post

Maths on the Back of an Envelope

Rob Eastaway is a recreational mathematician, author, speaker, and maths event organiser. His latest book, Maths on the Back on an Envelope (Amazon UK, Waterstones, Maths Gear (signed)), is all about how to (roughly) calculate pretty much anything.

Style

Maths on the Back on an Envelope is an easy-going and enjoyable read. It takes the reader through some methods of approximation of numbers, while showing the reader why being able to perform such approximations is a useful skill. As well as suggesting the use of approximation to check that the correctness of answers, or to work out the approximate size of answer that should be expected, the book also makes the very good point that often an approximation is the best that we can do, and giving answers to a greater-than-appropriate level of accuracy can be misleading.

Control

The book explains the methods of approximation in a very understandable manner, and also justifies their use and appropriateness. Throughout, the user is challenged to try out their newly found calculation skills; the solutions to these challenges are given the back of the book, alongside some discussion of some ways people go about answering them.

Damage

The discussion of estimation and accuracy in this book is very strong, and is not something I’ve read much about elsewhere. The book sets itself apart from other books by encouraging you to actively engage in tasks related to the material being discussed, and you may find yourself finishing it with a far greater understanding of what everyday numbers mean.

Aggression

Although many of the methods of mental or on-paper calculation discussed in this book will be familiar to the keen mathematician, this book is still an enjoyable read, and even the most capable calculator can benefit from thinking about the issues surrounding accuracy in this book. I’d most strongly recommend this book to those looking to improve their skills with numbers, or to improve their understanding of numbers around them an in the news, but there’s still plenty to enjoy here for others.

post

The Maths of Life and Death

Kit Yates is a senior lecturer in the Department of Mathematical Sciences at the University of Bath, who works in mathematical biology. His first book, The Maths of Life and Death (Amazon UK, Waterstones), is all about the maths of life and death.

Style

The Maths of Life and Death takes the reader on a tour of seven important areas of mathematics that underpin life and death. Many of the ideas discussed are related to medical and biological applications of maths and stats, and included stories about when misunderstanding or misinterpreting numbers could have (and sometimes have had) very grave consequences.

Control

The maths in this book is well explained, and the application to real life issues both makes the maths more accessible to the less mathematical reader, and makes the book more interesting to the knowledgable mathematician who may be familiar with much of the maths but will be less familiar with the practical contexts where it can be applied.

Damage

The strongest sections of the book are those in which Kit discusses medical statistics and disease modelling. As his own research is based near these areas, he is able to draw on his personal knowledge of these areas, while maintaining reader-friendly explanations of the maths involved. There are many books about biology and medicine aimed at the general reader, but the maths involved in these pursuits is rarely presented to such an audience: this is this book’s biggest strength, and it sets it apart from many other maths books.

Aggression

I would recommend this book to those interested in maths, and those interested in medicine or biology as they will get a lot out of reading about the maths underlying much of the work in these areas. I have a few people in mind who might be getting this one next Christmas…

post

Humble Pi

Matt Parker is a stand-up mathematician, YouTuber and all-round maths lover. You can read more about him in our interview with him that appeared in issue 09. His latest book, Humble Pi (Amazon UK, Waterstones, Maths Gear (signed)), takes the reader through a range of mathematical topics by looking at past errors that have been made in these areas.

Style

Humble Pi is a very entertaining read. Writing about mistakes, and the consequences of mistakes, allows Matt to include a number of amusing, and sometimes slightly frightening, anecdotes. These mistakes are used as an “excuse” to explain the underlying maths in an informative and engaging way.

Control

The mathematical ideas contained in this book are very clearly explained, and each one is attached to a real life mistake, making the importance of each bit of maths immediately clear.

Damage

As this book is about mistakes, and mistakes that have easily noticeable consequences make the best stories, the maths in this book is mostly that related to science and engineering. This means that the book spends time on topics that many maths books pass by, such as the resonance of bridges and financial maths. I enjoyed the financial maths section in particular, as this is an area that I don’t usually read about or spend much time thinking about.

