A conversation about mathematics, history, games and more, inspired by a Roman dodecahedron. Presented by Katie Steckles and Peter Rowlett.
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A conversation about mathematics inspired by a 3D wooden puzzle. Presented by Katie Steckles and Peter Rowlett, with special guest Grant Sanderson.
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The UK Government have announced the new set of King’s Birthday Honours. Here’s our selection of particularly mathematical entries for this year. If you spot any more, let us know in the comments and we’ll add to the list.
Get the full list from gov.uk. Spot anyone we’ve missed? Let us know in the comments.
It’s been quite a year. We introduced a totally new mathematics degree course, redesigned from the previous version. In addition, restructures and people leaving meant there were fewer of us teaching on the maths degree. All this together means I’ve been teaching new topics aplenty this year. Now we’re at the end of teaching, I’m looking back (and definitely not just looking for things to do that aren’t the marking I must be getting on with…) and thought I would write another of those self-indulgent blog posts that are probably only of interest to me.
This year I have taught over 200 hours across level 3, level 4, and level 6. At a high level, I have taught proof and mathematical thinking, mathematical modelling and simulation, methods in various areas, research and project skills, and maths and society. More specifically, I have been covering the following topics (some in greater depth than others!) [those marked * are new topics for me to teach this year]:
In 1693, Christiaan Huygens was struggling to learn the new calculus developed by his former student Gottfried Leibniz. He wrote to Leibniz asking for “any important problems where they should be used, so that this give me desire to study them”. Ever since, ‘when will I ever use this?’ is a common refrain, especially among engineering students — right?
A study published in 2020 had found engineering students preferred pure problems without context, but we weren’t sure — it turns out defining when a problem is and isn’t placed in context isn’t as easy as we thought. We wrote some questions that were either just ‘solve this equation’ or were dressed up with an engineering context, and asked students what they preferred and why.
We found pretty split preferences between contextual and non-contextual problems, and learned a lot about why different students prefer different sorts of problems and how they solve them (the quotes in the title give a flavour of this). The resulting article has just been published in Teaching Mathematics and its Applications. Check it out!
On the value of context in engineering mathematics problems: students’ perspectives by Patrick Johnson, Peter Rowlett and Alexandra Shukie.
I’m aperiodically working my way through Martin Gardner’s cover images from Scientific American, the so-called Gardner’s Dozen, attempting to recreate these in the LaTeX drawing package TikZ. View the previous attempts.
This time I chose January 1974. The cover image relates to the article ‘The combinatorial basis of the “I Ching,” the Chinese book of divination and wisdom’, reprinted as chapter 20 in the book Knotted Doughnuts and Other Mathematical Entertainments.
There seem to be a lot of numerical coincidences bouncing around concerning the new year 2025. For example, it’s a square number: \( 2025 = 45^2 \). The last square year was \(44^2 = 1936\), and the next will be \(46^2=2116\).
The other one you have likely seen somewhere is this little gem: that 2025 equals both \((1+2+3+4+5+6+7+8+9)^2\) and \(1^3+2^3+3^3+4^3+5^3+6^3+7^3+8^3+9^3\).
But there are more – after all, 2025 does appear in over a thousand search results at the OEIS. Here’s a little collection: