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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.
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.
It’s been some time since my last post. It’s like I found other ways to procrastinate rather than writing here. Anyway, while I could be complaining about the group project I’m working on, it’s easier to look to the future and ponder next year’s course options.
Let’s start with the awesome facts. From next year on we are talking about 100% choice. There might be some minor restrictions such as only being allowed to take one non-maths option but for all practical purposes we may see this as 100% sheer awesomeness.
I’ll start with the first term. I’ll be taking 4 courses in each term, so I’ll start by giving my 4 most likely choices followed by the B-list. So let’s hit it:
To start with there are 3 courses in the first term that I consider fundamental
Metric & Topological Spaces, Measure & Integration and Elementary Number Theory.
So it’s unlikely that I’ll drop any of these or postpone them to the 4th year as I consider them too important. The first two weren’t anywhere close to my A-list a year or so ago when I first started considering 3rd year options. To be fair, they don’t really look like fun, especially not the one on Metric Spaces as I know the lecturer to be quite awful. Nevertheless I believe their content to be rather important and as such they’re clearly on my A-list.
So what’s my 4th choice for the first term, you may wonder. It’s bound to be
Group Theory
Bit of weird course title, considering that we’ve covered group theory in two courses so far. I liked how when they presented next year’s course options they said: ‘If you enjoyed group theory so far you should definitely take this course. If you didn’t, you still should take it’.
So what’s on my B-list you may wonder. There are only 2 serious contenders
Discrete Maths and Games, Risks and Decisions
Discrete Maths is mainly about elementary coding theory. The lecturer is awesome and still, I probably won’t take it. One good reasons for not taking it is that chances are that this course and the one on Graphs and Optimization will get replaced by a proper course on Combinatorics. So that alone makes it worth waiting an extra year. That and the fact that the syllabus for Discrete Maths isn’t really mind blowing stuff. Games, Risks and Decisions used to be on my A-list for ages. It’s the only reason why I took Probability and Stats II this year and yet it got kicked off my A-list. Now frankly I believe it’s got some fun maths, but at the same time it’s also got some annoying probability distributions kind of stuff. Though the main reason simply is that I believe that I will benefit more from the other options.
So let’s move on to the second term. My choices are bound to be
Functional Analysis, Galois Theory, Group Representation Theory and Algebraic Number Theory.
You may have noticed a pattern in my choices. It’s pretty clear that all my choices are pure maths. There’s no applied, stats or methods courses on my A-list. Technically I don’t really know much about any of these courses. It’s one thing to read the syllabus description and look up stuff online but until one has covered and hopefully understood the material there’s no way of telling whether the courses are anywhere as interesting/fun/important as one thought they would be.
The only thing worth mentioning on the B-list is Scientific Computation. The cool thing about that course is that it’s 100% project work. This would mean one less exam in the summer term, but it would also mean one less awesome maths course.
So these are bound to my choices for all its worth. Choosing courses turned out to be much easier than I first anticipated based on the simple fact that a number of courses that would have been serious contenders aren’t running (for example Ring and Modules, Complex Analysis II and Linear Algebra and Matrices).
In case you’re desperate to see all the exciting courses I chose to miss out on you can find the guide to courses online.
Procrastination, oh sweet procrastination, thou shalst be my downfall.
Obviously revision time has always been the best time to indulge in the pleasures of procrastination. I’m sure the revisionistas will disagree but ’tis most important that one wastes significant portions of one’s day on the internets rather than squeezing obsolete knowledge on the mental hard drive. ’tis in this spirit that I bring you the first installment of this multipart-series – a best of procrastination, if you will.
Disclaimer: Procrastination should not be attempted by people who think it may interfere with them passing their exams.
Originally this was going to be a list of all the wonderful things you can find on the Internets with which to kill time and procrastinate like there’s no tomorrow, but the list was getting longer and longer and so I decided to have several installments, each for the categories under which I listed the links. Today you shall meet
Webcomics
We all know and love comics. Thanks to the web not only can we rss our favourite comics but we can stumble upon comics that are, in some cases, only published on the web, which is why we shall refer to them as webcomics.
Sinfest is my favourite webcomic. As much for the stories as for the drawing. I mean, how many comics feature god, the devil as well as talking cats and dogs? Obviously this comic and the next aren’t exactly politically correct. If you go to the archives and start with the very first episode you’ve got almost 3000 episodes to read through.
