I have just been told that my old Level 4 module G14FUN Functional Analysis (which has a large overlap with my current spring semester module G14FTA Further Topics in Analysis) has been translated into Chinese!
The link I have been given is http://open.163.com/special/opencourse/fanhanfenxi.html
Disclaimer: I cannot say anything about the quality of this site or of the translations.
Comments welcome!
[Note added November 2019: The links below no longer work. But I have now attempted to make the 2018-19 videos public at
https://echo360.org.uk/section/4c490e8b-27f7-4fb8-b97f-251bad1ed2ad/public
so hopefully those are now available.]
[Note added August 2018: The links below will stop working at some point, as we are switching over to a new Echo360 system. I’ll see if I can make some videos available on the new system. The YouTube and iTunes videos should be safe!]
This year (2016-17) will be my fifth year of teaching the first-year module G11FPM Foundations of Pure Mathematics. This is an introductory pure mathematics module designed to give students the background they need for further study of pure mathematics at university.
The complete set of videos from 2014-15 is available on YouTube and iTunes. But I have now also opened up the archives of all the Echo 360 recordings (also known as “Echoes”) from previous years. These have the (possible) advantage that you have two separate windows, one with the screen recording (the “screencast”) and one with the footage of me. These windows can be resized or hidden according to your taste!
I don’t advise anyone to watch four versions of every class! But if there is a specific point you are interested in, then there is a possibility that I did say something different about it each year.
The viewer should be warned that teething problems with the hardware and software resulted in a number of faulty recordings, mostly in the first two years. These problems have mostly been resolved now, and almost all of the recordings from 2014-15 and 2015-16 worked OK.
Here are links to the four Echo360 editions of the module G11FPM so far
https://lecturecapture.nottingham.ac.uk:8443/ess/portal/section/u_g11fpm_15-16_sep.000115
https://lecturecapture.nottingham.ac.uk:8443/ess/portal/section/u_g11fpm_14-15_sep.000114
https://lecturecapture.nottingham.ac.uk:8443/ess/portal/section/u_g11fpm_13-14_sep.000113
https://lecturecapture.nottingham.ac.uk:8443/ess/portal/section/u_g11fpm_12-13_sep.000112
OK, I decided that I was confident enough to use the Surface Pro for my Open Day presentations at Nottingham today. All the software operated as expected! I used Bluebeam PDF Revu 12 for PDF annotation, Pen Attention to highlight the pointer, and X-Mouse button so that I could programme the middle mouse button to give the keystroke I need to toggle the highlighting on and off. I also used Gunnar Andersson’s excellent software WZebra (see http://radagast.se/othello/download.html) to help with my fun morning talk on strategy for the board game Othello.
I am trying to decide on the best screen resolution to fit with the local data projection facilities. Currently I am trying both 1280 x 800 and 1280 x 960. Either way I sacrifice a bit of the Surface Pro screen. At the moment I prefer 1280 x 960 in order to have the full height available.
I like the way that the device detects the pen and can then ignore touch. That way I can continue to use the touch facility when I want to. On the other hand, sometimes I accidentally touch the screen with a hand/finger before the pen is close enough to the screen to disable this, with random results. This is no major problem so far.
I do keep accidentally clicking the right click button on the pen. I haven’t yet found how to disable this completely. By default Bluebeam activates the lasso tool when you right-click during inking, but I have turned that off and it now doesn’t matter if I accidentally click that button while writing.
Sometimes I found the device changed orientation without me deliberately changing a setting. It took me a while to realise that it has a genuine physical autorotate feature: just picking it up the right way round will sort out the orientation (and picking it up a different way may change the orientation to something you don’t want). So I am happy with this now.
My problem with the wireless regularly becoming inactive has gone away for now. I expect this will come back, and so I had still better try to find out what setting is behind this. It may be a power management setting: I saw something about this online while Googling on a related issue.
I should try out Camtasia and also Echo360 personal capture soon. (Perhaps the issues I had previously with Echo360 personal capture will be resolved when I use the Windows Surface (or by upgrades in the software since I last tried it). However, I wouldn’t want to use the device’s webcam for the video footage of me (it is too scary when a pen approaches the tablet!). As the device only has one USB port, I will either have to use a USB hub, or else change to a Bluetooth mouse, if I want to attach a USB webcam too. (I quite like the reliability of a wired mouse at the moment!) Comments and suggestions on this are welcome!
