My new book, Complex Analysis: An Introduction, is nearly finished. To help my students with revision I created a list of common mistakes and this forms a chapter in the book. As a lecturer with many years of experience of teaching the subject I have seen these mistakes appear again and again in examinations. I’m sure that, due to pressure, we’ve all written nonsense in an exam which under normal conditions we wouldn’t have. Nonetheless, many of these errors occur every year and I suspect something deeper is going on. What follows is not intended to be a criticism of my students, who, luckily for me, are generally hard-working and intelligent. Nor is it an attempt to mock or ridicule them. Instead the aim is to identify common mistakes so that they are not made in the future. And if this post seems negative in tone, the a later one is more positive as it delves into techniques that improve understanding. Imaginary numbers cannot be compared The first mistake is the probably the most common: the comparison of imaginary numbers. For example, students write for a complex number. This cannot be right. If were what does it mean for to be less than ? What is usually intended is the modulus of , i.e., . The point is, unlike real numbers, we cannot order the complex numbers. For example, which is bigger or ? This is difficult to decide! Since complex numbers can be identified with the plane ordering them is equivalent to ordering the points of the plane and clearly this can’t be done — at least not in any useful or meaningful way. One last point needs to be made. Although is incorrect, note that expressions like can be true if is...

The web comic xkcd is well-known for its humour. I’ve also got a soft spot for the educational infographics, such as the following. (Not all the information should be...

I’ve been working on other things for a while but have started to get moving on my latest project: Sequences and Series. This began with the leftovers from How to Think Like a Mathematician. I had written quite a few chapters on analysis, in particular, on the definition of the limit of a sequence. After all, the concept of epsilon-delta proof is a key topic to grasp in mathematics and require deep logical thinking for most students. Anyhow, the chapters had to go as the book would have been too long. I had intended to use them as a basis for a book on real analysis but got involved in a book on complex analysis. Next, one of my colleagues produced a book on real analysis! So rather than be ungentlemanly direct competition for him I’ve used my notes to create a website on Sequences and Series. It’s a bit basic at the moment (and has been up for a while) but I’ll add more this year. A book will follow in due...

This week the joint Gresham College and London Mathematical Society lecture will take place. Reidun Twarock of the University of York will give a talk Geometry: A New Weapon in the Fight Against Viruses. The details are on the Gresham College website. In case you can’t make the talk on Wednesday, then maybe there is a MathsJam near you on Tuesday. And if you can’t make either, then maybe you would like to see last year’s Gresham/LMS talk by Marcus du...

It has been a while since I posted a TED talk. There haven’t been many good ones in recent years. I enjoyed the one below (though I think he could have made clear that men respond the same way as women after asking the “What do you do?” question!). Further Reading The paper on the Honeycomb Conjecture by Thomas Hales starts off with a very good introduction before getting down to the higher level mathematics. Pappus of Alexandria Freeform Honeycomb Structures Not directly related but is an interesting paper from a conference I was at last...

The line up for this year’s London Mathematical Society Popular Lectures has finally been announced. As this year marks the 150th year of the LMS there are four lecturers instead of the usual two. We have Professor Martin Hairer, FRS – University of Warwick (and recipient of a Fields Medal last year) Professor Ben Green, FRS – University of Oxford Dr Ruth King – University of St Andrews Dr Hannah Fry – University College London The lectures will be at different times and different places, see the Popular Lectures webpage. Last year’s lectures are available...

The last post was a monster post. This one is a bit shorter as it exam time at my university so I’m a bit busy. Students these days have it easy with regards to exams. They are given far too much information about how to get good marks. When I was a lad we had to guess what an examiner wanted. Just look at the rubric of this 1980s exam (click to enlarge): I just love “Full marks may be obtained for complete answers to about FIVE questions”! And this is not an isolated case, I have a stack of exam papers like...