Jesus and Mo is most certainly blasphemous, politically incorrect and probably extremely evil. Don’t look at it if you’re easily offended, heck if you’re easily offended you should turn your computer off – don’t you know how dangerous the Internet is? Anyway, back to the comic. It isn’t drawn that well, but the concept is rather interesting; Jesus and Mohammed are roommates and they discuss various things, many of which are of a religious nature.
Diesel Sweeties is kinda weird and includes a girl with a robot boyfriend. The look of the comic reminds one of the computer games of the distant past when computer screens had a much lower resolution. Nevertheless it’s got its amusing moments. Obviously you shouldn’t read that kind of comic if robot sex offends you.
Cyanide and Happiness is alternating between offensive and just plain gross with the occasional silly moment thrown in for good measure.
Least I Could Do is hard to describe. Basically the main character Rayne is the most egocentric person ever and he does some outrageously silly things. Like using ninja stars to send invitations to a party.
Boy on a Stick and Slither and Count Your Sheep is what I’d call really cute stuff. And we all know that every once in a while what one needs is cute stuff.
xkcd describes itself as a webcomic of romance, sarcasm, math, and language. I really like their disclaimer which reads:
Warning: this comic occasionally contains strong language (which may be unsuitable for children), unusual humor (which may be unsuitable for adults), and advanced mathematics (which may be unsuitable for liberal-arts majors).
If the classics are more what you’re after check out Comics.com which labels itself the home of comics on the web.
This should be enough to keep you busy for a while. The next installment will follow whenever it’s ready. In the meantime I have to cover a fair share of maths for the group project which started yesterday. I’ll tell you what it’s about once I figure it out.
Regular readers will have noticed that there was nothing regular to read in the last few weeks. Some may have wondered whether I had been cast into the dark pits of hell. The reason for my absence was only marginally more entertaining; I was busy revising and sitting exams.
Fortunately today was my last exam but instead of going out and partying I will grace these pages with a summary of these very same exams. Being extremely original I will summarise them in the order in which they happened.
Probability and Statistics II
This exam was just insane. It looked like nothing one would have expected. Not like the coursework and not like any of the past papers. Every question was either really obscure or if it looked familiar it was much harder than usual. Everybody hated this exam and I doubt anyone got close to acing it. It was so bad someone should have broken down and cried during the exam. I’m sure most of us felt that way but having someone actually break down makes great fodder for four o’clock tea conversations. The bittersweet thing is that just before the exam I was thinking that it was kind of sad that I wasn’t going to take any more stats courses next year now that I actually really started to understand the material. I guess I didn’t really understand it after all. On an upside; from next year on I’m only taking real maths courses.
Vector Field Theory
This was a reasonably hard paper which begs the question whether the lecturer acted on his threats. He used to complain that no one showed up to the problem solving classes (which are optional) and threatened to make the exam harder if this was to stay that way (thinking that no one showing up was an indication that everyone finds the course easy). Which was stupid on so many levels. First off there was a gap of something like 4-6 weeks in which he didn’t hand out any problem sheets so if we don’t have any problems to solve why would anyone show up to problem solving class? (To clarify material covered in lectures, you say? But no, the lectures and lecture notes were completely useless, no one in their right mind would go to the source to clarify the material) As an aside I and a few of my colleagues like to refer to these simply as problem classes and say they’re only for people who have problems. Anyway, at the end of the day the course covers mostly trivial material so even though the exam was harder than usual it was still mostly straightforward if you understand what you’re doing (having done complex analysis makes understanding some of the material even easier). The only strange bit was question four and I still managed to frantically figure out most of it in the last 5 minutes of the exam.
Differential Equations
That exam was pretty standard. As a matter of fact if you look at the last 5-6 years worth of past papers you always see the same type of questions. So preparing for it wasn’t too difficult. Unfortunately he chose the most annoying ODE for the 5th question (seriously, the Bessel equation is such a pain in the neck). I might’ve still scammed my way to half the marks on that question. The rest was pretty easy.
Complex Analysis
Considering I only started really understanding this course a few weeks ago it could have been much worse. I could do most of the questions though there were always a few tiny things I couldn’t complete. In hindsight I should’ve tried to understand the course significantly earlier. It wouldn’t have necessarily made much of a difference for that particular exam but really understanding the material makes revision so much easier. (This is a non-trivial statement no matter what you think) Furthermore once I started understanding it I also started appreciating it. So let me say this; Complex Analysis is actually really neat stuff.
Analysis II
That exam went all right even though I know of at least two mistakes I’ve made. One of which I realised while waking up two days later, which is an odd way to notice your mistakes (maybe I should nap during exams). The problem with this course was that I really understood it in the first term and didn’t look at it during the second term. Shockingly enough that was enough to forget quite a bit and no longer be as fluent in it as I used to be.
