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Dynamic generation of maths questions
I was recently asked about my MSc dissertation (by someone who may choose to ‘out’ themselves here, but as it was a personal email I won’t name them). In my dissertation, for a Masters degree in computing in 2003-4, I developed a system for pre-processing MathML code using PHP to include pseudo-randomised values in the questions for an e-assessment tool. The title is ‘Asking Questions With MathML: dynamic treatment of XML and pseudo-randomised mathematics assessment’.
The query was from someone who is training to be a maths teacher and is doing some web development. They had seen mention of my MSc dissertation topic on this blog and asked where they could read more about the underlying web technologies. Here, basically, is what I replied.
Interesting Esoterica Summation, volume 8
Mathematicians! Stop what you’re doing! I’ve almost certainly got something more interesting for you here. It’s been a good while since I last updated you on the contents of my Interesting Esoterica collection, and I have a proportionate number of mathematical curiosities to entertain and bewilder you with.
In case you’re new to this: every now and then I encounter a paper or a book or an article that grabs my interest but isn’t directly useful for anything. It might be about some niche sub-sub-subtopic I’ve never heard of, or it might talk about something old from a new angle, or it might just have a funny title. I put these things in my Interesting Esoterica collection on Mendeley. And then when I’ve gathered up enough, I collect them here.
In this post the titles are links to the original sources, and I try to add some interpretation or explanation of why I think each thing is interesting below the abstract.
Some things might not be freely available, or even available for a reasonable price. Sorry.
What do these three pictures have in common?
What do these three pictures have in common?
The first is the bust of Nefertiti, an Egyptian queen. The bust is now in the Neues Museum in Berlin and is one of the most beautiful works of art. Nefertiti is translated as “a beautiful woman has come”. The word nefer is in this case translated as ‘beautiful’.
The second is a drawing of a Grecian urn by Keats. Keats’ Ode on a Grecian Urn ends with the line “Beauty is truth, truth beauty,”.
The third picture is part of the Moscow Mathematical Papyrus from ancient Egypt.
Probability of dealing four perfect hands of cards in a world of random shufflers
A couple of months ago (really? Two years?! Man!) I posted about an extraordinary coincidence: in a game of whist at a village hall in Kineton, Warwickshire, each of four players had been dealt an entire suit each. My post ‘Four perfect hands: An event never seen before (right?)‘ discussed this story. What really interested me was that the quoted mathematical analysis — and figure of 2,235,197,406,895,366,368,301,559,999 to 1 — appears to be correct; what lets down the piece is poor modelling. The probability calculated relies on the assumption that the deck is completely randomly ordered. Apart from the fact that new decks of cards come sorted into suits, whist is a game of collecting like cards together, so a coincidental ordering must be made more likely. Still unlikely enough to be worthy of mention in a local paper, maybe, but not “this is the first time this hand has ever been dealt in the history of the game”-unlikely.
Anyway, last week I was asked where the quoted figure 2,235,197,406,895,366,368,301,559,999 to 1 actually comes from. Here’s my shot at it.
Carnival of Mathematics 104
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of October, and compiled by Shecky Riemann, is now online at Math-Frolic.
The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.
Why maths isn’t like science (and may be evil)
Yesterday I gave a talk to the Nottingham Trent University Maths Society, ‘A brief history of mathematics: 5,000 years from Egypt to Nottingham Trent’. I had a slide in this where I said something about what the Greek style of proof means for mathematics. It has helped me put my finger on something of why mathematics isn’t like science, and I thought I would share it here so I can look it up when I’ve forgotten again.