Surface Pro 4: Episode 7

Latest developments

  • I have started to make some use of “pinch and spread” to give myself larger areas to write in when necessary.
  • I am starting to have some problems with the display port adaptor. Because I currently use the Surface on a sloped laptop stand on top of a blue plastic box (to give myself extra height and a better writing angle), the VGA cable can pull on the adaptor, and it can wobble and lose connection. Last lecture I solved this by wrapping the slack of the VGA cable over the top edge of the Surface, which reduced the tension. Hopefully the problem won’t get any worse.
  • Something bad has happened to the tip/nib of the stylus. Hopefully replacing the nib will fix that! That is, if I can find the set of spare nibs.
  • Having reduced the number of unwanted menus from touching the bottom part of the screen, I have now started getting unwanted BlueBeam menus from touching the right of the screen. I am beginning to think that I am always going to have more trouble with touch than without it. The benefits of touch at the moment are panning using touch (which is good) and pinch and spread during annotation (which I am starting to use a bit). But the unwanted menus are definitely a nuisance, and I am not sure I have the skill to avoid them.

Surface Pro 4: Episode 6

Latest progress with my Surface Pro 4:

  • I moved the taskbar to the top of the screen, and this has helped a little with the “unexpected menus” problem.
  • Another thing that helps with the unexpected menus, and which also helps with my handwriting (slightly), is  if I try to avoid writing too near the bottom of the screen. It is better for me (using touch control to pan) to move the relevant area up slightly when I want to write there, if it is too near the bottom of the screen at the time. I haven’t yet taken advantage of the pinch and spread zoom features to give myself more space to write between lines, but I do have that option too.
  • I am experimenting with some printed handwriting rather than joined up writing. It is slower, but probably easier to read in my case! Where I use my usual joined up writing, writing larger and more slowly helps.
  • I have switched to Bluebeam’s “classic” menu (but not the full “classic mode”), as this provides a little more space (vertically) to write on the screen. I have also chosen not to automatically show tabs, and that provides another bit of vertical space.
  • I have moved to a thicker line width, and this helps with the earlier problems when Bluebeam makes my strokes thinner afterwards. Generally I don’t get unexpected gaps appearing in my text now. I still haven’t found out why Bluebeam is doing this or whether I can stop it. But I still prefer Bluebeam to the alternatives at the moment. (I am still using Bluebeam 12. Possibly the latest versions have eliminated this issue?)

Surface Pro 4: Episode 5

Continuing my adventures with my Surface Pro 4 ….

I observed today that  one of the main sources of “mystery menus” appearing is when my left hand touches the bottom left of the screen unexpectedly. I’ll just have to get used to avoiding that one in particular.

I rebooted the machine yesterday hoping that this would leave it in the best possible state for today’s lecture. But when I got to the room today the Surface Pro 4 could not detect the pen or my hand. Only my mouse worked. Fortunately the machine is fast, and rebooting was very quick. (It is just as well the machine didn’t have lots of updates to install though!)  After that I had no problems with the pen, and (as mentioned above) touch was working a bit too well!

One student (so far) has pointed out politely that my handwriting can be difficult to read. Looking at recent classes, I can see that I should try to keep the writing big, and perhaps avoid the temptation to cram too many comments between the lines of my PDF skeleton notes. Either that or practice a bit more! I could also consider printing instead of joined up writing, or just write slower. Not that my handwriting was ever that good, but I do feel it has become a little worse this year. Whether this is just aging, eyesight, lack of practice, or the machine’s doing is not obvious to me. I think I would have even more trouble with a smaller screen, though. So I don’t think I could get by with a Surface 3.

Adding new pages in Bluebeam is easy in theory: I just need to click on the blank page icon in the bottom right corner of the window. However I am finding it a little harder to click this icon than I used to. Either the pen/screen interaction needs re-calibrating, or I should use the mouse, or maybe just put my glasses on! I should certainly take my glasses with me when I go round the room in workshops, as I am finding it hard to see the students’ attempts properly otherwise.

My pace in today’s workshop (Workshop 4) was definitely off: we didn’t get through as much as I wanted. Fortunately the later questions were covered in previous years’ videos. (See for links to the G11FPM Echo360 video archives from the autumns of 2012, 2013, 2014 and 2015.) So anyone who does want to see the remaining details of this version of the proof of Bezout’s Lemma can find them there. (The whole workshop is devoted to slowly building up a proof of Bezout’s Lemma, with the students proving a set of easier facts first about sums of multiples of integers.)

Surface Pro 4: Episode 4

I am continuing to use my Surface Pro 4 for PDF annotation in my first-year lectures.

Although there are many good features, I am still having some problems with unexpected menus opening up.

