Last week I updated my personal and work web sites for the first time in far too long and I changed the look of this blog. It doesn’t work perfectly yet as some of the colours and spacing are wrong. And I should get rid of that banner at the top – it’s looking a bit old. On a different topic, I’ve been criticized over on the TES forum for my mechanic analogy. I thought it was good analogy, but PaulDG disagrees: As with all analogies, and having only read those few paragraphs of his work, I’m afraid it looks to me as if he’s the sort of “expert” who’s got us into the problems we’re currently in. Ouch. He then gives a straw man a thorough thrashing and finishes with Houston appears from his analogy to be in favour of understanding without skills. This seems rather illogical: Houston wants students to do more of A and less of B therefore he doesn’t want students to do any B. To be honest I can’t see how anyone could have such a reading of what I said. I was tempted to jump into action with a shout of “Someone is wrong on the internet, I must intervene” but after some reflection I decided to just read the rest of the thread. So, the thread itself is about a very important topic — maths projects in schools. As someone who is trying to prepare a projects module for second year students I am aware how difficult it is to prepare good projects. The problem at all levels, school or university, is that it is very hard to set “medium strength” projects – they are either too easy or too hard. I think the key difficulty is...

## Painting by numbers – restoring frescoes...

posted by Kevin Houston

You may have seen in the news this week that an elderly amateur attempted the restoration of a religious fresco. The result is pictured below. I took the picture from the BBC article that you can read here. By coincidence this week I saw an article by Carola-Bibiane Schönlieb on the mathematical technique of inpainting. This allows restoration of damaged pictures by using some mathematical process to fill in the damaged part. A particular common method is to use diffusion equations – the idea is that we use something like the heat equation. Imagine the ink on the border of the damaged region as being like heat and the heat travels into the region through conduction. Compare the two images below take from a preprint by Schönlieb and others. The top one is a vandalized picture and the bottom is the version restored through a diffusion equation method. Most people probably wouldn’t realize that the picture had been repaired unless they’d been told. Schönlieb and others have worked on restoring the following Austrian fresco Here’s a picture of the proposed restoration (unfortunately only in black and white): The pictures come from a paper which contains the details. The article I saw this week is more accessible and can be read in the Matlab Mathworks...

## The algorithm that runs the world...

posted by Kevin Houston

A colleague in the School of Mathematics, Richard Elwes, has the front cover story of New Scientist. You can read the full article on the Simplex Algorithm...

## Hannah Fry: Is life really that complex?...

posted by Kevin Houston

Mathematics talks at TED are rather rare so I was keen to link a recent talk from TEDxUCl by Hannah Fry which was about the applications of mathematics to complex problems such as human behaviour. After watching it I hummed and hawed. On the one hand this is a very well presented and explained talk (and this is even more impressive as the speaker is a fairly newly-minted PhD). On the other hand, it doesn’t feature much maths and crucially, for me at least, I wasn’t sure that anything has been proved. It wasn’t clear to me that any models have been developed. The wording at the end is fairly vague. Saying “Once we have done this…” leaves open the possibility that it has not been done yet. She also says “we can almost begin to talk about…” which is again too vague. Anyhow, in the end I decided to link to it. It’s only 10 minutes long and does give you some idea where things are headed. The end of the talk is mostly about predicting crime, something I looked into a few years ago when a local policeman contacted the School of Maths for help after watching the TV programme Numbers about a crime fighting mathematician. Unfortunately I was unable to help him with his enquiries as at the time the mathematical models for crime prevention and detection were very poor. The current video sort of claims they have been improved. I...

## A Mathematician Comes of Age by Steven Krantz...

posted by Kevin Houston

I’m a big fan of Steven Krantz. His book on teaching mathematics is the one I recommend most to beginning maths lecturers. The second edition is a must have since it contains short replies to his book from other lecturers, some of them highly critical. Currently, I’m reading his recent book A Mathematician Comes of Age. This is concerned with how a mathematician becomes mathematically mature. From the back cover: “It describes and analyzes how a student develops from a neophyte who can manipulate simple arithmetic problems to a sophisticated thinker who can understand abstract concepts, can think rigorously, and can analyze and manipulate proofs.” I must admit I’ve been diving in and out of the book at random and although I don’t agree with everything he says (or agree with the inclusion of certain topics – why are North Americans so concerned about “Math anxiety”?) there are thought-provoking passages every page or so. The parody of the Evolution of Teaching Math on page 49 is very funny and includes 1980s: A framer sells a bag of potatoes for $10. His production costs are $8 and his profit is $2. Underline the word “potatoes” and discuss with your classmates. Leaving aside the humour, I particularly like the section on Reading and Thinking (p95): It has been observed [No reference given – KH] that the key things that a good teacher does are engage the students in the learning process pace the students teach the students to read Now, reading mathematics is something I’ve thought about and try to get my students to do, see Chapter 2 of How to Think Like a Mathematician (follow the link for free samples of chapters 3 and 4). Like in HTTLAM Krantz mentions the importance of reading with...