We take a short break from revision to bring to you the following video:

Great song with a pretty neat atypical skateboard video.

I came across two really neat videos from the Web2Expo.

The first one is by Clay Shirky and it’s about the “cognitive surplus” and how sitcoms are to the 20th century as gin was to the industrial revolution:

http://web2expo.blip.tv/file/855937/

The second is by the Fake Steve Jobs. While I don’t find his blog quite that funny the clip was hilarious:

http://web2expo.blip.tv/file/858285/

Check them out.

In the meantime I shall go back to revision.

There is surely no more reliable way to kill enthusiasm and interest in a subject than to make it a mandatory part of the school curriculum.

This is just one quote from the superb article A Mathematician’s Lament. Go ahead. Read it, you know you want to.

Turns out I’m rather busy this (academic) year which probably explains my lack of posts so far. So to break the silence let’s review the courses I took last term.

Elementary Number Theory

The title of this course is misleading in two ways. Elementary certainly doesn’t mean easy, it supposedly refers to number theory using only elementary methods and let’s face it this is sometimes harder than using more advanced techniques. This incidentally is the other misleading aspect of its title. There’s a great deal of group theory and bits and pieces about rings and fields to be found in the course. Nonetheless this was actually my easiest course last term (simultaneously I know people who called this their hardest course). Overall I enjoyed this course. The lecturer was fairly entertaining and the material covered is pretty neat too.

Metric and Topological Spaces

Of all the courses I took last term this course has the best set of lecture notes. You can easily read through them and most of the course makes perfect sense. Furthermore most proofs are rather short and appear straightforward. On the other hand this course had quite likely some of the hardest exercises. There were a few questions on the problem sheets (assessed ones) that took me several hours to figure out. I don’t know if this is a general characteristic of analysis courses or whether I simply have more of a knack for algebraic courses, but I really have the impression that if you really understand everything in the lecture notes then questions in algebra are often really straightforward whereas questions in analysis can still take ages. Nonetheless, I thought this was a pretty good course, much better than expected (especially considering that the same lecturer gave the worst lecture of my second year when substituting for another lecturer).

Group Theory

This was a much anticipated course as we finally covered things such as conjugation which I had already seen in my first year project. The lecture notes were slightly disorganised, but overall I’m satisfied with the course. Though I still have to get the hang of semi-direct products.

Measure and Integration

This was by far the hardest course I took, not just last term but in my entire academic career. I still don’t fully get all the material in the course, but while revising over the holidays I started to understand a great deal of the material. Now I still have several exercise sheets to go over and see whether this new found understanding can be applied to the exercises.

Hopefully I’ll be able to find some time this term to ensure that I don’t forget everything that was covered in the last term. After all it’s always better to polish material over Easter rather than having to relearn everything. Though I already know that I’ll have to do a lot of work for Galois Theory this term as the lectures were pretty awful so far. Then again I’ve had so many ridiculously bad lecturers over the last few years that I got really good at teaching myself the relevant material.

A came across Scout Niblett’s song Kiss on a Too Pure Radio Sampler yesterday and I like it a lot. It’s even got a really neat music video. So do check it out:

Some of you may remember part I of this highly successful series on great ways to waste your time online. Today’s topic:

Music

Obviously thanks to the web you can listen to thousands of different radio stations. Nevertheless I’ll only list a few things of interest.

fm4, which has always been my favourite radio station, has created a platform for bands to present their material. To be specific that platform is for Austrian bands as fm4 is an Austrian radio station. Nonetheless there’s a lot of great music by unsigned bands to check out in the Soundpark. Also they host the protest song contest every year and you can listen to the finalists here. At any rate, it’s always a good idea to tune in to fm4 as they play great music all day long.

Another great place for music is npr. I especially like their live in concert series. I’ve listened to quite a few great concerts so far, for example Regina Spektor, Okkervil River, Nellie McKay and the New Pornographers. Another great thing on npr is Project Song, which seems to be a very recent show on which they give an artist 48 hours, a range of topics to choose from and a studio and document the resulting song. So far they’ve only had Stephin Merritt of the Magnetic Fields, but it’s a fun video to watch.

Now I don’t remember if I ever pointed out that I’m a great admirer of Henry Rollins‘ work, especially of his talking shows, and for some time now he’s also hosted his own radio show called Harmony in my Head. You can download past shows from the Rollins archive. I’ve listened to quite a few of his shows and I’m sure his ecclectic taste in music will beat up anyone elses ecclectic taste in music.

Another radio show I’ve enjoyed listening to is Zoe’s show. Her taste in music is apparently so awesome that the Beastie Boys let her open for them @ the Greek in LA. Unfortunately she doesn’t seem to be doing shows regularly, but whenever she does a show I’ll usually gladly listen to it.

I think this should be enough to keep you from getting anything productive done for quite some time. If you ever get really desperate just tune in to ICradio, we’ve started putting more recent music on the out of hours sustain system so you might even enjoy some of the music.

I’ll end this post by linking to Public Enemy’s video for their latest single ‘Harder Than You Think’ because it’s clearly a brilliant song

I’ve never been much of a Killers fan but I’ve got to say that their latest song is pretty damn awesome. Of course it helps that it features Lou Reed.