I am now trying out a Surface Pro 4. I have installed Bluebeam PDF Revu 12 on this for now, along with Kenrick Mock’s latest version of Pen attention for Windows 10. I’ve also attached a wired USB mouse, and I am using X-Mouse Button Control to get the required toggle keystroke {ctrl}{alt}{f9} from the middle mouse button.
I will report back as and when I iron out a few wrinkles!
My wife, Uta, is graduating this summer at the end of her BA (Hons) Fine Art degree at the University of Nottingham.
The Fine Art Degree Show (including some of Uta’s work) opened June 11th and finishes on Sunday 3rd July.
See http://www.lakesidearts.org.uk/exhibitions/event/3134/fine-art-degree-show.html for details of the show, and http://www.uta-feinstein.com/ for more of Uta’s art!
As part of our attempt to bring up our children to be bilingual, we all mostly watched German TV when the children were young. One particularly good programme was (and is) the entertaining and informative “Die Sendung mit der Maus”. I learned something new every week from that programme!
This evening we watched some of a spin-off evening quiz programme Frag doch mal die Maus! (Currently available at http://www.wdrmaus.de/maus_wall/frag_doch_mal_die_maus.php5?detail=080420162015 ) The questions are quite interesting and fun.
At one point the teams had to estimate the number of blades of grass (main stem only) on a football field. I won’t reveal the “official” answer they suggested, but I will say that the two teams’ estimates differed by a factor just over 40. But how should you judge the winner here? In this case, the lower answer was “closer” numerically, but not of the correct order of magnitude, while the other answer was of the correct order of magnitude, but further from the official answer numerically. I thought that answer was better, but I think the other answer took the points.
(Would it be better to take logs?)
My colleague Thomas Sotiriou has sent me the following information about recent public engagement outreach events he has been involved in, with videos available.
We had two outreach events in the last few months. One was about gravitational waves and the other was a series of four public talks celebrating the centennial of General Relativity. All talks for both events have been recorded and can be found here (together with more info about the events)
My readers may know that I do a lot of research on Swiss cheeses (though being mathematical, they tend to have infinitely many holes) [Note added: the Swiss cheeses, not the readers!].
My latest joint paper on Swiss cheeses with my research students Sam Morley and Hongfei Yang, Abstract Swiss cheese space and classicalisation of Swiss cheeses , has just been published in Elsevier’s Journal of Mathematical Analysis and Applications. Thanks to funding from the EPSRC, this article has been made Open Access, so anyone can access the final published version free of charge at
http://dx.doi.org/10.1016/j.jmaa.2016.02.004
Of course much of the material is beyond the level of the typical undergraduate course. Nevertheless, students in 3rd/4th year might get something from looking at this. Abstract Swiss cheese space itself is really just a product of a sequence of standard spaces, but with elements interpreted as sequences of centres and radii of “abstract” discs. The two basic elementary geometric lemmas could probably be taught at GCSE!
I have compiled a somewhat biased selection of links which I issue at the maths outreach events I run at the University of Nottingham.
Here is what I provide at the moment!
_____________________________________________
Some useful and interesting links, selected by
Dr Joel Feinstein, Outreach Officer,
School of Mathematical Sciences,
The University of Nottingham
You may also find it useful to look up some mathematical topics on Wikipedia!
When I set a question asking students to prove things, the most common question I get is “How do I start?” Further investigation often reveals that the students don’t remember the definitions of the terms that appear in the question, and have not developed fluency in one relatively routine aspect of doing proofs: make sure that you know what the information you have been given means.
For those students on my first-year, first-semester module on pure maths, mathematical reasoning using definitions, proofs and examples is completely different from what they have seen at A level. My emphasis on the importance of precise definitions is seen by some as rather dry. But I am trying hard to help students to practice working with definitions, proofs and examples as much as possible for themselves.
In my first-year workshop this week, I had a question asking students to prove that if you compose two injections you get an injection, and if you compose two surjections you get a surjection. It took me a few minutes to realise that I was going to have to write the definitions of injection and surjection up at the front, because that was where most people were stuck. I’ll probably include a reminder on the worksheet next time!
The “How do I start?” issue (relating to working with definitions) is not just a first-year phenomenon: it persists through second and third year, and not just in workshops, but also in coursework. I think that I’m going to have to find some new, more exciting, ways to get this idea across, and to try to help students to get past this initial obstacle so that they can spend their time thinking about the interesting bits instead!
