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Handbook of Writing for the Mathematical Sciences

Nicholas J. Higham
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Amy Ackerberg-Hastings
, on
Printed writing guides continue to be important tools in all professions for turning students, practitioners, and faculty into fluent communicators. In mathematics, two main references have endured across three decades: Nicholas J. Higham's Handbook of Writing for the Mathematical Sciences and Steven G. Krantz's A Primer of Mathematical Writing.  Higham(University of Manchester, UK) and Krantz were preceded by two MAA Notes volumes—1989’s Mathematical Writing, by Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts; and 1990’s Using Writing to Teach Mathematics, edited by Andrew Sterrett (both of which can be accessed as e-books for free by MAA members). All of these books exist alongside various manuals that address how to employ the vocabulary of mathematics, such as Jerry Trzeciak’s 1995 Writing Mathematical Papers in English: A Practical Guide and Charles Wells’s 2014 Handbook of Mathematical Discourse.
The first editions of Handbook of Writing and Primer were reviewed jointly by Gerald B. Folland in the October 1998 Mathematical Monthly. Both books also went a surprisingly long time between editions. After 19 years, Krantz completed a second edition in 2017; Robert W. Hayden prepared an MAA Review. Twenty-two years after the 1998 second edition of Handbook of Writing, SIAM presents a third edition, which is the book under review here.
Higham has reorganized most of the chapters and updated the suggestions for further reading, but unsurprisingly the most substantive alterations respond to the dramatic changes in technology and professional practice that have unfolded over the past two decades. The role of the internet in research and communication is a thread throughout the book, of course. The chapter on LaTeX is expanded and accompanied by a new chapter on workflow, which discusses text editors, markup languages, organization of files, and tools such as spelling and grammar checkers. Higham also added chapters on writing blog posts and books, preparing indexes, and refereeing and reviewing, recognizing that even students often engage in professional activities beyond writing a thesis, presenting talks and posters, and publishing articles.
Even though I talk about writing with mathematics colleagues and know enough LaTeX to typeset book chapters from a template, I have not previously used Higham’s manual since my training is in the history of technology and science and my teaching career has unfolded within history programs. My evaluation of the book’s strengths and weaknesses is therefore informed by my longstanding love affair with Kate Turabian's Manual for Writers and Booth, Colomb, and Williams’s The Craft of Research. Like those books, Higham puts considerable effort into writing clearly and describing the nonlinear process of writing in as logical an order as possible. Unlike their aim at multidisciplinary audiences, he includes a chapter on writing conventions and best practices specific to mathematics that addresses the fundamental components of mathematical papers. The rest of the topics are fairly standard for a writing guide. For example, Higham’s chapters on grammar and usage go into some detail on how to avoid common errors. The chapters on the writing and revising process mainly emphasize structure and format (writing titles and abstracts, including tables, and the like) rather than exploring the mix of creative and tedious effort that goes into explaining one’s research in writing, something The Craft of Research does particularly well. Higham’s chapters on the various forms of professional writing give some attention to how these forms differ and why each kind of writing matters, but these chapters are brief summaries rather than step-by-step guides. The book closes with a list of commands for generating symbols in LaTeX, a glossary, and a 363-item bibliography.
I would recommend this book to instructors who are looking for a “one-stop-shopping” reference for students who are beginning to write mathematics, particularly if they themselves are fans of Higham’s style and approach. However, while I think supporting SIAM by purchasing its publications is laudable, my eyebrows did rise at the price tag for this book—current editions of Turabian, The Craft of Research, and the LaTeX manual on my bookshelf combined cost less than Handbook of Writing, with some funds left over to defray the cost of a guide to writing proofs, which I would probably also want to use if I were teaching students mathematical writing. (To be fair, SIAM’s student price is equivalent to any two of the three books I own.) Meanwhile, students using Handbook of Writing will still need a separate citation guide, while some of its sections, such as grammar and refereeing, can be covered just as well with free websites, such as those assembled by many colleges’ writing centers. So, some professors may prefer to read selections from this book as well as a few other choices for mathematical and general audiences before deciding whether to add it to their textbook list.
Amy Ackerberg-Hastings ( supervised the senior theses of over 200 undergraduate history majors at University of Maryland Global Campus (formerly University of Maryland University College), receiving Outstanding Adjunct Faculty and Teaching Recognition Awards for her work. She also co-wrote the curriculum for the history program’s three-course sequence in building research and writing skills—Historical Methods, Historical Writing, and Senior Thesis in History—and selected course materials when all three courses transitioned from purchased textbooks to Open Educational Resources.