Although readers may be aware of some of the the famous mistakes, such as the wobbly Millennium Bridge or Pac-Man breaking on the 256th level, there are many great stories here that readers will not be familiar with; and readers may well not know the true mathematical reasons behind the more famous stores.

Aggression

Overall, Humble Pi is both fun and interesting, and I would highly recommend it. I have in fact already given it to two friends as a present, and might be gifting it to more people this year now that the cheaper paperback is out.

post

So You Think You’ve Got Problems?

Alex Bellos is a writer and broadcaster, and is The Guardian’s puzzle columnist. His latest book, So You Think You’ve Got Problems? (Amazon UK, Waterstones, Guardian bookshop), is a collection of puzzles.

Style

So You Think You’ve Got Problems? contains 125 puzzles, plus a selection of shorter ‘teaser’ puzzles spread throughout the book. Between the puzzles, Alex tells us of the historical context of the puzzles, points out connections between puzzles, gives small hints, as well as discussing what makes a puzzles good.

Control

The book ends with answers to all the puzzles, including clear explanations of how these solutions can be found.

Damage

As anyone who follows his Guardian puzzle column will know, Alex has very good taste in puzzles. Unsurprisingly, therefore, this is a great collection of puzzles, and there is plenty in this book to keep you thinking for a long time. I do a lot of puzzles, and some of the puzzles in this book were similar to puzzles I’d seen before, but there were plenty that were not familiar to me and lots of new situations to think about.

Aggression

I’d recommend this book to anyone who like puzzles and can think of a few people who I could give this to next Christmas…

post

Here Come the Numbers

Kyle D Evans is maths teacher and an award-winning maths communicator and musical comedian. Hana Ayoob is an illustrator, science communicator, and creative producer of science events.

Together, they are the creators of Here Come the Numbers (Amazon UK, Waterstones, Explaining Science Publishing), the fourth book on the Chalkdust Magazine Book of the Year 2019 shortlist.

Style

Here Come the Numbers is a rhyming picture book. Each page of Here Come the Numbers features rhymes about numbers alongside illustrations of the ideas involved. At first glance, it looks like a children’s book, and it starts as many children’s maths books start: with small positive integers. But unlike many children’s maths books, it doesn’t stop there.

Damage

Here Come the Numbers quickly goes beyond the topics contained in your usual learning-to-count book. It introduces the reader to prime numbers, with illustrations of rectangles of objects to show factorisations, before touching on Pythagorean triples, negative number, and even Fermat’s last theorem. It does this while maintaining the easy-to-read and child-friendly style.

In a few places in the book, the reader is encourage to think about something, for example which squares can be broken into two smaller squares. These prompts provide the reader with opportunities to investigate mathematical ideas themselves.

Control

The ideas in Here Come the Numbers are very clearly articulated, and the illustrations work really well alongside the text to make the ideas easy to visualise.

Aggression

I would strongly recommend this to parents of young children, and I am eagerly awaiting the day when my niece is old enough to read it with her.

post

The Art of Logic

Eugenia Cheng is a mathematician who is currently Scientist-in-Residence at the School of the Art Institute of Chicago. You can read more about her in our interview with her that was printed in issue 08. The third book on the Chalkdust Magazine Book of the Year 2019 shortlist is The Art of Logic: How to Make Sense of a World that Doesn’t (Amazon UK, Waterstones), Eugenia’s effort to drag formal logic down from its ivory tower and modern political discourse up from the gutter, and sit them round a conference table for a long overdue reconciliation.

Style, control, damage and aggression

Eugenia has grand ambitions in her latest book. When I first picked it up I confess I assumed that it wasn’t really aimed at me, a mathematician, and someone who is already reasonably well versed in formal logic. To some extent this is true of the first of three parts of the book, which surveys the essentials of propositional and quantifier logic. It does this however through the lenses of some of the hottest points of contention in modern social and political discourse: gone are the dreary predicates and facile conclusions of other treatise on logic, instead we learn implication by interrogating white privilege; negation by negotiating Brexit; and quantifiers by questioning sexism.

