# Category Archives: Mathematics

## May Fest 2013 at the University of Nottingham

Hi everyone,

The University of Nottingham’s May Fest this year will be on Saturday 18th May, 11AM to 5:30PM.

For more details, see http://www.nottingham.ac.uk/mayfest/index.aspx from where I quote:

Saturday 18 May!

Following four successful years The University of Nottingham will once more open its doors to the local community for May Fest 2013. Come along and join in with the free, interactive activities for all ages and interests.

The May Fest programme is now available from http://www.nottingham.ac.uk/mayfest/documents/mayfestprogramme2013.pdf

Here is what we are offering in Maths:

Casino Royale
Try your luck at the roulette table (no real money involved!) and learn how
to solve Rubik’s Cube. Or look at fascinating mathematical exhibits, games
and puzzles while chatting to staff and students.
Time: Just drop in 11am-5.30pm.
Location: Room C20, Portland Building (No.7).
Recommended for age: 3+

## (OT) Pablo Neruda’s body to be exhumed

No connection with maths, but my brother Adam Feinstein has been called in by the BBC today as an expert on Pablo Neruda. A judge in Chile has ordered the exhumation of Neruda’s body in order to investigate allegations that he was poisoned in 1973.

## Can you detect computer-generated proofs?

In a fascinating development over on Gowers’s Weblog we have just been told that in an earlier post (where we were asked to compare sets of three proofs for results in elementary metric space theory) in each set of three proofs one was computer-generated, one written by a maths undergraduate and one by a maths PhD student.

Given this information, we are now asked to vote for which ones we think are computer-generated. This  latest post and poll is at

http://gowers.wordpress.com/2013/04/02/a-second-experiment-concerning-mathematical-writing/

I have my own ideas, but I’m not going to reveal them at this point (if ever!)

## Seeking a two-button tablet pen

It may be because my hands are too large, but I do keep catching the right-click button on any of the tablet pens I have. In the end I have had to disable this button, even though it is rather useful to have it bring up a pop-up menu with some key-strokes for when I am in tablet mode. (I could take a  USB keyboard with me of course. Maybe I’ll get a small wireless USB keyboard in order to provide convenient keystrokes when necessary.)

The tablet control panel indicates that it can support a two-button pen, but I have yet to find one that works. We have tried a Wacom Bamboo pen

http://www.amazon.co.uk/Wacom-Pen-for-Bamboo-option/dp/B00169JAVO/ref=pd_rhf_se_p_t_2_6NR5

but unfortunately my Lenovo tablet can’t see it.

Are there any two-button tablet pens out there which will work on my Lenovo tablet?

## What to do when your tablet PC loses track of its pen

Today was the first time that my Lenovo tablet PC lost track of its pen (this was fairly common on my previous tablet, a Toshiba Portege).

When this first started happening to me, I used to restart the tablet in order to get it to rediscover its pen. Then I discovered that it was sufficient to close the laptop and reopen it (getting it to sleep and then wake up).

Today I had actually just finished the class when it happened. Now the “autorotate” settings on my tablet are such that it has a rethink if you change from tablet to laptop mode. That turns out to be sufficient for it to find its pen again! So, if this happens in the middle of a class, I will see if I can get away with simply twisting the screen and twisting it back.

## G11FPM Foundations of Pure Mathematics

This year was my first go at teaching the autumn semester first-year module G11FPM Foundations of Pure Mathematics at Nottingham. It was also my first attempt at recording an entire module using the resident Lecture Capture systems, rather than Camtasia on my laptop.

There were some teething troubles with the technology, so not all lectures were captured successfully. I also plan to make some changes for next year (including improving the communication between my brain and my mouth in places!). So next year I may make a full set of videos available on YouTube, iTunes etc.

You can now view all of the Echo recordings from this year’s attempt (in a variety of different ways), via the feed

or directly from the Echocenter at

http://uilapech01.nottingham.ac.uk:8080/ess/portal/section/u_g11fpm_12-13_sep.000112

Comments on the technology and/or pedagogy are welcome!

## Lenovo tablet pen problems

OK, it looks as if there are some differences between the Lenovo tablet pen and the Toshiba tablet pen. I can use either pen on my Lenovo tablet, but my writing style gives trouble with the Lenovo pen and not with the Toshiba pen.

I have a sample PDF comparing the results, based on a “just firmer than medium” Tip Feel option in the Pen Tablet Properties control panel Pen tab.

