# You're reading: Travels in a Mathematical World

### 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.

### 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.

### Recent history

I am preparing a talk for our undergraduate Maths Society (perhaps ill-advisedly) with the title ‘A brief history of mathematics: 5,000 years from Egypt to Nottingham Trent’. This will be a stampede through some very selected hightlights, starting with some arm waving about pyramids and ending with something modern. In fact, as well as some recent results that have been reported on this site this year, I intend to end with a recent piece of research published in the department (and a colleague has promised a nice picture of a brain for this).

Relatedly, a colleague who teaches on our Financial Mathematics degree suggested I include Black–Scholes in my talk, as one of the most recent results included in an undergraduate degree. It’s from 1973. Can we do better? I asked Twitter.

### Emergency Maths Arcade (Or, suggestions of pen and paper mathematical games)

Last week we had a crisis at work — we misplaced the key to the Maths Arcade cupboard, in which we store the games (don’t ask!). So I was on the look out for something to do without opening the cupboard — i.e. on pen and paper — and I turned to Twitter for help. What suggestions did I get? What did we do in our Emergency Maths Arcade? Read on.

### My teaching in 2013/14

Some people have expressed an interest in what I am teaching this year. Here it is.

### ‘Low barrier, high ceiling’ and the Maths Arcade

I’ve been catching up with the TES Maths Podcast. I just listened to episode 7, towards the end of which guest Brian Arnold shares ‘the Frogs puzzle’. You probably know this, but if not Brian points to the NRICH interactive version which explains:

Imagine two red frogs and two blue frogs sitting on lily pads, with a spare lily pad in between them. Frogs can slide onto adjacent lily pads or jump over a frog; frogs can’t jump over more than one frog. Can we swap the red frogs with the blue frogs?

You know the one? You can play it with coins or counters or people. Anyway, host Craig Barton refers to this as “low barrier, high ceiling”, in that

anyone can do a few moves. So there’s your low barrier, but you can take that, the maths that that goes into! You can extend it to different numbers on either side, everything’s in there.

Much as I dislike the term because it sounds jargony, I realise it describes something I’ve been explaining all week.

### Ten years of part-time working

In summer 2003, I put my MSc in computing into part-time mode to take up a part-time job in e-learning in maths at the University of Nottingham. Since then, I have done various combinations of paid work and education, until I handed in my PhD this summer. Viva notwithstanding, I am now only working on one activity: I am a lecturer of mathematics.

This week, I started a full-time contract in this role. This means I am full-time on one activity for the first time since summer 2003. In recognition of this, I hope you won’t mind a little self-indulgence on my part. I have quickly mocked up the following image showing my part-time working life over recent years. Here’s hoping for a period of greater stability in full-time working.