Some of these are caused by my hand hitting a key point near the edge of the screen (my Bluebeam PDF Revu settings mean I should have no problem with touch in the middle of the screen.) But I think my main problem is caused by the side button on the stylus. This generates a right click. Now I already told Bluebeam not to use right click to activate the lasso while I am inking, which helps.  But you can still get right-click menus appearing due to accidental right clicks. I would rather like to be able to deactivate the side button on the stylus, but I haven’t found any way to do that. (Does anyone know if it can be done?)

There are also some menus which suddenly appear and where I can’t yet duplicate the operation that brought them up. I think that touch is involved. Maybe I’ll get to the bottom of this some time!


Applications of complex numbers

Here is my latest announcement to my first-year students.


In the spirit of “applications of pure mathematics”, I thought I would say something about applications of complex numbers.

According to the Wikipedia page

complex numbers were first introduced by an Italian mathematician, Gerolamo Cardano, during his attempts to solve cubic equations in the 16th century.

You probably all know the quadratic formula. There are similar but more complicated formulae for solving cubic and quartic polynomials. The search for a similar formula for the quintic proved fruitless, and in fact there is, in general, no such formula for solving the quintic. The relevant area of mathematics is Galois Theory. This is off-topic today, but see if you want a flavour. This is not to say that quintics don’t have roots (they do!), just that you can’t always find a formula for them using the coefficients and nth roots etc.

This is all well and good, but inventing some apparently fictitious numbers in order to find solutions where you didn’t have them before may not feel like much progress. But the amazing thing is that “pure” theory of complex numbers, complex functions and complex analysis has applications almost everywhere you look, and not just within mathematics.

If you have studied physics, you  may already have met complex numbers and functions when looking at impedance, phase angles, and oscillating currents. Wikipedia mentions practical applications in many other fields. I’m only going to mention a small number of things today, but you could look at

for more.

In first year calculus, when you study differential equations, you will see some complex numbers come in when looking for solutions. They then go away again, because you want to find solutions using real numbers. But the exponentials of imaginary numbers lead you to use the functions cos and sin in your solutions.

In second-year complex functions you will see how the beautiful theory of complex functions enables you to use “residue calculus” to quickly find the exact values of “improper integrals” that look a little tricky otherwise, such as

\int_{-\infty}^{\infty} \frac{dx}{1+x^4}\,

and many far more complicated examples. In fact this topic is enough on its own for an third-year project! But you could see

for a few more examples.

I think that it is remarkable that the most efficient way to calculate this kind of real integral involves using the theory of complex functions as (mostly) developed in the 19th century, especially the work of Cauchy and Riemann.

I could say much more here, but for now I’ll just mention that these methods become crucial again for calculating the Laplace transform and inverse Laplace transform, which have too many applications to list here! See, for example,

Best wishes,

Dr Feinstein

Applications of “pure” mathematics

I have just posted the following message in my first-year pure maths module’s announcements forum.


Hi everyone,

With its emphasis on abstraction and rigorous logical thinking, you may wonder whether or not the Pure Mathematics you are learning in G11FPM actually has applications in the “real world”.

In fact I did mention some applications in the first lecture and workshop: for example, secure transactions on the internet depend on encryption algorithms, many of which which have their basis in Number Theory, especially the theory of prime numbers. See, for example,

In fact, whichever area of mathematics you work in, rigorous logical thinking is rather important (although this may not always be apparent at undergraduate level).

Have a look at the page

for a rather good discussion of just how important Pure Mathematics is.

However, I will admit that the main reason that I do research in Pure Mathematics is because I think it is beautiful and fascinating, rather than because I expect my work to have applications in the “real world”.

The area of mathematics you choose to specialize in is largely a matter of taste. I know that not all of you will find Pure Mathematics to your taste. Still, I will do my best to introduce you to the flavour of the subject. After that it is up to you!

However, I plan to post a few more messages in this thread giving some more applications of “pure” mathematics.

Best wishes,

Dr Feinstein

Polls in classes

I use mobile device based voting via Google forms in my classes, and this has generally worked well. But there can be problems! I have just posted the following message in the forum for my first-year module.


Hi everyone,

I’d like to make a plea for people to take the polls/votes in classes seriously. Well, I think many of you do already, but there appears to be significant distortion introduced by those who don’t.

These polls and the associated discussions between students have an important role in your learning, and provide an opportunity for a form of interaction in the large class we have.

You are already getting most of the benefits if you are attempting the problems and trying to persuade your neighbours that your answers are right. Explaining your reasoning to another student is a very good way to solidify your own understanding of the material! From this point of view, distortion in the vote/poll doesn’t matter so much. However, I would like to be able to gauge how well the class is following at a particular point, and whether I need to explain the question again or give extra hints.

It is hard for me to judge what the situation is if the results are distorted. So please do take the votes seriously, so that I can take appropriate action based on the results.

Best wishes,

Dr Feinstein