As you can see from the sample PDF, with the Lenovo pen, a stroke is added joining the bottom of the final g to the dot of the i, while there is no such issue with the Toshiba pen.

[And it is supposed to say "very fast" not "very last!"]

Either I need to press less hard, or actively stop the pen when I finish the final g, or I should just use the Toshiba pen!

Hi everyone,

With my old Toshiba tablet PC coming to the end of its natural life, it is time for me to look at alternatives.

I have tried using my iPad 2, but I write too fast for it: it can’t keep up with me! So either I need to write more slowly, or I need a more powerful processor. In any case, if I do want to continue using Camtasia etc., I really need a powerful machine to process audio input + two video streams while running some significant software such as Bluebeam PDF Revu to handle the PDF annotation.

Unfortunately there are no longer very many genuine tablet PCs out there. Still, my department (The School of Mathematical Sciences at The University of Nottingham) has now purchased two Lenovo ThinkPad X230 Tablets for us to try out.

This is a promising machine, which runs the 64-bit version of Bluebeam very nicely. There are some curious features though! Thanks to David Hodge for working out some solutions to these issues.

This tablet PC appears to be designed so that you should use secondary landscape rather than primary landscape when in tablet mode: otherwise the screen slopes downhill away from you! However:

• With wireless on, it says that you are not allowed to use secondary landscape. (This appears to have its root in radiation legislation.)
• By default, when you use a data projector, having the tablet in secondary landscape will produce upside-down output on the data projector screen.
• There is only one programmable tablet button, which by default is set to rotate the screen orientation.

For the first of these, you can turn wireless off. But this could be a problem if you actually need the wireless internet in your presentation. Other solutions are rather drastic, so if you do need the wireless internet it may be better to use primary landscape instead, along with a suitable laptop stand to counter the slope.

For the second, there are lots of options available in the advanced display options. David Hodge found various ways to make this work. You need to be connected to an external display in order to change the relevant settings and save a new profile. And we still need to find a short cut to select this profile when you arrive in the room and attach the projector: otherwise you  have to navigate the menus each time.

So where are these settings? You can right-click on the desktop (I use press and hold with the pen), choose Graphics Properties, and make sure you are in Advanced Mode. You can then change properties of each display you are attached to. The Built-in display is the tablet’s own display, while the data projector output corresponds to the Monitor settings.

When I tried things last Friday, I did end up with some bizarre effects: at one point all my displays were showing the way I wanted, but the tablet pen position was 180 degrees out from where the pointer appeared. That was fun! Anyway, with David Hodge’s help, today I have gone for using the tablet in primary landscape, but setting the display option for the Built-In display to “Rotate to 180 Degrees”, while keeping the Monitor rotation option as “Rotate to Normal”.

It is also possible to use the tablet in secondary landscape, set the Built-In display rotation option to “Rotate to Normal”, and set the Monitor rotation option to “Rotate to 180 degrees”.

Whichever one you go for, you should save the profile with a sensible name. Once you detach the monitor, it will probably throw you out of your named profile. (This can also happen whenever you change screen rotation etc., depending on your set-up). So you will want to be able to reload your preferred profile easily. Once we figure out a short cut for this, we’ll let you know! For the moment, right-clicking on the desktop  allows you to choose

Graphics Options -> Profiles -> Display Profiles -> Your named profile

(but you can’t switch to the new profile unless you are connected to an external display).

Regarding the tablet buttons: you can assign different keystrokes to “press” and to “press and hold”. I am currently using “press” to activate Pen Attention, while I am using press and hold to produce “f11″ . Our IT support people have suggested that it may be possible to add things to the context menu (right click), so that will probably help. But it is still rather more restrictive than the six different programmable actions available using tablet buttons on my Toshiba.

## (OT) Give as you live

Off-topic, but a worthy cause …

I’ve started using “Give as you live” to generate some money for NSPCC.

They have auto-generated an invitation message for me to pass on, so here it is:

_____________________________________

Hello,

I’ve found a new way to raise money for charity. All I do is shop online.

Give as you Live brings together thousands of stores that have signed up to donate a percentage of every purchase I make online to NSPCC – without charging me a penny more. Stores like John Lewis, Tesco and Expedia all donate to NSPCC when I shop with them online – and I don’t have to reach deeper into my pocket.

