All entries for Wednesday 23 September 2009

September 23, 2009

Choosing 2nd Year Modules

Inspired by this post, I decided to talk about the different modules I plan to take this year. If you're not a maths person, you can take pleasure in knowing that you will never have to know about this stuff. Also, it's a good way to get an idea of how many different areas Mathematics cover. It's not just one big 'Maths' module.

First, the compulsory ones (Core modules):

Second Year Essay: I have a friend who studies Politics (at Warwick). She always has at least two essays she's working on. We Maths students, on the contrary, only have yearly essays, which is of course totally sweet. And as if that weren't enough, we also get to choose the topic! I haven't decided on that one yet, though I'm wavering between Mathematics-of-Card-Shuffling and Something-To-Do-With-Chaos-Theory. The maths behind the Rubik's Cube could also be fun to have a look at, but I wonder if my tutor would accept that.

Differentiation: You'd think that by the end of our first year Maths course we would at least have covered differentiation. But oh no, it has only just started. From what I've gathered, it's about differentiating several functions of several variables. A generalised notion of a derivative, basically.

Vector Analysis: I've heard it's a bit like Geometry and Motion, with paths and trajectories and areas and surfaces and volumes and change of coordinates and all that.

Analysis III: I know what this is all about: formally defining integrals. Judge all you want, but I actually liked Analysis I and II. Learn and understand definitions of intuitive notions ("increasing", "tending to a limit", "continuous" ...), and rigorously work from there to prove complex theorems that often seems dead obvious when you think about them, that's what I like. Also the overall direction was very clear. I think I'll like this.

Algebra I: Also known as Advanced Linear Algebra. I wasn't too keen on Linear Algebra last year; it went from being mind-numbingly boring to over-your-head difficult. But I've made peace with eigenvalues and eigenvectors over the summer, so I think it'll be all right in the end. It'd better be; it's compulsory.

Algebra II: This is basically Group Theory, as far as I know. We touched a bit of Group Theory in college, and since then it has had a few cameo appearances in lectures. I don't understand what all the fuss is about, the definition of a Group seems rather straightforward to me, albeit a bit pointless. I hear Group Theory is a crucial concept in Mathematics, though.

Now we get to the optional ones, of which I still have to take a certain amount:

Metric Spaces: There's something magical about this. I've read ahead on this topic, and every time I read something new, I get this tingling feeling of delight in my stomach. There's just something neat about visualising metric spaces in your head. Maybe it's because I know that this is what leads to Topology, that it gets me so excited. Metric Spaces, please don't disappoint me.
This isn't strictly speaking a compulsory module, but one must take either that or...

Partial Differential Equations. And I've chosen both. PDEs don't appeal to me in the same way Metric Spaces do, but I've been told it's a useful tool to have. Although I know exactly what the module is about -- it's differential equations, but using partial derivatives instead of normal ones (duh) -- I have no idea of the difficulty, the concepts, the scope or whether I'm going to like it or not. We shall see.

Geometry: I want to do Geometry. Proper, formal geometry. Yes.

Mathematics of Random Events: The title sounds tantalising, but I guess the content is what matters. From what I can tell from the description on the Maths Department's website, this is something of a mixture between Analysis and Probability. While I adored Analysis, I abhorred Probability, so this is going to be an interesting one. But come on, "This module aims to provide an introduction to the mathematical ideas and language underlying the notion of randomness, which permeates through much of modern mathematics, as well as statistics and probability theory." I mean, who can resist that?

Stochastic Processes: Another module linked to probabilities. As much as I dislike probability, it is an important area in the mathematical world, and I know I can't try to work my way around it. So I might as well meet it face on, with my head high and a positive attitude. Besides, we did a bit of stochastics in college, and that wasn;t too bad. Also, I like the idea behind random walks, and that's one of the topics that will be covered, I believe.

Mathematical Economics A: Last year I did Introduction to Quantitative Economics, which was essentially Economics from a mathematical point of view. The one aspect I really enjoyed about the module was Game Theory. Game Theory is, in a nutshell, a mathematical study of what happens when two people play a game but they don't know what move the other person is going to do. Rock-paper-scissors style. Now, Mathematical Economics A is all about Game Theory, and nothing else it would seem. And I think it's fun.

Mathematical Methods for Physicists II: I'm no physicist, but this module was recommended to me by an older student, because it provides a nice introduction to something called Fourier Analysis. I have no clue what that is, but it comes up in later years and is a big thing. It should also be noted that while the word 'Physicists' is in the title of the module and while the exercises will probably be Physics-oriented, the actual content of the module is (apparently) purely mathematical. Which is a good thing.

Quantum Mechanics and its Applications: Last year I did Quantum Phenomena which was okay, if not a bit dull. Quantum Mechanics should provide a more mathematical and abstract presentation of Quantum Physics, which is just the way I want it. I am, however, taking this module tentatively, because I've been told it's a heavy load and it might not be so fun in the long run. But I want to give it a chance.

C programming: For the uninitiated, 'C' is the name of a programming language. I really like programming, although I would still qualify myself as a beginner. It's a kind of hobby for me, except I ought to spend more time doing it if I want it to become a serious pastime. Last year's module about Java programming was a good introduction to Object-Oriented Programming, but according to my friend and local Computer Scientist, Sarah, C is a much better language for programming games, a skill I would love to develop and perfect. After all, why else would you want to program?

Finally, there's Russian for Scientists. I definitely won't be doing this for credit, but I'm considering doing it for fun anyway, because I love languages and because I have a Russian-speaking friend. Plus, being able to say that you know a bit of Russian sounds awesome. Doing it for no credit also means I can easily drop it if it becomes too much of a burden.

All that brings me to a total of 173 CATS. The minimum is 120, maximum 180, and recommended maximum 150, the most sensible thing to do for me is to drop one or several of these modules as soon as I know which ones displease me the most.

Little side note explanation here: non-UK people often get confused when I talk about CATS, the Credit Accumulation Transfer Scheme, since they are used to ECTS, the European Credit Transfer System. ECTS is part of the Bologna process to make educational systems in Europe more comparable, which is why most European countries now use ECTS -- except England. The systems can still be compared, though, as 1 ECTS point = 2 CATS points. The irony is that "ECTS" is an English abbreviation.

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