Archive for the ‘Math’ Category.

6th January 2003, 05:44 pm

I’ve just been to our local Føtex where I bought some chocolade for my
exam tomorrow in Abstract Algebra. I’ll also take some bottles of CocaCola
with me so that I can get enough energy for the brain :-)

I’ve also been at the University of Aarhus today to hear the last
words of wisdom from our lecturer and to talk with our instructor. There I
found out that a Rasmus Villemoes has published a full solution to the
exam questions from the previous years. And a very good solution that
is. I’ve been training with these questions myself for the last couple of
days, and there has (unfortunately) been a couple of questions that I
couldn’t answer. So it’s interesting to see how simple and elegantly you
can solve most questions — I hope it’ll help me tomorrow. –Martin
Geisler

28th June 2002, 08:21 pm

No more exams! I had my last exam last Tuesday: Calculus. It went fantastic
— I got the grade 13 which is the top grade in the Danish school-system!

The exam was an aural exam with 30 minutes preparation. I was so lucky that
I got “The Complex
Exponential
Function” as my
question. That was probably the easiest question among the 15 that I had
to choose from. The other questions were about things like the length of
a curve in
**R**^{n},
Fourier Series and so
on — much harder questions. I don’t think I would have gotten a 13 if I
had gotten one of the other questions… perhaps 10 or 11 instead (there’s
no 12 in the Danish grade system).

But that doesn’t matter: I got the question and after waiting 30 minutes I
told them everything they wanted to know about it. They then asked me some
questions about other things, such a Fourier
Series. That also went
well — It’s not that I bad at handling Fourier
Series, it’s just that
most proofs are terribly long and boring. In the end the censor got
curious: he wanted to know if the Exponential
Function had an
inverse function,
e.g. he wanted me to talk about the complex
logarithm. We haven’t seen
this in our books, but I did manage to find some of the formula for *z*
given *w = e*^{z}:

*e*^{*x + iy*} | = | *u + iv ⇒* |

*x + iy* | = | ln(|*u + iv*|) + *i* arg(*u + iv*) |

The formula is found by taking advantage of, that *|e*^{z}| = |w|
and arg(*e*^{z}) = arg(*w*). Here we have that *|e*^{z}| =
e^{x} and that arg(*e*^{z}) = *y* and the result follows
easily from that.

19th June 2002, 08:34 pm

I’ve just received a preliminary score for my written test in Calculus —
I got 92 points out of 100. This is just a quick count done by my
lecturer, the censors have yet to see it, so the score might shift a
little. I’ll know my final score after my aural test this Tuesday —
that’s just five days away! But so far it looks good :-)

I’ve been rehearsing with Jérémy since the written test six days ago —
we’ve been training from 14:00 to ~19:00 each day. There’s 31 questions
and only 10 days to train, so it’s been a busy week. But we’re getting
there, we now have four days to discuss the last 12 subjects.

13th June 2002, 02:45 pm

Yes!! Today I had my last written exam in this round. That means that I’ve
had three of my four exams — the last one is aural Calculus
(mathematical analysis).

Todays test was written Calculus. I believe it went pretty well — I
answered all the questions, and with the help of my TI89 graphics
calculator
I was able to check most of my answers. It’s a fantastic help to have a
calculator that can do symbolic manipulation — many of the calculations
were quite long and boring, and the risk of making a little mistake was
high. I cought myself saying “2 × 3 = 5″…

I now have about ten days to prepare for the next and final exam. I have to
make an outline for 31 subjects in those ten days, so there’ll be plenty to
do. But we get 30 minutes to prepare ourselves at the exam, so I don’t
think it’ll be that bad — or perhaps I’m just being optimistic :-)

3rd April 2002, 11:30 pm

Manitou and I met yesterday and made a couple of
Java assignments which were overdue. We
implemented a Heap using the Locator pattern and a Vocabulary using a Trie
— it was a very good learning-experience to actually implement these ADTs
instead of just talking about them.

We also talked about other things — we met at 14:00 and went home again
at 23:30 so there was plenty of time :-) One of the things we discussed
extensively was, that he had a book, which said, that the set of all
subsets of the empty set, which is denoted 2^{∅}, is {∅, {∅}}. I
don’t believe that this is true — the only subset of ∅ is ∅ itself, so I
would say that 2^{∅} = {∅}. If 2^{∅} = {∅,
{∅}}, then that would imply, that ∅ ∈ ∅ which is
clearly false, as the empty set is *empty*. We’ll ask Jørgen
Hoffman-Jørgensen about it — he should know as he’s our teacher in
Probablility Theory.