Algebra II
This is the only exam where I am reasonably happy with my performance. But then again this is my favourite subject and the one I’m best at, so I could be expected to do well. The exam was fairly straightforward even though it included a tricky question which I’ve managed to get wrong (after being half way there that is), though it should only be worth a few marks. So all is well, if you disregard an imperfection in one of my proofs which I’ve also realised a few days later when waking up.
Rings and Fields
This exam was mostly all right. Though I was surprised at how much of this material I managed to forget over Easter. Since I used to really understand it at the end of last term I didn’t spend much time revising it over Easter and unfortunately managed to lose touch with it enough to suffer the consequences at least a little bit. Trivia: This was the only exam where all 5 questions fit on one side.
Numerical Analysis
When I took this course in the first term I thought this was going to be one of the easiest exams to do well in. Especially since the lecturer said that one usually only has to ace 4 of the 5 questions to get full marks on the paper. When looking at past papers I quickly realised why this was the case. That exam is notoriously difficult to complete in two hours. Take the first question for example. The second part alone takes ages to compute. It’s just using Givens rotation matrices to solve an overdetermined system. Now considering that we’re not allowed calculators it seems to take forever to do the matrix computations (heck, just writing down all these matrices takes ages). The other questions aren’t much better. They’re crammed with stuff you need to do and none of it is really trivial. To make one more point; I needed an extra booklet for Rings and Fields, whereas for this I almost needed two extra booklets, the only reason I didn’t was that I seriously started cutting down on readability and careful arguments, still could have done with extra time though.
In closing I notice the same thing I did last year. There’s not one exam I’m really happy about. There was only one in which I was done early (Rings and Fields – where early means 10 mins before the end).
So what are the lessons we’ve learned?
Don’t take Stats. Keep revising throughout the year. Look at past papers early as it may influence how to revise more efficiently.
One extra thing I’ve learned which isn’t really related to exams per se is to really understand a subject. I mean really understand it. Take Algebra II for example. I thought I really understood it. I hardly did any revision and it’s still bound to be my best result. Nonetheless there are a number of results in the lecture notes that I do not fully grasp. For the most part you could simply consider them subtleties. But in order to fully understanding a subject you also need to grasp its subtleties. So from next year on I’ll try to really understand the courses I’m taking. Which shouldn’t be impossible, after all it’s not like I’m choosing some nonsense like Stats.
I started this post on Sunday but then my computer started acting up and since then I was too busy procrastinating to finish it.
Now that the Easter holidays are over ’tis time for another revision update.
We have two more weeks of revision left before the exams start and we certainly feel less ready than we did this time last year, but it’s hopefully nothing that good work can’t fix.
So let’s see, where do we stand and what’s our battle-plan for the next two weeks.
Vector Calculus and Differential Equations
Let’s do the decent thing and put both methods courses together. Tomorrow we’ll pick up a number of books from the library which includes cool things like Schaum’s Outline, on such beautiful subjects as Vector Analysis, Differential Equations and Fourier Analysis. Mainly to have more questions to practise with. After all these courses boil down to being able to use the methods and the more practise one has the better.
Probability and Statistics II
Even after having done most problem sheets I still find the course awful. I should be able to do most things but I can’t yet say that I feel confident. I’ll try to distill the essential part of the course and ensure that I really understand this (as far as is possible given the annoying subject matter).
Numerical Analysis
I used to feel good about this course but I’ve had to review my views after glancing at some past papers. I expected the exam to be mainly about applying the material but unfortunately being able to prove most of the main results is also a very important aspect so I’ll have to study these bits as well. But apart from this I don’t see any difficulties.
Analysis II and Complex Analysis
Still a bit rusty on Analysis II but overall I’m feeling all right about it. Complex Analysis on the other hand used to be awful until last Saturday when I’ve spent the time I had to wait at the airport, etc. to really go over the notes and I’m really starting to get it. So much so that I disagree with one part of a proof and don’t understand why some of the non-examinable proofs are non-examinable. Now I need to let this new found knowledge sink in to be able to apply it to typical exam questions.
Algebra II and Rings and Fields
I’ve done very little on these courses for very simple reasons. On one hand these are some of the last exams so we still have plenty of time for revision and on the other hand we do understand the material really well. For Algebra II we simply need to start doing a few questions to get in the groove again and for Rings and Fields we need to memorise all the proofs as the exam is unfortunately really big on bookwork (at least this is our conjecture after seeing the past papers).
