Walking Randomly

It’s that time of year again – a time when your thoughts naturally turn to what Christmas presents you might buy for the geek in your life.  If you are a geek yourself then this is an easy exercise – just think what you might want yourself and buy that.  Geeks know what other geeks like you see!

What if you are not a geek though?  How do you work out what your nerdy friend would like most for Christmas?  What you need, dear reader, is a geek guide – someone of the nerdy persuasion who can help you separate the geek wheat from the nerd chaff.

Now if you have read much of my blog you will have probably come to the conclusion that I am a geek (or possibly a nerd – the difference is subtle) and so maybe you are thinking that I can help you.  Well, maybe I can – but only for a certain type of geek.

You see, there are many varieties of geek and each one has different needs and wants, thus making it impossible to write a post entitled “Christmas gifts for geeks” which will please everyone.  So, I am going to concentrate on gifts for the mathematically inclined which includes (but is not limited to) mathematicians, scientists, engineers and, most importantly…..me!  Many of my friends read this blog and so this post is mainly a shameless hint dropping exercise but it is possible that it will be of use to other people as well.

In addition, if you actually buy any of these books using the links in this post then I will earn some commission from Amazon without it costing you a penny extra.  Doing this helps support Walking Randomly and is greatly appreciated but I really won’t mind if you choose not to.

Books

For the mathematician in your life you almost certainly cannot go wrong by buying them a book – just make sure that they haven’t already got it!  Another tip is ‘don’t try to be too specialised’ – advanced textbooks may well be useful but they are not (often) much fun and Christmas presents are supposed to be fun!

With these thoughts in mind I will separate this section into two parts – books I own and books I wish I owned.  In addition, I will only consider the lighter side of the mathematical spectrum (for a given value of ‘lighter’) so these books should be of interest to mathematicians of any level – from high school students to research scientists.  The large number of equations that some of them contain may make them look like text books in some cases, but let me assure you that they are (mostly) easy reading.

Books I own – and highly recommend

• “e”, The Story of a Number by Eli Maor.  Some numbers are so important that they get whole books written about them and e (sometimes known as Euler’s number) is one of them.  It’s a constant that certainly gets around as it appears in all manner of places from compound interest to calculus with detours through subjects such as complex analysis and trigonometry. This book is easy to read and contains a mixture of mathematics, history and biography.
• An Imaginary Tale: The Story of “i” by Paul Nahin. I’ll never forget the look on my dad’s face when he asked what I was learning at University and I told him ‘they are teaching us about imaginary numbers.’ It didn’t exactly strengthen his faith in further education I can tell you!  It turns out that  the term ‘imaginary’ is an unfortunate byproduct of history and if you delve into the mathematics then you’ll soon learn that not only do imaginary numbers exist but that they form the basis of one of the most beautiful and powerful areas of mathematics there is.
• Gamma: Exploring Euler’s Constant by Julian Havil. Everyone has heard of Pi, quite a few people know about e but you’ll be hard pressed to find a non-mathematician who knows about Gamma. Impress the mathmo in your life by giving them a book about a mathematical constant that has been seriously undersold by its PR team. It contains some heavier mathematics than the books mentioned above but it is still accessible to good high school students and undergraduates.  I’m still working my way through it to be honest and loving every minute.
• Flatland: A Romance of Many Dimensions by Edwin Abbott.  We live in a three dimensional world world (some say 4, some say 11 but for the sake of this note I am saying 3) but what would it be like if we inhabited a world of only 2 dimensions.  Imagine how life would be in such a world and how we would react to a mysterious visitor from the 3rd dimension.  Edwin Abbott did exactly this and in the process wrote a satire on Victorian England (the book was written in 1884, making this a very early example of science fiction).  This is a very charming (and very cheap) book that was first recommended to me by a fellow physicist.
• The Music of the Primes by Marcus du Sautoy.  Prime numbers fascinate us, there can be no denying that, and in this book Marcus takes us to meet some of the people and mathematics behind them.  Some reviewers complain about the fact that the mathematics isn’t detailed enough but then others may well say that it is too mathematical – writing popular maths books is a difficult game.  Personally I think he had it just right and told a great story with just enough maths to keep it from being a book on history rather than a book on maths .  Whenever I wanted more detail I looked to other sources and this got me reading more books on number theory.  This is precisely what popular maths books should do in my opinion – invite the reader in….show them enough to whet their appetite but not so much that it scares them off,  point them in the direction of further study and leave them wanting more….
• The Man Who Loved Only Numbers by Paul Hoffman.  This is a book about the life of an extremely eccentric mathematician called Paul Erdős – one of the most prolific writers in mathematics apparently. Erdős was a strange character but an extremely well respected mathematician.  This book is serious easy reading and contains a lot less actual math than most of the other books I mention here. I have a copy in my office and many people have borrowed and enjoyed it – only one of them was a mathematician by training. This is a great book.  In fact I am going to read it again on the train home this evening.
• Inside Your Calculator: From Simple Programs to Significant Insights by Gerald Rising. “Sir, how does the calculator know the sine of a number?” I innocently asked my teacher at the end of a maths lesson back when I was far too young to have a scientific calculator.  He blustered for a bit before answering ‘It stores them in memory – it’s just a big look up table’.  I was deeply suspicious.  That would take a lot of memory I thought!  A lot more than my cheapo calculator had that’s for sure.  So how do calculators do this stuff?  This book makes a good job of explaining the detail (hint…CORDIC).
• Surely You’re Joking, Mr.Feynman! by Leighton, Feynman and Hutchings.  Richard Feynman is an all time hero of mine and this book is a collection of anecdotes about his life.  If memory serves me there is not a single equation in this book but I would be surprised to meet a mathememtican who doesn’t enjoy it.  Wanna see the human side of a genius?  Buy this book then.

