[Mat06] szerintetek melyik tárgyat válasszam?

[Pintye Norbert]

Hello!

I have already attended all of these lectures, so I'm going to write a
short (as you have probably realised, english) description about them.
(Of course in my viewpoint.)

Theoretical Computer Science: If you would like to learn more about
Turing Machines, computational complexity (e.g. P, NP, Recursive
Algoritms), and Lambda Calculus, this is the right course for you. You
could use the book "Ivanyos, Rónyai, Szabó: Algoritmusok", it covers
all of the topics mentioned except the part Lambda Calculus, but I
have a good (english) note about it. There were homeworks at each
week, none of them from the unsolvable "Oh my God" kind. There were
two tests, the first one was harder, but the final grades were shaping
pretty well.

Albebraic and General (or Common?) Combinatorics: This was the one I
liked the least of all. It covers symmetric polynomials, Young
Tableaux (plural form of tableau) [a special king of tool providing a
convenient way to describe the group representations of the symmetric
and general linear groups and to study their properties], Matroid
Theory and Hyper Graphs. The were three lecturers, three tests (not of
the easiest kind). I think in defult of time we just blocked in these
topics.

Commutative Algebra and Algebraic Geometry: ho-ho-ho, my personal
favourite (and good enough for my MSc Thesis :)). I do not recommend
this for *you* despite it seems paradoxical, but I have a good reason.
It uses and requires lots of algebra that I'm sure you (and everybody)
have not learnt enough yet (and mind that you are studing applied
mathematics). Of course the lecturer tries to stop this gap. So, in
deed, if you are capable to learn 3x more than before, and interested
in a very dynamic and diversified science, (and if and only if this is
the case), then you're welcome to subscribe. For the sake of clarity,
it is still possible to have very good results. By the way, Algebraic
Geometry is concerned with the relationship of Algebra and Geometry
(not surprisingly). It takes a set of polynomials (in fact a radical
ideal in a polynomial ring) and defines geometric objects (in fact
closed sets and hence topology) as the common zero locus (root) of
them. Then it defines maps (in fact polynomial rational maps of some
kind) on geometric objects and morphisms between them, and studies how
they interact. As a goal, it turns out that we can do the whole thing
not only with ideals of a polynomial ring but with any ring endowed
with an identity element. Ok, ok, you may say, but what's the point?
Why is it interesting? Well, if you're interested in cryptography,
elliptic curves are part of this science. For example one may show
that the points of these curves form an additive (abelian) group. Etc.

Representation Theory: Discover it yourself :). Beside Group Theory,
now I feel I know nothing about math. It covers Group Actions, Lie
Groups, Lie Algebras, and the representation of Lie Algebras. An
algebraic object is just too abstract that no one (not counting the
fanatics of algebra) can deal with it, so after representing it in an
appropriate (handy) structure (like a group of automorphism), one can
deduct more about its behaviour. You could find out more about the
group structure of manifolds (continuous group actions) and the
tangent space at a particular point of them. As before, hardly algebra
(and topology) oriented, but the representation part is easy. I
enjoyed the lessons.

Differential Geometry and Topology: I think it's not your cup of tea.
Tensor products, sheaves and Cohomology Theory of Vector Bundles of
Differential Forms (in fact only sections of them). If you have not
learnt much topology before, it will be completely strange and
uncomprehending. If you want to learn Algebraic Geometry, it is
useful. Also this is the case if you are interested in differential
forms (e.g. Special Relativity Theory and Maxwell's Equations). Just
to know that your thursday starts with 4 hours of this intensive
lesson (with exercises) is a nightmare, believe me, so I'm not that
shallow to recommend, but If you are still capable, just subscribe and
blow your mind, because it has some really interesting parts.

That's all folks!

For further questions please feel free to contact me.

Wish the best, gruff

2010/7/18 Viktor Szabó <szaboviktor1988 at gmail.com>:
> Sziasztok!
> Egy kérdésem lenne Felétek így a nyár kellős közepén: az alábbi három tárgy
> közül egyet föl kell vennem (mert eddig csak 3 témakörből választottam
> tárgyakat, de 4-ből kell) :
>
> Elméleti számítástudomány
> Algebrai és általános kombinatorika
> Kommutatív algebra és algebrai geometria
> Reprezentációelmélet
> Differenciálgeometria és topológia
>
> Szerintetek melyiket lenne érdemes, Ti melyiket ajánlanátok leginkább?
> (Nehézség, számonkérés, oktatás érthetősége szempontjából stb.)
> Előre is köszi a segítséget!
> Viktor
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