ongoing research.
• Sylvester’s law of inertia, as taught in undergraduate linear algebra courses, continues to be a useful tool.
• Sylvester gave the first definition of a function of a matrix, the study of which has in recent years has become a very active area of research.
• Sylvester’s resultant matrix, which provides information about the common roots of two polynomials, has important applications in computational geometry and symbolic algebra.

Sylvester’s collected works, totalling almost 3000 pages, are freely available online and are well worth perusing: Volume 1, Volume 2, Volume 3, Volume 4.

In a subsequent post I will write about Sylvester’s life.

David Broomhead passed away on July 24th, 2014 after a long illness. David was a Professor of Applied Mathematics in the School of Mathematics at the University of Manchester. I got to know him in 2004 when the Victoria University of Manchester merged with UMIST and the two mathematics departments, his at UMIST and mine at VUM, became one.

David was a truly interdisciplinary mathematician and led the CICADA (Centre for Interdisciplinary Computational and Dynamical Analysis) project (2007-2011), a £3M centre funded by the University of Manchester and EPSRC, which explored new mathematical and computational methods for analyzing hybrid systems and asynchronous systems and developed adaptive control methods for these systems. The centre involved academics from the Schools of Mathematics, Computer Science, and Electrical and Electronic Engineering, along with four PhD students and six postdocs, all brought together by David’s inspirational leadership.

One of the legacies of CICADA is the burgeoning activity in Tropical Mathematics, which straddles the pure and applied mathematics groups in Manchester, and whose weekly seminars David managed to attend regularly until shortly before his death. Indeed one of David’s last papers is his Algebraic approach to time borrowing (2013), with Steve Furber and Marianne Johnson, which uses max-plus algebra to study an algorithmic approach to time borrowing in digital hardware.

Among the other things that David pioneered in the School, two stand out for me. First, he ran one of the EPSRC creativity workshop pilots in 2010 under the Creativity@Home banner, for the CICADA project team. The report from that workshop contains a limerick, which I remember David composing and reading out on the first morning:

One who works on Project CICADA
Has to be a conceptual trader
Who needs the theory of Morse
To tap into the Force -

The workshop was influential in guiding the subsequent activities of CICADA and its success encouraged me to organize two further creativity workshops, for the numerical analysis group and for the EPSRC NA-HPC Network.

At the CICADA Creativity Workshop, November 2010.

The second idea that David introduced to the School was the role of a technology translator. He had organized (with David Abrahams) a European Study Group with Industry in Manchester in 2005 and saw first-hand the important role played by technology translators in providing two-way communication between mathematicians and industry. David secured funding from the University’s EPSRC Knowledge Transfer Account and combined this with CICADA funds to create a technology translator post in the School of Mathematics. That role was very successful and the holder (Dr Geoff Evatt) is now a permanent lecturer in the School.

I’ve touched on just a few of David’s many contributions. I am sure other tributes to David will appear, and I will try to keep a record at the end of this post.

Photo credits: Nick Higham (1), Dennis Sherwood (2).

Creativity Workshop for EPSRC NA-HPC Network

The EPSRC Network Numerical Algorithms and High Performance Computing, coordinated by David Silvester and me, came to the end of its three-year term in May 2014. One of our final activities was a two-day Creativity Workshop, held at Chicheley Hall just before Easter.

The workshop was advertised to network members and we were able to accept all applicants. The 23 attendees comprised PhD students, postdoctoral researchers, faculty, and HPC support experts from Cambridge University, the University of Edinburgh, Imperial College, The University of Manchester, MIT, NAG Ltd., Queens University Belfast, STFC-RAL, UCL, and the University of Tennessee at Knoxville, along with an EPSRC representative.

The workshop was facilitated by creativity expert Dennis Sherwood. I explained the idea of these workshops in an earlier post about a creativity workshop we held for the Manchester Numerical Analysis Group last year. The procedure is for the attendees to work in groups tackling important questions using a structured approach that encourages innovative ideas to be generated and carefully assessed and developed. The key ingredients are

• a group of enthusiastic people,
• careful planning to produce a set of nontrivial questions that address the workshop goals and are of interest to the attendees,
• a willingness to adapt the schedule based on how the workshop progresses.