Try it out. You can sign up and download Give as you Live in seconds, and then you just need to start shopping. What could be easier?

http://www.giveasyoulive.com/invite/R9UvZgo2iHtKlO3MaYnxxT-2F-2BoUa8

Thanks,

Joel

## Feedback on G11FPM exam

Well I survived marking 221 first-year exam scripts for G11FPM Foundations of Pure Mathematics (though it did take me a long time to get through them).

I then wrote a set of model answers which probably  included about 4 sides of comments, and a separate feedback document on common errors and pointers for improvement (another 4 sides). Far more people are looking at the solutions than reading the separate feedback document, so it is probably good that I included some of the comments there.

I’m not going to reproduce the full set of comments here. Instead I’ll try for a very concise summary. [I failed on the "very concise" bit.]

Students were generally good at checking whether relations were reflexive, symmetric or transitive, could do long division to find recurring decimal expansions of rational numbers,  could calculate very fast and accurately when multiplying permutations, and could convert permutations between two-line form and disjoint cycle form.

Students also made very good use of modular arithmetic, correctly establishing what the possible cubes are modulo 7, and then (as indicated as one possible method in the question) using this to prove that there are no integer solutions to the equation $3 x^3-14y^2=2$.

That was the good news!

Students did not do well on stating standard definitions of concepts or giving standard statements of lemmas. But some bookwork proofs were reproduced correctly. This suggests that, after just one semester at university, the importance of knowing (and understanding)  the main definitions and statements accurately may not yet have sunk in.

The single biggest problem with definitions came with the definition of injective for functions. Most students wrote that this meant that every point of the domain is mapped to a unique point of the co-domain. Many of them don’t really believe that, as was shown by the functions they suggested when asked for examples with various combinations of properties (but some of them really did appear to believe it).

This was a bit disappointing, because I know this common error well from teaching 2nd-years (and 3rd-years), and I had been hoping to nip it in the bud. I had hoped that discussing graphs of functions properly might help, especially the fact that (for us) functions are never “one-to-many”. Certainly there were indications in classes (with voting using the voting packs) that the ideas were making sense. But in the end, I think the unfortunate (but standard)  term “one-to-one” always ends up being thought of as the opposite of “one-to-many” instead of “many-to-one”. I’ll have to try another strategy next year. Maybe I won’t even mention the term “one-to-one”!

The big statement that very few students could remember was that of Bézout’s Lemma. This hadn’t come up in the previous three years, so perhaps students assumed it wouldn’t come up this year. However we did dedicate an entire workshop to proving it this year.

I won’t mention all the difficulties students had with constructing their own proofs or thinking up examples with specified combinations of properties. I will say that students need to practise these skills more. (In my feedback I have suggested that my big question sheet on Definitions, Proofs and Examples might be one place to start.) I will mention a few common problems: many students suggested that integers that were divisible by $2^{4/7}$ must be even, or that if $m^{7/4}$ was divisible by 2 then $m$ must be even (or similar). Many students claimed that if $m^7$ was divisible by 16 then $m$ must be divisible by 16. More generally students often claimed that if $a|bc$, then $a|b$ or $a|c$ (in settings where $a$ was not prime, or at least was not known to be prime).

There is more that I could say, but I think that is enough for now!

## G11FPM exam

In just over an hour, 228 first-year students are due to sit the final exam for my first-year module G11FPM: Foundations of Pure Mathematics.

Good luck to everyone taking the exam (… and good luck to me with the marking over this coming week)!

As I haven’t taught this module before, marking these exams will be very instructive for me. The only regret I have is that I have no control experiment to see whether my new style of teaching with the voting packs has actually helped or not. Perhaps I should have postponed the use of voting packs for a year? Having completely rewritten the notes to fit with the new style, I don’t think I can return to my previous style next year …

Anyway, I will probably report back later on some common errors., and how these might possibly be addressed.

## Sequences and their properties

Hi everyone,

I made three short videos on sequences and their properties as part of our local Core Topics in University Mathematics series, available on YouTube at

Two of these three videos of mine on sequences are there already, with the third one due out next week.

Solutions to the quiz will be out at the end of next week!

Solutions are now available on YouTube at

## Core Topics in University Mathematics

Hi everyone,

It looks like our new videos are coming out on schedule!

See

In particular, the first of my videos on sequences and their properties is available at

## 2012 in review

The WordPress.com stats helper monkeys prepared a 2012 annual report for this blog.

Here’s an excerpt:

4,329 films were submitted to the 2012 Cannes Film Festival. This blog had 29,000 views in 2012. If each view were a film, this blog would power 7 Film Festivals