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40 REVIEWS The Princeton Companion to Applied Mathematics

by Nichloas J. Higham (editor), Princeton University Press, 2015, £77, US$ 99.50, ISBN: 978-0691150390

Review by David I Graham

The rst question that to be generally good. In terms of self-containedness, comes to mind when some of the contributions in the later parts require reviewing a book like prior knowledge not fully detailed in the introductory this is “Why?” A Google parts, though more detailed investigations utilising search for “Applied Math- the reference lists should mean an interested reader ematics” nds 382 mil- would be able to ll the gaps. lion pages related to the subject, many of which Returning to the material covered, Part IV is really will be very detailed and the heart of the book. It describes in considerable with access to anima- detail (over 400 pages), forty “Areas of Applied Math- tions and relevant computer code as well as links to ematics” including straightforward choices such as related work. The editors are, of course, well aware various avours of mechanics, dierential equations of this and try to answer the question themselves. In and numerical methods but also less obvious areas the Preface they claim that the distinguishing feature such as algebraic geometry. There is a very readable of the book is that it is “self-contained, structured contribution on “Symmetry in Applied Mathematics", reference work giving a consistent treatment of the which starts from the symmetries of plane gures subject”. and goes as far as symmetry breaking, with much discussion related to the various symmetries seen in The book is in eight parts and runs to almost 1000 Taylor–Couette uid ow between co-rotating cylin- pages. There is certainly a serious attempt to be self- ders. The author confesses that the article “barely contained, with the rst part containing the longest scratches the surface”. A typical example for this articles in the book, dening basic language and part is the ten page contribution on “Fluid Dynamics”, terms from coordinate systems through calculus up which rattles along at great pace, covering everything to operators and stability. The second part then from 2-dimensional streamlines through ight aero- briey reminds the reader of essential concepts from dynamics up to ow instability — enough material to asymptotics to wave phenomena. These are arranged ll a decent course module. Similarly, the nineteen in alphabetical order, occasionally meaning that there page contribution on “Numerical Linear Algebra and is no natural ow from one contribution to the next. Matrix Analysis” is a comprehensive collection of the The structure becomes more free-form as we get main results relating to matrix computations and further into the book. This is inevitable given the notes some useful ‘must have’ references. I have to great variety in topics covered. With over 160 authors confess that some of the other contributions are contributing to the articles, consistency was always rather dry for my taste, though the articles generally going to be dicult to achieve and there is consider- represent excellent starting points for further inves- able variation in the later parts, especially in the level tigation — which is one of the great strengths of the of detail and follow-up information. One contribution book as a resource. in Part V has a reference list of one item, namely a book written by the contributor himself. Conversely, Parts V (“Modelling”), VI (“Example Problems”) and the exemplary contribution on nancial mathematics VII (“Application Areas”) together give us 64 dierent in Part V provides not only an excellent reference examples, averaging at around ve pages in length. list but also a discussion of what to look for in each Several of these — including a contribution on “Sport” of the references. Overall, the reference lists seem that strangely covers only sailing, rowing and swim-

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REVIEWS 41

ming — are related to uid dynamics, meaning that My nal thoughts are that this book is an excellent there is some repetition between articles. The article resource for any mathematics departmental library. on “A Symmetric Framework with Many Applications” The articles cover a vast array of dierent applica- outlines a nice example of a unifying viewpoint for tion of mathematics and are generally well-written minimisation problems of various kinds. As a com- with useful reference lists. In particular, the book rep- putational applied mathematician, I welcomed the resents an excellent launch point for individuals such contributions in Part VII related to historical develop- as project students looking for an area of Applied ments in programming languages (and the confusion Mathematics to investigate in greater depth. to which dierent conventions can lead) and the future in terms of high-performance computing. David Graham A particularly interesting feature of the book is the David is a Senior Lec- last Part (VIII), which oers some “Final Perspectives”. turer in Applied Mathe- I found many of these contributions to be extremely matics at the University thoughtful and useful, including advice on how to of Plymouth. His main read Mathematics articles or to write articles or even research interests are general interest books. As an author of reasonably in developing and using large fortran codes myself, I found the sections on numerical methods for “Reproducible Research” and “Experimental Mathe- uid dynamics. David is a keen footballer and, in matics” to be especially thought-provoking. decreasing order of competence he also plays guitar, banjo, ukulele and bouzouki.

The Turing Guide

by , , Mark Sprevak and Robin Wilson, Oxford University Press, 2017, £19.99, US$ 29.95, ISBN: 978-0198747833

Review by David Glass

For several decades and work, is an excellent contribu- after his tragic and tion to this development and the growing literature untimely death in 1954 on Turing. at the age of just 41, very little was known about The book consists of forty-two chapters divided ’s important into eight sections, with the rst section providing work at biographical material. The rst chapter provides a during the second world brief sketch of Turing’s life, with a helpful timeline war. However, as the of key events, while in the second chapter, entitled full scale of his achieve- ‘The man with the terrible trousers’, Turing’s nephew, ments in codebreaking Sir John Dermot Turing, provides a unique family and the relevance of the wartime eort to the history perspective. The third chapter is a compilation of of computing became clearer, Turing’s reputation extracts from papers and reminiscences of the late has increased dramatically. By providing a very wide- Peter Hilton, who worked with Turing for the last 12 ranging and yet accessible account of Turing’s life years of Turing’s life. According to Hilton, Turing was

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