Here is a message I just sent to my first-year students at Nottingham ….
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Hi everyone,
You have now seen a bit of modular arithmetic, which you can also think of as introductory number theory. Prime numbers and modular arithmetic are the key to the “public key” encryption systems used on the internet whenever you visit a secure website (https). You can learn more about all this in later modules.
Today’s classes included some tricky concepts. Many of you will still be wondering about “squares modulo 7”.
Perhaps modulo 10 is a bit easier to think about here? Remember that, for non-negative integers, working modulo 10 is like ignoring everything except the last digit, so all non-negative integers end up being treated as being between 0 and 9, and you have multiplication tables including 9×6=4, 2×5=0, 8×7=6, etc. (mod 10).
So what are “squares modulo 10”? Well, what are the possible last digits of squares of integers?
First note that squares of negative numbers are just the same as squares of positive integers, so there is no need to check those.
Checking the last digits of the squares of 0, 1, 2, 3, … we see the pattern
0, 1, 4, 9,6,5,6,9,4,1,0,1, 4, 9,6,5,6,9,4,1,0,…
and this repeats forever. Note that 4^2 and 6^2 end in 6, 3^2 and 7^2 end in 9, etc. This is not a coincidence, because 6 is congruent to -4 modulo 10, so 6^2 is congruent to (-4)^2=4^2 (mod 10).
The repeating of the pattern with period 10 is also no surprise, because (n+10)^2 is congruent to n^2 (mod 10).
Conclusion: no matter which integer you square, the final digit of the square will be one of 0, 1, 4, 5, 6 or 9. You can’t get anything else.
This is because we are using the decimal system. If you use octal (base 8) instead, the same thing happens when you work modulo 8: for non-negative integers, just look at the last base 8 digit. Modulo 8 you get 3×3=1, 2×4=0, etc.
I hope this helps a bit!
Best wishes,
Dr Feinstein
I’m currently at the 23rd international conference on Banach Algebras. This year we are at the Fields Institute in Toronto.
They are recording videos of all of our talks: see http://www.fields.utoronto.ca/video-archive/event/394/2015
My talk isn’t there yet (at the time of writing), but the talk of Sam Morley (one of my PhD students) is ready.
There have been lots of excellent talks, as you would expect from the list of speakers.
Now I just have to dodge the thunderstorms this evening …
My wife Uta and I met at the Nottingham Symphony Orchestra (we both play violin). I’m not playing with them at the moment (“I’ll be back!”), but Uta is.
Their next concert is coming up this Saturday 11 July 2015, Albert Hall, Nottingham, 7:30 pm.
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Overture Euryanthe
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Weber
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Forest Murmurs
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Wagner
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Violin Concerto in D major
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Tchaikovsky
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Symphony No.1 in C minor
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Brahms
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| Soloist: Martyn Jackson |
It should be great!
Follow the link to the Nottingham Symphony Orchestra web page for more details.
At the end of my module G11FPM Foundations of Pure Mathematics this year, one of the anonymous comments I received (on Student Evaluation of Modules) was that there appeared to be almost no maths in the module, only logic.
Of course this was only one comment from a class of over 200 students, but it left me wondering if I could do (even) more at the start of the module to warn them that much of pure mathematics at university is very different in nature to almost anything they will have seen at A level. Of course that is what my first lecture is intended to do, along with my class on “About this module”. But could I do more?
Today I gave my 30-minute “Taster Lecture” on Pure Mathematics as part of our Open Days for prospective applicants. I started the lecture by saying “Pure Maths at University is really very different from anything you will have seen at A level, because (etc.) … and some of you may not even recognise this as mathematics! But it really, really is …” (or words to that effect).
One of my colleagues tells me that one of the visitors was complaining after the lecture, saying something like “I was expecting a sample maths lecture, but that was really just logic!”
Back to the drawing board ….
Tomorrow I will start the talk by telling them “It’s maths, but not as you know it!”
Aargh! I thought I would use the MediaSpace editing tools to delete the confusing blank few seconds at the start of my recent Cardiff talk, but instead I deleted the rest of the talk from MediaSpace, leaving just a blank 7-second video. (I never did like reading instructions …)
Oh well, I have the original mp4 file, so I’ll just have to upload it again and have another go!
Explaining mathematics 