In a book which is ostensibly advocating for the broader use of abstract logic across all modes of discourse, part two comes as a refreshing riposte to that particular brand of mathematician who holds their subject as not merely superior to all others, but also claim its logical basis as an unimpeachable ziggurat. Cheng is not only forthcoming about the limits of logic, but actively embraces them as the way in to productively unifying the logical and emotional approaches to argument, discussion, and consensus.

This sets the stage for part three, where the promise of the subtitle is repaid. It provides a practical guide for how normal people (and indeed mathematicians) can actually apply ideas from formal logic to every day situations, as well as to interrogate their own beliefs and justifications for those beliefs. It is also an opportunity for Cheng to lay down her vision of the ideal format of interpersonal arguments and political discourse, and what it means to be an intelligently rational person. Contrary to the perhaps widely held belief that logic and emotion are antithetical – that the only things emotion can bring to an argument are fallacies – Cheng argues that logic and emotions not only can coexist in a rational debate, but must coexist. She writes “I think we can use this superpower [intelligent rationalism] to help the world bridge divides, foster a more nuanced and less divisive dialogue, and work towards a community that operates as one connected whole.”

Overall then I think the book succeeds in being approachable for someone with no training in formal logic, while still being engaging enough to sustain the interest of a professional mathematician throughout. From the start with an apparent oxymoronic title, at every stage Cheng manages to subvert the expectations of the reader as to the scope, applicability, and practicality of logic. The core message of the book, which if it can be reduced to a single word would be empathy, is hardly a novel one; the novelty comes from the framework with which Cheng approaches the topic, and this really makes this book stand out.

post

A Compendium of Mathematical Methods

Jo Morgan is a maths teacher, poster of high quality teaching resources, tweeter, and organiser of excellent events. The second book on the Chalkdust Magazine Book of the Year 2019 shortlist is A Compendium of Mathematical Methods (Amazon UK, Waterstones, Foyles), a book written by Jo containing various methods for completing mathematical tasks that you need to do at school.

Style

This book presents multiple methods for performing common school-level mathematical tasks, such as subtraction, multiplication, simplifying surds, and polynomial division. These range from the most common methods that most readers will be familiar with to more unusual and unknown methods (often due to being older and not longer fashionable).

Control

The book presents multiple examples of each method alongside very clear explanations of the what is being done. For the less familiar methods, explanations of how the method works are given, alongside some historical or geographic context of where any why these methods were/are used.

Damage

This book presented many methods that I was unfamiliar with, and I had lots of fun working out how these methods related to methods I was more familiar with and how they worked. I particularly enjoyed the polynomial division section, where methods equivalent to polynomial long division, but with steps in which it was much more clear what was actually being done to the polynomial, were shown.

Aggression

I would strongly recommend this book to my maths teacher friends, and wish I’d had a copy of it when I used to be a maths teacher myself. I’m less likely to recommend it to my non-teacher friends, as the book has a clear teaching focus, but I know a few non-teachers who would find the discussions of different arithmetic methods interesting.

post

Geometry Puzzles in Felt Tip

Catriona Shearer is a maths teacher who posts lots of really good geometry puzzles on Twitter. The first book on the Chalkdust Magazine Book of the Year 2019 shortlist is Geometry Puzzles in Felt Tip (Amazon UK ), a book containing all the puzzles that Catriona posted in 2018.

Style

This book is very pretty, each page contains one puzzle with a description and a large (hand-drawn in felt tip pen) diagram.

Control

If you like geometry puzzles, then you will love this book as it is full of creative puzzles that will get you thinking. This book is especially good if, like me, you often miss Catriona’s puzzles on Twitter and want a way to catch up with them.

Damage

The puzzles in this book were created by Catriona, and almost always involve situations I have not puzzled about before. This makes the book great for seasoned puzzlers who are running out of new puzzles.

Aggression

I would strongly recommend this book to friends, especially those who are into puzzles. I’m very much hoping that a follow up book of puzzles from 2019 will be coming out soon…