Yesterday I’ve changed my overall revision approach. I used to try to cover absolutely everything to have a shot at acing a few exams but the approach turned out to be too boring to keep up. Instead I’ve decided to look at the big picture and start with those things that I find more difficult. I might still get around to cover almost everything but it’s definitely more interesting to tackle the more difficult bits first rather than covering every set of lecture notes from beginning to end. Ah well, we’ll see how well this new approach will go.
It’s been some time since I’ve last wrote anything but I was busy revising – after all that’s what the Easter holidays are all about.
Almost one month ago I sketched an outline of how well revision should go. Now I’ve had two weeks of continuous revision and I guess it’s time for an update.
Analysis II
I did go over Analysis I first and I’ve gone through the lecture notes for Analysis II and Complex Analysis. As I’ve said Analysis II shouldn’t be too much of a problem and I stand by this statement, though I had to realise just how much I’ve forgotten or more precisely how rusty my skills have gotten. So the most important thing for this half-unit is to practice a bunch of questions and get a feel for it again.
Algebra II
I went really crazy and revised all my first year Algebra notes before looking at Algebra II. This really shouldn’t be a problem. I still knew most of it and what can I say, it’s my baby, I just dig this stuff.
Vector Calculus
Goodness, have I forgotten a lot or have I forgotten more?! Still, in principle it’s not too bad but I really need to practice this stuff. Problem sheets and exams could be enough but I’ll borrow Schaum’s outline: Vector Analysis when I’m back in London and do plenty of those questions as well. Still, I still assert that the course is trivial – unless there are some really insane questions on the exam.
Probability and Statistics II
I don’t know if I still think that this course sucks the most. I aim to do 2 hours a day just going through problem sheets and worked examples and I really start to get the hang of it. Though I still think this exam might turn out to be one of the hardest. For the record the hardest calculus questions and craziest integration tricks I’ve come across in the second year were all in this course – go figure.
Numerical Analysis
So far I’ve done 1/3 of the problem sheets and covered maybe half the notes, mainly because I take it easy and spread it out to keep the material alive as the exam is going to be the last. Though so far things look pretty bright. The hardest part is Gradients and Hessians but a bit of practice should fix whatever difficulty we might encounter.
Complex Analysis
Going over the lecture notes and doing the penultimate problem sheet made me think that we are totally screwed. Granted I probably overreacted. I literally will have to slowly work through the entire course again to get a feel for this stuff – for I never got it. I blame all the boring repetitions of past material it successfully drowned out the more difficult new stuff. But once I work through it from start to finish I should get it.
Rings and Fields
This was pretty laid back as it was fresh in my memory. Though I was surprised to find myself realising quite a lot of subtle facts that I hadn’t really fully appreciated so far. So I’m really chuffed. Though today I worked through a past paper and glanced at a few others and I’m not too impressed. The past papers are perfect for rote memorization. Every question asked for a few definitions and then a number of standard proofs. Basically 99% bookwork. I’d be kind of disappointed if the exam turned out to be that way. The progress tests were definitely more interesting. It’d be sad if the conceptually most difficult course could be aced by memorising the lecture notes without understanding any of the material.
Differential Equations
Working through the lecture notes I find that I have indeed been correct and the relevant material fits on less than 10 sheets of paper. Go figure. As with Vector Calculus the important bit is practising many standard questions. After all it’s a methods course. In some ways I think it’s actually easier than Vector Calculus. The notes were much worse but a lot of the methods are actually piss easy.
To summarise; things aren’t looking too bad but it’s definitely more work than last year – though I believe it is realistic to aim for higher marks than last year (would be rather neat).
PS: One can tell that I’m working more than last year simply by realising that I’m getting up for revision on most mornings – I mean I, of all people, get up before 12. Go figure.
I can’t believe we’ve only got two weeks of term left. This is so scary. We’ve failed to continually revise last terms material which means that some of our revision time will be wasted on relearning stuff we used to know. But let’s have a list:
Analysis II
This should be all right. I’ll actually go over Analysis I from last year first and then revise both Analysis II and Complex Analysis as there is so much overlap between these courses.
Algebra II
There are two possible approaches as I understand the material really well. Either I keep it light and revise it using as little time and energy as necessary to do well or I put in a fair bit more work into it to literally kick ass in the exam. I guess this will depend on how much time I need for the other half-units.
Vector Calculus
As I started this blog after this course was already over you missed out on much bickering and complaining. Though at the end of the day this course is actually trivial. It’s a methods course so you only need to be able to apply the methods no in-depth knowledge or understanding is necessary (I don’t even think it would be beneficial in any way). So going over the problem sheets and doing past papers should do the trick.
