Tag Archives: mathematics

Fields arranged by purity (new take)

Epistemological philosophers were pure before it was cool…

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A mathematician’s nightmare: Lockhart’s lament

I might have posted this already, but here it is again for George! One of my favourite texts written by a mathematician about mathematics and the way in which it is (but ought not be) taught.

https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

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Group theory in simple English

Are you sick of academese? Or maybe your field really is so hard that the thought of explaining your research to your grandma has never even crossed your mind? Now you have a chance to explain a hard idea (e.g., your research topic) in simple words – in fact, with only the 1,000 most used words! A friend who is a group theorist has just made group theory sound awesomely simple: 

A group is a set of things with a way of putting two things together to get another thing. One type of group is all the ways of moving three things in space to a different place, and in fact if space was “bigger” we could get a bigger group by having more things to move. If we only do some but not all of these moves we can get a smaller group, but sometimes this will only be a little bit smaller than the group that we started with. I am interested in trying to find all of these slightly smaller groups in the situation where we are trying to move ten add six or ten add seven things.

And here is a longer explanation of Hilbert’s Hotel:

The House of Mr Hilbert:
Suppose that you are a person who has a big house where other people can give you money in order to come and live in a room for a short time. (click here to read the rest) …

Try it out here and post the results in the comments!

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What should we teach to liberal arts students who will take only one math course?

Interesting discussion about what and how much mathematics university students on liberal arts courses in the US should know on mathoverflow – here

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The price of a citation, or How did King Abdulaziz University get in the world’s top 10?

According to a great recent blogpost by Berkeley academic Lior Pachter, there is something very fishy about university rankings.  In last week’s global university ranking published by the US News and World Report (USNWR), the top 10 universities listed in mathematics are:

1. Berkeley
2. Stanford
3. Princeton
4. UCLA
5. University of Oxford
6. Harvard
7. King Abdulaziz University
8. Pierre and Marie Curie – Paris 6
9. University of Hong Kong
10. University of Cambridge

The USNWR rankings are based on 8 attributes:

– global research reputation
– regional research reputation
– publications
– normalized citation impact
– total citations
– number of highly cited papers
– percentage of highly cited papers
– international collaboration

Now, how did KAU end up in the top 10?  Its chair received his PhD in 2005 and has zero publications.  Its own PhD programme is only two-years old. It has separate campuses for men and women.  The author, and probably many other mathematicians, have never heard about KAU. Apparently, the secret of the ranking success lies in the fact that,

“[a]lthough KAU’s full time faculty are not very highly cited, it has amassed a large adjunct faculty that helped them greatly in these categories. In fact, in “normalized citation impact” KAU’s math department is the top ranked in the world. This amazing statistic is due to the fact that KAU employs (as adjunct faculty) more than a quarter of the highly cited mathematicians at Thomson Reuters. “

The article goes on with a very interesting and evidence-supported discussion of the ranking system, and of the particular approach taken by KAU in order to put itself on the world’s mathematical map. There are also comments by various academics, a few of whom work for KAU. Well worth a read if you have time to be scared about the $$$$$future$$$$$ of global academia.

Pachter’s blogpost raises some very interesting questions about the future of global academia. First of all, it is not at all surprising that universities from the periphery (the “global south”, as we sociologists like to call it) are trying to gain prestige and put themselves out there.  It is also not surprising that some, which are very affluent, will attempt to buy their way in the global academic system. In fact, by doing so, they are merely using loopholes and bugs – which to them are “features” – in the ranking and prestige system created by old-world academia. Our indignation at this, while justified, is also somewhat hypocritical: after all, they are simply taking the “money makes research go round” principle that bit further. Academics and administrators in US and European universities should take this as a warning – a mirror held up to our own academic institutional  practices which may be less blatant and aggressive, but are nevertheless often the same in their nature.  UK universities in particular – more so than in the rest of Europe, but still less so than in the US – are also doing their best to hire highly-cited academics.  I’m not at all worried about universities from other places taking the lead in research, and no doubt many of the names on the list are doing just that.  What is really worrying is the increasing overreliance on numeric indicators of academic quality as a substitute for much more detailed, more qualitative indicators.  I think that we… or someone? but who? well, we – vice-chancellors, academics and administrators – should take the hint from KAU’s success on paper and change the system of science quality assessment not just by tightening existing loopholes, but by not relying on simplified indicators at all.

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What do zombies have to do with maths?

UK maths educators are going more and more overboard in their attempts to make maths popular with young people.  Consider this Halloween special by the Oxford Science blog:

Or maybe I’m just too old to understand what the hype with zombies is all about. More pure human maths for me, please.

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Maths, active learning and metacognition

An interesting article about a new book which explains how we learn to learn, and how to teach students how to think: “Critical Maths for Innovative Societies: The Role of Metacognitive Pedagogies”.

“College professors often point out that their students never learnt how to learn. Derek Cabrera was surprised to find that even the “cream of the crop of our education system” was not good at dealing with novel problems in unstructured assignments. As PISA shows, across OECD countries, about one in five students is able to solve only straightforward problems – if any – provided that they refer to familiar situations. Too often, we teach students what to think but not how to think.

Yet, there is an engine we can use for that and it is called metacognition, which means “thinking about your thinking”, and regulating it. Metacognitive pedagogies improve academic achievement: content knowledge and understanding, and the ability to handle routine and unfamiliar problems. And they also boost affective outcomes, reducing anxiety and improving motivation. Struggling students greatly benefit from these pedagogies, but not at the expense of higher achievers.

Metacognition is about taking ownership of your learning and maximising it. “It turns you from being a consumer of learning to being a researcher, a co-producer, an explorer and that’s a much more exciting, exhilarating world. You discover how to learn better” Stephen Heppell argues. He also points out that metacognition makes students “do 20% better – you get an extra Friday every week”.”

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Hitler becomes a maths supervisor

P.S. This video, created by some very observant maths undergraduate, develops an already established tradition of video spoofs based on Bruno Ganz’s earth-shattering performance in the German historical film “The Downfall”.  The video surfaced on the Internetz late yesterday night and caused uncontrollable midnight laughter in our sociological-mathematical household (and, I’m told, not only in ours). Not everyday I come across such superb fieldwork materials! I have no clue how to use it in research, though, so for now I will just keep laughing, if you excuse me.

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Escher, Tile Transformations, Mathematics, Art and Games

I want this game!

Also, last week I went to a super cool event in Berlin called “BMS Friday”. BMS is the Berlin Mathematical School, and the “BMS Friday” is a regular lecture on a Friday (not every Friday sadly) in which a mathematician explains his or her research to a mathematical, but not specialist, audience. PhD students at the BMS actually have to attend these lectures. Horrible to be forced to attend that sort of thing, isn’t it 😀

The lecture I heard was by Craig Kaplan of Waterloo University, London, and it was about the mathematics of Escher’s paintings. Here is a 2008 paper with pictures, and a neat classification of the different transformations Escher used. Kaplan edits an interesting Journal of Mathematics and the Arts

Craig Kaplan at the Urania in berlin, giving the BMS Friday talk on 6 June 2014

Craig Kaplan at the Urania in berlin, giving the BMS Friday talk on 6 June 2014

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and another website about parquet deformations

Ever since, my walking through Berlin has significantly slowed down, because I’ve been unable to stop staring at tiles and shapes. I’ve even tried cycling on the pavement which wasn’t a good idea

tiles

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