Books I wish I owned (feel free to buy one for me if your mood takes you that way.)

• The Princeton Companion to Mathematics Edited by Timothy Gowers (click here for his blog) – This beautiful looking book is for the more serious mathematician but it is the sort of thing that will remain on their bookshelf for years to come.  Essentially it is a guide to as much pure mathematics as you can fit into a single volume and would be a perfect addition to any mathematicians library.  It’s a bit expensive but looks like it’s worth every penny.
• Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi by Martin Gardner. Martin is something of a legend among recreational mathematicians and has many books and articles to his name. He wrote the ‘mathematical games’ column for Scientific American for many years where he picked up a large following among mathematicians at all levels. This book is a collection of some of the best of his Scientific American articles that have been expanded with updates and new material.  Even if you only have a passing interest in mathematics – this looks like a good book to get.
• Bad Science I feel like I know Ben Goldacre well and yet I have never met him but his blog and column in the Guardian have kept me entertained and informed for years.  An expert in refuting dodgy statistics and sham science, Ben takes no prisoners.  I find his writing extremely entertaining as well as providing much food for thought so naturally I would like his book.  Where is the maths connection?  Well, maths is often abused by the media and it’s often statistics that gets abused.  Ben tends to have a lot to say about that.
• An Adventurer’s Guide to Number Theory by Richard Friedberg.  I have no idea what this book might be like but I enjoy number theory, I like the title, it gets good reviews and it’s reasonably priced.  Sounds good to me.
• Digital Dice Computational Solutions to Practical Probability Problems by Paul Nahin.  I have a couple of Nahin’s books and they are both great so I am guessing this one will be just as good.  From what I have seen, he includes lots of simulations in MATLAB.  Randomness?  MATLAB? Nahin?  Of course I want this book.
• Nonplussed: Mathematical Proof of Implausible Ideas by Julian Havil.  There are a lot of true facts in Mathematics that make you say ‘no way – that can’t be true’ when you first hear them.  I have said this to myself several times over the years and it usually takes a good, solid proof (along with several concrete examples) before I concede the point.  By the sound of it this book is choc full of this sort of thing.
• Euler’s Gem: The Polyhedron Formula and the Birth of Topology by David Richeson.  Euler’s name seems to be everywhere in mathematics – you only need to look at this list from Wikipedia to get an idea of just how pervasive his ideas have become.  I have never seen this book and I don’t know much about his polyhedron formula but I do intend to find out.
• The Drunkard’s Walk: How Randomness Rules Our Lives by Leonard Mlodinow.  When you write a blog called ‘Walking Randomly’ you really should have some books about randomness on your shelf.  That’s partly why this one is here.  The good reviews don’t do any harm either.