Probability and Statistics II
This course sucks so much I don’t even know where to start. This will literally erode most of my revision time. I pretty much have to start from scratch again. I’ll just work through all the problem sheets again while making notes based on what insight I gain when solving these totally pointless exercises. Passing will be easy but doing really well – that’s going to take some hard work.
Numerical Analysis
This course is basically applied linear algebra. So in theory it’s not going to be much work though there is a lot of stuff to remember. And compared to some other courses the exam questions aren’t bound to be trivial. Though according to the lecturer you only need to get full marks in 4 of the 5 questions to get full marks on the exam. So from this point of view I am aiming at full marks, though I’d prefer to get full marks on all 5 questions – just to be safe.
Complex Analysis
In some ways this course is really boring as there is so much overlap with some of the other Analysis courses. In many respects we really started getting down to the real stuff in the last few weeks so it’s hard to say what the best approach for revision will be.
Rings and Fields
This course is pretty strange. I thought it would be similar to group theory and I really get group theory but I turned out to be wrong. While in principle rings are a special kind of group and fields are a special kind of ring the subject is very different in feel than group theory. In many respects I find it easier to relate most of the material to elementary number theory. So far it took me ages to get to grasps with the subject matter but lately I start to get a feel for it. I believe the revision shouldn’t be too much of a problem.
Differential Equations
The worst course of the entire year, scratch that, the worst course of the entire degree so far (hopefully we won’t come across anything that can beat that). So far I had to borrow 5 books from the library to get a professional treatment of the different things we’ve covered so far (when I say covered I mean what was meant to be covered based on the syllabus). But as far as revision is concerned I understand most of what we did so far and I’ll figure out the rest quickly enough so revision will be as straightforward as Vector Calculus.
So that’s it. Two weeks is really too short to be on top of everything before starting revision, but I feel confident that everything will be all right once the holidays start.
I’ll start off with a nice link to a video of Jean-Pierre Serre lecturing on how to write mathematics badly. It’s somewhat entertaining though I did find it slightly too long.
On another note I’ll have a bit of a rant on today’s methods lecture. The audience was far too noisy (frankly can we drown some of these people?) and we had a substitute lecturer, and he did make a few mistakes though overall I think I may call today’s lecture the best methods lecture this academic year.
We did a worked example on Fourier Transforms and I must say that is some very powerful stuff. So dispite my usual dislike of methods courses I must say that the impossible has happened and I have found something useful in this course. Sweet. I’m glad that happened. We’ve got 4 weeks left in this term and so far I found this academic year rather tedious and boring. It felt like we haven’t learned much, especially not much exciting material. Though I did revise some of last term’s courses and there was way more exciting stuff in Algebra II than I remembered.
Still, I am really looking forward to the end of term. OK, who am I kidding, I’m really looking forward to the next academic year, it’s high time for more exciting maths, seriously.
Let’s start by ridiculing the description of Conservapedia first (italics = my ranting):
Conservapedia has over 3,400 educational, clean and concise (so concise it’s usually void of content) entries on historical, scientific, legal, and economic topics … Already Conservapedia has become one of the largest user-controlled free encyclopedias on the internet. Which is really hard, I mean how many large user-controlled free encyclopedias can you think of? (hint: starts with W)
Conservapedia is a much-needed alternative to Wikipedia, which is increasingly anti-Christian and anti-American. On Wikipedia, many of the dates are provided in the anti-Christian “C.E.” instead of “A.D.”, which Conservapedia uses. Christianity receives no credit for the great advances and discoveries it inspired, such as those of the Renaissance or the burning of witches, I mean those were the days...
One of the total highlights of the page is its Examples of Bias in Wikipedia. It is only fair to assume that this is either made up or the writer doesn’t know the definition of bias, which is likely given the level of ignorance that can be found in some, possibly most(*), of the entries on Crackpotedia (*)alas I have real things to attend to.
While deconstructing the site might be fun, it’s utterly not worth it, so I shall just post a very nice example of a hilarious contradiction that can be found on it. Compare the following two things:
The term “Common Era” (CE) is an attempt to erase the historical basis for the primary calendar dating system in the Western world.
with
Considering how strongly these guys feel about the whole anti-christian conspiracy (it’s obviously totally unfair how these atheists go after that poor christian minority) it’s hilarious to find that they also have this awful liberal bias and use CE instead of the correct AD.
And now for a totally obvious conclusion; will Crackpotedia ever be successful? Clearly not. The simple reason why Wikipedia is successful is that it is useful, which obviously can’t be said about this pseudo competitor.
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