Usually I am against books offering general study advice, I favour those that focus on a particular subject. (Which is why I wrote How to Think Like a Mathematician. Mathematics students may also be interested in Lara Alcock’s How to Study for a Mathematics Degree.) I’ll make an exception for Cal Newport’s How to Become a Straight-A Student. Let’s get the bad stuff out of the way first. The subtitle is The Unconventional Strategies Real College Students Use to Score High While Studying Less which, along with the book’s other marketing, makes the scam-like sounding promise that you can do less work and get better grades. This can of course happen but does lend the book a feeling of too-goo-too-be-true. Furthermore, the book could do with some trimming of excess material though, at 216 pages, it is quite short for this type of book. The book could do without the regular mentions of partying and beer swigging but I suspect I’m not the target market for those bits. But leave aside those problems. Why would I recommend the book? Essentially, most of the advice is good. There is the standard stuff that all students know that they should do: get plenty of rest, eat properly, do your work in the morning between lectures to gain a sense of accomplishment. The non-standard stuff is good too. He doesn’t advocate lots of highlighter pens or even a highly detailed to do list. Instead he mostly focusses on the methods for efficient and effective learning. For example, on page 105, he talks of the Quiz-and-Recall method, [emphasis mine] Whether it’s philosophy or calculus, the most effective way to imprint a concept is to first review it and then try to explain it, unaided, in your own words....

My unscheduled summer hiatus from blogging arose from a family emergency that meant I was in stuck in Brazil for about 5 weeks. Not a bad place to be stuck but under the circumstances it was difficult to find time to finish my planned summer posts. For example, I had planned to post about the Fields Medals and as it happened lost the opportunity to report from Brazil about a Brazilian winner. The short story is that, to me, the Brazilians seemed mostly proud but surprised that a Brazilian was even in the running. The hiatus also meant that the deadline for my next textbook wooshed by. Ok, in reality I was never going to make it but I’m even further behind than expected. Anyhow, service will resume when I get back on track after all the time lost. For instance, I’ll let you know what the book is...

The London Mathematical Society runs a regular Popular Lectures Series. These are mathematics lectures by (usually) research mathematicians. In recent years a pair of lecturers has performed in London and Birmingham. This year they will be given by Julia Gog and Kevin Buzzard. (The London performance was last night and the Birmingham one is in September.) If you haven’t got tickets, then the good news is that the lectures are recorded and put online. Currently, an admittedly incomplete, collection of previous lectures is hosted in two different places: Lectures from 2008-2013 Lectures from 1986-1996 Previous speakers have included Sir Tim Gowers, Sir Roger Penrose, Reidun Twarock, Matt Parker, Mark Miodownik, Ray Hill, Vicky Neale and Dorothy...

I haven’t posted in a while for many reasons. One of which is that I’ve been trying to finish a textbook. My target date is July 31 to have the final draft finished. I’m not sure I’m going to make it… Anyhow, I noticed that the Beatles’ first film A Hard Day’s Night is being rereleased. ‘But what’s the opening chord to the title song?’ I hear you say. Funny you should ask, that gives me a chance to show again my modest attempt at solving the...

The name Martin Gardner is familiar to most mathematicians. He wrote numerous on mathematics from a culture and leisure viewpoint. (You can find his books on Amazon.) Next week Persi Diaconis will give a talk at the British Mathematical Colloquium (BMC) on the life and work of Martin Gardner. The BMC is an annual gathering of research mathematicians in the UK and beyond. Diaconis’ talk is a public lecture so anyone may attend but a (free) ticket is required. Details of the talk are here. I’ll be attending so do say hello if you see me. For all of those unable to attend but want to know a bit more about Gardner then Diaconis has co-written a biography of Gardner (as well as a great mathematical magic book). There is also a recent article in the New York...

Today is St. Valentine’s Day, the day in much of Western culture arbitrarily designated to be the day for love. So let’s see what mathematics has to say on the subject. Finding a relationship with someone special is often about being introduced to people and sifting out the inappropriate. It seems clear that there is plenty of scope for the application of statistical techniques to the processes of meeting and weeding. First up is a great video from the ever-so-slightly geeky Amy Webb, who used mathematics to calculate the odds of finding a mate in Philadelphia. After producing a figure of 35 suitable men satisfying her criteria in a city of 1.5 million people she realized that she would have to turn to maths for help. There’s even a book, Data, a Love Story. Over on Wired, Chris McKinlay’s attempts to hack OKCupid’s online dating service is profiled. The article left me in two minds. Is this is great use of mathematics or is it just a bit creepy? Seemingly, the approach worked for him and no one is reported injured, so perhaps I shouldn’t judge. As a bonus, Wired also produced a handy infographic slideshow describing tips for improving online dating profiles. Top tips: Avoid Karaoke, get into surfing. My favourite though is that it is more attractive to mention “cats” than “my cats”. If everything goes well with the dating, then how do you arrange the wedding? “With maths” is not the standard answer. The Guardian reports on a statistically modelled wedding. This solves the centuries old problem of how to write the guest list. After all, you don’t want too few guests or too many accepting. Next post: Calculating the likelihood of...