Simply brilliant. I keep listening to it over and over again.

Unfortunately my hard drive crashed so I’m late posting this brilliant video clip.

A good old school sketch from A Bit Fry and Laurie:

I know it’s been ages since I’ve last posted, but what can I say sometimes I’m taking procrastination to entirely new levels.

I’m sure I’ll eventually get around to writing something halfway interesting, in the meantime check out CNNs Podcasting and watch Stephen Colbert on Larry King Live. It’s even more awesome than you’d expect.

Now that I’ve completed my second year here at Imperial College in
London I figured I’d update this thing again. Furthermore I’m doing it the lazy way. Since I like to keep my A-level maths teacher posted on how things are going I figured I’d mainly rip off the mail I sent him. So here we go:

This year we’ve had the following courses; Algebra II, Analysis II,
Probability and Statistics II, Numerical Analysis, Vector Calculus,
Differential Equations, Complex Analysis, Rings and Fields.

Algebra II was pretty straightforward as I had seen most of the group
theoretical part while working on my first year project (ie. normal
subgroups, even and odd permutations) and the part on vector spaces
was pretty all right too. So all in all it was one of the more
enjoyable courses.

Analysis II built on what we had done in Analysis I in the first year.
The idea of the course is to provide a rigorous foundation for the
integral and differential calculus. So there are things such as the
Intermediate Value Theorem, the Mean Value Theorem, etc. and the
course more or less ended with the Riemann integral. Next year I’ll
probably take Measure and Integration where we get to cover the
Lebesgue integral and other hopefully exciting measure theoretical
things.

Probability and Statistics II was not quite as boring as its
predecessor but still highly annoying. For some reason the stats
courses seem to have been designed for maximum confusion. While I had
a rough idea of what it was all about at A-level the lecturers have
now managed to make me lose touch with every aspect of the subject.
This course was especially amazing in the sense that it managed to
include the worst aspects of pure and methods courses. On one hand we
are given the rigorous definitions, eg. that the probability space has
to be a sigma algebra but we never build on these rigorous definitions
and instead are just expected to apply a bunch of methods without
really knowing why they work or why we would use them in the first
place. So this is quite likely the last stats course I’ll ever take.

Numerical Analysis was a pretty good course. It’s mainly about
orthogonality and we covered things such as the Gram-Schmidt
algorithm, Givens rotations and QR factorization.
Overall it felt a lot like a pure maths course as everything was
proved and we weren’t subjected to any kind of hand waving.

Vector Calculus and Differential Equations were definitely the two
worst courses this year. Mainly because the lectures and lecture notes
were completely useless. Which is kinda hard to believe considering
that most of the content of these courses is pretty straightforward.
So I essentially had to teach myself these courses out of books, so
far the only courses where I was forced to rely on books. Other than
that I didn’t find them particularly interesting. I have a tendency to
find methods courses mainly pointless as they only teach us methods
without understanding why they work or why we would want to use them
in the first place. Hence it is no surprise that we won’t choose any
methods courses next year.

Complex Analysis turned out to be better than I remembered once I read
through the entire notes at the end of the Easter holidays. The main
problem with that course was the amount of repetition. There is so
much material that we had covered before in Analysis I and II, so it
is no surprise that I stopped paying attention in lectures early on.
Seriously, I can’t believe we wasted the first three lectures on an
introduction of the complex numbers after we covered them in at least
three courses in the first year.

Rings and Fields was the conceptually most difficult course so far but
at the same time this makes it one of the best courses we had the
pleasure of taking. Unfortunately Rings and Modules isn’t running next
year so the only way we get to build on the material we’ve covered in
this course is by taking Galois Theory, Group Representation Theory
and Algebraic Number Theory next year. Though it’s a small price to
pay.

Overall the summer exams went all right, except for Probability and
Stats II which was several orders of magnitude harder than the past
papers we had seen, also most of the other exams were somewhat more
difficult than usual. Nevertheless I am confident that I have passed
all of them.

After the exams we’ve had about four weeks to work on a group project.
When choosing the three areas we’d like to work in I chose Algebra,
Numerical Analysis and Analysis, thinking I really had chosen three
pure courses, but as it turned out choosing Numerical Analysis meant I
ended up doing a highly applied project with some Matlab coding. The
project title was Computing Phase Transition Phenomena in Wetting
Problems. I know a lot more about wetting problems than before but I
can’t really pretend that I understand any of it. At least we won’t
have any group projects anymore. The group I was in was for the most
part great, but the topic was a bit of a downer. The next time we’ll
get to do a project will be the fourth year project that counts for
1/4 of the final year mark and since I’m mainly choosing pure courses
I guess it’s safe to say that I won’t be doing an applied project  then.

From next year on we don’t have any compulsory courses so my choices,
based on what courses are supposedly running next year, are:

Metric and Topological Spaces, Measure and Integration, Group Theory,
Elementary Number Theory, Functional Analysis, Galois Theory, Group
Representation Theory, Algebraic Number Theory. I might also be
checking out the lectures for the fluid dynamics courses after I’ve
seen some of the cool simulations the Applied Modelling and
Computation Group are coming up with.

Anyway, all in all it was a pretty good year, though I’m really
looking forward to the exciting courses I’m going to take next year.