I transformed my PhD work into a 5-day mini course for Grade 10s through The Brilliant Club. I am making the course material available here. Contact me or write in the comments for more resources and help using them!

Below is an excerpt of a case study that I wrote for The Brilliant Club:

My Scholars Programme, “How to Make a Mathematical Discovery,” is designed to introduce the idea that maths is much bigger than practicing algebra and arithmetic, or applying such concepts to solve real-life problems. Research mathematics is also about exploring ideas, identifying patterns, and connecting concepts through mathematical abstraction. Why do mathematicians see a teacup and a donut as being the same thing? (Hint: consider the handle). My course gives pupils the opportunity to rediscover the main theorem of my PhD thesis by playing with a set of 3D-Printed tiles, specially designed for the programme. Not a single equation is solved and not a single expression is evaluated.

The outcome of the course was generally positive, in spite of it being conceptually challenging. All 12 of my pupils submitted their final illustrated essay assignment and passed the course, six of them with 1sts, two with distinction, and a third pupil will have her assignment published in The Scholar. I am extremely proud of them! These quotes speak for themselves: “I’ve never got maths before, but I get this!” “I thoroughly enjoyed the program and I miss it already :)” “I loved this programme and the programme has definitely solidified my dream to carry on with maths in the future. From a parent, “May I just thank Alejandro for working with _ throughout the programme. The marking comments were very positive and were a real boost to _’s confidence, and I feel she gained a lot from the programme.

Congratulations to Katie Hancock. Her work on tatami tilings were published in The Brilliant Club’s journal, The Scholar!

K. Hancock, supervised by A. Erickson. How to make a mathematical discovery: The tatami restriction at large, The Scholar, Vol. 1, No. 3, pp. 20-22, July 2015. (Alternate links hosted on my website: Whole issue Just the article)

Tatami Mini Course Resources

Download the full mini course pdf (14MB).

Download the tatami-theorem supplement.

There are a few other handouts that I can locate upon request. Below is an excerpt from the last activity before the final project (i.e., Katie Hancock’s work, above), showing how far the students go in just a short time.

Unsuspecting, I picked this classic baby toy up at a local charity sale. As it turned out, it harbours a little combinatorial challenge that I never suspected! The toy is a set of five stacking cubes with a different face on each face. Save for size, the cubes are all the identical; flower, hexagon, square, triangle, circle, and the open face.

As I was playing with it I thought, “Can I stack the cubes such that no two shapes coincide?”. Fun!

This is the same as asking if you can orient 5 6-sided (axis-aligned) dice so that no two dice show the same number on the same side.

Is there more than one way to do it? Can it be done with 6 stacking cubes?

Having grown up around SLR cameras, I have always had an appreciation for the superior image quality that a “proper” camera is capable of. I have owned severalof them, and I am quite familiar with the technical aspects of exposure and depth of field. A tipping point occured, however, when I got my hands on a Sony alpha A7 this year. I went on to read The Landscape Workshop by Ross Hoddinott and Mark Bauer, and dove into capturing the rural landscape around my home in the North East of England. Here is one of my “keepers”:

Here is another one:

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I am a Canadian citizen, resident in England, and I have recently learnt some things while getting a UK Driving Licence. First and foremost, the following website is a gold mine:

HOW TO EXCHANGE A CANADIAN DRIVER’S LICENCE FOR UK LICENCE

Read that whole webpage.

There were a few details missing, however, as regards insurance and provisional entitlements, and I will fill those in here. As you will learn at gregwtravels, you can exchange you Canadian licence for a Category B restricted to Automatic (this is code 78).

The first thing I can confirm is that you do not need to have your photos signed if you send in your Canadian passport (i.e. you do not need a UK passport). At the time of this writing gregwtravels says “I take that to mean that an up-to-date Canadian passport is identity enough.”. Yes, it was enough for me, and if you read the instructions that come with the D1 form, you can reassure yourself of this.