One needs only look at some of Fomenko’s monstrosities to see that mathematics and art don’t always mix well. Exceptions are rare with Escher the benchmark for excellence. A recent Wired article on the Venezuelan artist, Rafael Araujo, describes how he produces his mathematically constructed pictures. I can see these joining Escher’s pictures on the walls of mathematicians throughout the world over the next few years. The full article is here but you can also see stunning examples on his...

Belated Happy New Year! Here’s another of those short educational TED videos. This time on the Hilbert Hotel. (A cartoon Hilbert does seem to make an appearance but it is hard to tell as he isn’t wearing the hat. Do you think Hilbert wore that hat just once and had the misfortune of having it appear in his most famous picture?) Anyhow: You can find out more at the TED Education page for the video. Oh, and this week is the last chance to win a signed copy of Simon Singh’s book on The Simpsons! See...

Should have posted this the other day: Last Friday Radio 4 transmitted a programme on maths and magic entitled, Maths and Magic! It features Jolyon Jenkins investigating the connection between the subjects in the title. You can hear it here for at least a few days. There are links on the web page but I thought I should add some. One of the magicians, Alex Stone, wrote one of my favourite books of the year, Fooling Houdini, which is about how he realized he was a terrible magician and devoted himself to changing that by immersing himself in the study of magic. He also does the same trick as Jenkins and there is a deeper explanation of it in the book. The Radio 4 website also lacks links to MathsJam and to James Grime, a contributor to Numberphile. Furthermore, the website cites Persi Diaconis as the sole author of Magical Mathematics when in fact it was co-authored by Ron Graham. And on the subject of Radio 4, today’s Infinite Monkey Cage isn’t about maths but is well worth a listen because of the excellent contributions from James...

This is a rather belated review of Simon Singh’s talk on The Simpsons and Their Mathematical Secrets given for the Leeds Skeptics in the Pub in the Victoria Hotel pub. (There’s a chance to win the book, details below.) The Victoria is not a large pub so I did wonder where the audience was going to fit. In the end I counted nearly 100 people and this did not include those standing in the corridor or in the street outside. The Sardine Conjecture for @SLSingh at @leedsskeptics pic.twitter.com/XqE0p3lOs5 — Martin Iddon (@WalrusofComms) October 20, 2013 The talk is in two halves, the first covers the book and in the second Singh bravely invites questions on any topic connected to his work. The book part of the talk, accompanied by slides, delves into the mathematical backgrounds of the writers of The Simpsons and Futurama and how they inserted mathematical jokes into the programmes. Some of this was familiar as I’m a fan of both shows (though The Simpsons seems to have jumped the shark a while ago — Ned secretly married Mrs Krabappel!?) but Singh has done his homework and gained access to the writers so there is plenty here that was new to me. One of my favourite bits from the book wasn’t mentioned in the talk — there was a theorem invented purely for an episode of Futurama. So, the first part of the talk was about the book and during the interval Singh signed copies. Afterwards he did a question and answer session which amongst other things covered libel laws, Fermat’s last theorem, the Big Bang and quack medicine. The tour continues for another month, details can be found here. A great talk – you won’t be disappointed if you go. —-...

In this post I interview Richard Elwes, author of a number of maths books in recent years. He has kindly agreed to give away signed copies his two most recent, Mathematics in 100 Key Breakthroughs and Chaotic Fishponds and Mirror Universes. For a chance to win all you have to do is sign up for my newsletter, see the right sidebar or the bottom of this post. I’ll get my daughter to randomly pick two winners from the list of subscribers in a couple of weeks. On with the interview… Hello Richard! I think we first met when you were a PhD student here at Leeds. Can you give a quick account of your background to help people get a feel for where you are coming from? I initially followed a conventional academic path: I studied maths as an undergraduate at Oxford, and then moved north to Leeds to start a PhD in 2001, where I met you among other excellent people. My research at that stage was in the general field of mathematical logic. Afterwards I held a postdoctoral position in Freiburg in Germany, and at some point after that I somehow found my way into writing about maths for the general public. Apart from books, I’ve written for the New Scientist, and for the excellent Plus magazine online. In fact I got my first break there, when I won their New Writers’ competition in 2006, with an article about the classification of finite simple groups (http://plus.maths.org/content/os/issue41/features/elwes/index). Your book Maths in 100 Key Breakthroughs came out last month. What’s it about? Who is it aimed at? It’s aimed at anyone who finds the idea of maths interesting and appealing, but who doesn’t want to drown in equations and jargon. So it’s written with...