The workshop was targeted at researchers working at the interface between numerical analysis and high performance computing. The aims were to share ideas and experiences, make progress on research problems, and identify topics for research proposals and new collaborations.

The topics addressed by the groups were sensitivity in sparse matrix computations; programming languages; deployability, maintainability and reliability of software; fault-resilient numerical algorithms; and “16th April 2019″.

The notes for the last topic began “It’s 16th April 2019, and we’re celebrating the success of our network. What is it, precisely, that is so successful? And what was it about the decisions we took five years ago, in 2014, that, with hindsight, were so important?”. The discussion led to a number of ideas for taking the activities of the network forward over the coming years. These include

• organizing summer schools,
• producing a register of members’ interests and areas of expertise,
• exploiting opportunities for co-design across communities such as algorithm designers, NA specialists and domain scientists, and
• creating opportunities targeted at early career members of the network.

As an ice-breaker and a way of the participants getting to know each other everyone was asked to prepare a flip chart containing a summary of their key attributes, why they were attending, and something they have done that they feel particularly good about. These were presented throughout the two days.

Presenting my “Who I Am”, with Post-its behind me containing ideas written down by participants during the workshop.

Dennis Sherwood has produced a 166-page report that distills and organizes the ideas generated during the workshop. Attendees will find this very useful as a reminder of the event and of the various actions that resulted from it.

The Venue

Chicheley Hall, is a historic country house located near Milton Keynes. It was purchased a few years go by the Royal Society, who turned it into a hotel and conference center, and it houses the Kavli Royal Society International Centre. It’s a terrific place to hold a small workshop. The main house and its meeting rooms have a wonderful ambience, the 80-acre grounds (complete with lake and dinosaur sculpture) are a delight to walk around, and each of the 48 bedrooms is named after a famous scientist.

Photo credits: Nick Higham (1,2,4,5,6), Dennis Sherwood (3).

Videos of Lectures from Gene Golub SIAM Summer School 2013

Videos of lectures given by four of the five lecturers at the 2013 Gene Golub SIAM summer school at Fudan University in Shanghai are now available on the summer school website.

These include the five 2-hour lectures from my course on Functions of Matrices. Here is a summary of the contents of my lectures, with direct links to the videos hosted on YouTube.

• Lecture 1: History, definitions and some applications of matrix functions. Quiz.
• Lecture 2: Properties, more applications, Fréchet derivative, and condition number.
• Lecture 3: Exponential integrator application. Problem classification. Methods for $f(A)$: Schur-Parlett method, iterative methods for sign function and matrix square root.
• Lecture 4: Convergence and stability of iterative methods for sign function and square root. The $f(A)b$ problem. Software for matrix functions.
• Lecture 5: The method of Al-Mohy and Higham (2011) for the $\exp(A)b$ problem. Discussion of how to do research, reproducible research, workflow.

A written summary of the course is available as Matrix Functions: A Short Course (MIMS EPrint 2013.73).

The video team, visible in the photo below that I took of my audience, have done a great job. The music over the opening sequence is reminiscent of the theme from the film Titanic!

As a reminder, other relevant links are

My Mac Setup

I came to Macs quite late, switching to Mac laptops in 2009 because of the quality of the hardware. Over the last year I have taken my 13-inch MacBook Pro Retina to China, the USA and Europe. With the World Travel Adapter Kit to allow hassle-free power connections, this is the ultimate machine for travelling.

I still use Windows desktop machines, but switching between Mac and Windows machines is easy nowadays thanks to three things: almost all the software that I use runs on both systems, Dropbox allows easy sharing of files between machines, and Windows and Mac OS X have converged so as to have very similar features and capabilities.

Most of my core applications are open source: Emacs, Firefox, Thunderbird, Git for version control, Cyberduck (for ftp and ssh), and TeX Live. Mac-specific software includes iTerm2 (a replacement for Terminal), Path Finder (an enhanced Finder), Skim (PDF viewer) and Witch (app-switcher, Cmd-tab replacement). And for numerical and symbolic computation I use MATLAB.