To fully understand the codes on your licence, you should refer to the following document:

Information on driving licences INS57P

The INS57P is the pamphlet code at the time of this writing, in case the link goes dead. You should be able to find the same pamphlet by searching for INS57P driving licences.

INS57P also tells you that you can find your provisional entitlements on your “Counterpart Driving Licence”, which is the paper document that came in the mail with your photocard. This is where you can verify gregwtravels’ claim that you can drive a Category B (without restriction) as a provisional driver. I have checked with a human at the DVLA, to confirm that you must be accompanied by a fully licenced (IN THE UK) Category B driver for this to work (i.e. not your Canadian partner who is still on their international driver’s licence).

The next question for me was “How do I insure myself to take the test in my own car?”. You need insurance that covers you as a provisional driver, plus the car must have its own “full” insurance. This cost me 85 GBP from , but at the time of this writing, I have not confirmed that my setup works. That is, I think I am covered because:

• I also own the full car insurance (with my wife also listed),
• I own the car,
• the car is the correct category (B) and below the maximum value,
• the car is taxed and MOTed; and,
• I am provisionally entitled to drive this type of car. There are three pitfalls, however, that might apply (which I will clear up when I talk to a human at provisionalmarmalade); perhaps owning the main insurance voids the provisional insurance; and, perhaps the insurance is not valid during the test (this is apparently the policy of ecar insurance!); perhaps the fully UK Category B licenced driver needs to be listed on the full insurance of the car. Update: The following quotes from my insurance terms and conditions (and schedule) clear up the above doubts, more or less confirming that I am covered during my test, and that I can drive when supervised by a driver meeting the conditions mentioned: “Driver to be accompanied — (Name) We will not provide cover while your vehicle is being driven by, or is in the charge of, the person(s) named above unless that person is accompanied at all times. The accompanying person must be 25 or over and must hold a current full UK driving licence which has been issued for at least three years. These restrictions do not apply if the accompanying person is a Department of Transport approved driving instructor or examiner.” and “Emergency and ‘Get Your Vehicle Home’ Cover While you are receiving driving tuition or undergoing an official DSA practical driving test, we will extend the cover if it is necessary because of an emergency or other exceptional circumstances to allow your accompanying full UK licence holder (who must be over 25 years of age and must have held such licence for a minimum of 3 years or who must be a qualified DSA Examiner) to drive the insured vehicle in order to complete the journey.” The full terms and conditions are available on their website here, and I have posted a copy here. To book the test itself, I went to the website recommended on gregwtravels called Book your driving test. I called the DVSA booking support number, and chose options 02, and then option 6 (other). (I was tempted by option 2, DVLA enquiry at phone 03007906801, but I do not think this is a correct option.) The test cost me 62 GBP. Finally, I did book one driving lesson, which cost 44 GBP., , ,

If you have ever traveled to give a mathematical talk at a conference, you may have encountered the following situation:

1. Your slides are in LaTeX (beamer).
2. You would like to leave your laptop at home.
3. You have a tablet or smart phone.
4. You would like to be able to make last minute changes to your slides.

I have found a cloud-based solution to this problem, but first, I’ll give a backup solution: Use TeamViewer to log into a computer back home to compile LaTeX.

The real discovery, however, is cloud.sagemath.com. One of its many features (for mathematics-related sciences) is a full latex installation. It also has a nice interface which makes it easy to batch upload your LaTeX source files.

Hardware Requirements: Smart phone or tablet with an adaptor for usb drive. USB drive.

Upload your LaTeX source to the cloud and test compile while you are at home. Put any files you might change into your tablet and make sure you have a .tex-capable editor installed. Upload a changed file to the cloud, use the compile command in your mobile browser, and then download the compiled pdf. Use you adaptor and file browser on the tablet to put the pdf onto a USB drive, and you are good to go!

Now hopefully you won’t have to make a change to your slides, but it is still better than lugging your laptop around on the vacation you tacked onto the all-expenses paid conference ;)0614Screen Shot 2014-06-17 at 13.29.30.png, , ,