The week has been so busy that posting this has been delayed – I’ve been to London, Birmingham and Sheffield in the last three days. I did manage to install for a newsletter sign-up form for the blog. You can see it in the sidebar unless my hacks to the code have destroyed it for your browser. Please sign up if you want to know about maths articles, events, etc. Back to business. Simon Singh‘s new book, The Simpsons and Their Mathematical Secrets, is as the title suggests about the mathematics occurring in the long running cartoon The Simpsons. Now, I knew there were plenty of maths gags in the Simpsons but I’m surprised he has filled a whole book. Maybe he also includes stuff from Futurama which was packed with maths gags and even led to a lecture by Sarah Greenwald. This became a DVD extra on Bender’s Big Score (The audience features Simpsons and Futurama’s creator Matt Groening.) Singh’s book is not out yet but you can read an article about it in last Sunday’s Observer. He’ll be doing a (rather small) tour to promote the book, details are on his website. I’m planning to be at the Leeds event so maybe I’ll see you...

The ruler has remained unchanged for thousands of years. Now it has been updated! You can read more (but not much) at Anirudh Sharma’s website, Creative Applications, Gizmag, and...

First a plug for the next Maths Jam in Leeds: It will be on Tuesday 23rd at 7pm in the White Swan (it’s pretty much next to the City Varieties). I’ll be there (I know that if don’t publicly commit to it, then I’ll miss it) so maybe I’ll see you there! Here’s a link to a rather good Ted Ed video on Zeno’s paradoxes. I wish I had seen this before I gave my History of Maths course this year, it would have been quite useful despite its simple nature. There is a page for further information on the this...

This is a strange one: How to make edible conic sections! You can find the details at Evil Mad Scientist. If you enjoy maths-related cooking, then see my post on Tau-nados. Does anyone else have any other...

The usual busyness at the end of the teaching term and a holiday last week have meant that I’ve not been posting for a while. Today’s post is a short one from me directing you to a fairly long post by Stephen Wolfram on his recent visit to the Leibniz archive in Hannover. Read it...

I never miss a chance to rummage around in second-hand book shops. In the past bargains were easy to come by but now the internet has killed that off. Now all books are priced pretty much the same and I no longer have the experience of approaching the counter carrying a much-underpriced book with the feeling that I am stealing from the shop and am about to be discovered. Those days are gone. As they are not experts, unfortunately charity shops price their books by consulting the web. This leads to setting the price of some dog-eared copy at just below the price of a mint condition one. Also, I miss the end-of-search feeling as I come across a long sought-after book. These days if I want a book I can find it on Amazon or Abebooks in minutes. The latter is my favourite second-hand book-seller site. They often send me emails about books and a recent one is worth sharing. One of the most expensive sales on the site in March was a book by Lagrange. The relevant part of the article is the following. Our list also includes an historic textbook from 1788 that has had a lasting influence on mathematics. Sounds a bit dull? Not at all. Méchanique Analitique by Joseph Louis Lagrange sold for $13,112. Born in Italy, Lagrange became a famous academic in France and Germany, and managed to survive the French Revolution despite the carnage surrounding him. Méchanique Analitique advanced analytical mechanics beyond the work of Isaac Newton and Galileo Galilei. He wrote the book while in Berlin where he was director of mathematics at the Prussian Academy of Sciences. It was his greatest piece of work, although he contributed widely to mathematics and astronomy. He laid down...

Recently, an acquaintance from my days as a researcher at Liverpool University alerted me to the existence of the Museum of Mathematics in New York. My acquaintance, Janet West, was a PhD student when I was at Liverpool and is now involved in the museum. There’s plenty of stuff online to look at but I would like to draw your attention if you have not already seen it to a lecture by Colin Wright. Colin is well-known in the mathematics communication community as he probably does more mathematics talks in schools around the country than anyone else. His main talk is about the mathematics of juggling. You can see him talking on to the BBC about it by clicking this link. (Note that the headline says he is a teacher whereas in fact his job is in marine navigation!) Colin gave a talk at the Museum of Maths in New York which was recorded and is on YouTube. You can even buy a DVD version. Teachers: If you are interested in seeing his talk at your school, then go to his...