A password manager is essential nowadays. I use 1Password, which runs on all my Apple hardware and Windows, and I sync it via Dropbox.

On the iPhone a couple of free apps are proving very useful. MapsWithMe gives offline maps downloadable by country, and since it only needs a GPS signal it’s great for finding where you are while on a train, or in a foreign country. As long as I have the iPhone in my pocket, Moves is good at counting my number of steps per day, which is sadly all too low, and records my time spent travelling. It also has the handy feature of showing on a map where you have been, which is useful if you are lost and want to retrace your steps.

On my MacBook Pro I have File Vault turned on, so that the hard disk is encrypted. I’m impressed with how little overhead this creates with the Core i7 Ivy bridge chip and an SSD. I also like the way File Vault works with Find My Mac to trap thieves via the Guest account (as detailed in this article)!

I continue to use Windows desktop machines. Two particular reasons are that I have not found Mac programs that match the functionality of Xyplorer (file manager) and Fineprint (printer driver), which I use many times every day.

This post is a modified version of an article titled “My Setup” that appeared in MacUser magazine, November 2013, page 126.

400 Years of Logarithms

The logarithm was first presented in John Napier’s 1614 book Mirifici Logarithmorum Canonis Descriptio (Description of the Wonderful Canon of Logarithms). Last week I was celebrating 400 years of logarithms at the Napier 400 workshop held at the ICMS in Edinburgh and organized by NAIS. The previous such celebrations had been in 1914 and, as one speaker remarked, it is nice to participate in an event held only once every 100 years.

This one-day workshop included talks by Mike Giles on computing logarithms and other special functions on GPUs, and Jacek Gondzio on the history of the logarithmic barrier function in linear and nonlinear optimization.

My interest is in the matrix logarithm. The earliest explicit occurrence that I am aware of is in an 1892 paper by Metzler On the Roots of Matrices, so we are only just into the second century of matrix logarithms.

Photo and Tweet by @DesHigham: “@nhigham introduced by Dugald Duncan at @ICMS_Edinburgh”.

In my talk The Matrix Logarithm: from Theory to Computation I explained how the inverse scaling and squaring (ISS) algorithm that we use today to compute the matrix logarithm is a direct analogue of the method Henry Briggs used to produce his 1624 tables Arithmetica Logarithmica, which give logarithms to the base 10 of the numbers 1–20,000 and 90,000–100,000 to 14 decimal places. Briggs’s impressive hand computations were done by using the formulas $\log a = 2^k \log a^{1/2^k}$ and $\log(1+x) \approx x$ to write $\log_{10} a \approx 2^k \cdot \log_{10}e \cdot (a^{1/2^k} - 1)$. The ISS algorithm for the matrix case uses the same idea, with the square roots being matrix square roots, but approximates $\log(1+x)$ at a matrix argument using Padé approximants, evaluated using a partial fraction expansion. The Fréchet derivative of the logarithm can be obtained by Fréchet differentiating the formulas used in the ISS algorithm. For details see Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm (2012) and Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number (2013).

As well as the logarithm itself, various log-like functions are of interest nowadays. One is the unwinding function, discussed in my previous post. Another is the Lambert W function, defined as the solution $W(z)$ of $W(z) e^{W(z)} = Z$. Its many applications include the solution of delay differential equations. Rob Corless and his colleagues produced a wonderful poster about the Lambert W function, which I have on my office wall. Cleve Moler has a recent blog post on the function.

A few years ago I wrote a paper with Rob, Hui Ding and David Jeffrey about the matrix Lambert W function: The solution of S exp(S) = A is not always the Lambert W function of A. We show that as a primary matrix function the Lambert $W$ function does not yield all solutions to $S \exp(S) = A$, just as the primary logarithm does not yield all solutions to $e^X = A$. I am involved in some further work on the matrix Lambert W function and hope to have more to report in due course.