[Mat06] szerintetek melyik tárgyat válasszam?

[Viktor Szabó]

háj!

ájszink ájvill csúz dö förszt van...

tenkjú, Norbert! :)

Viktor

2010/7/18 Pintye Norbert <norbert.pintye at gmail.com>

> 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
> > _______________________________________________
> > Mat06 mailing list
> > Mat06 at lists.math.bme.hu
> > https://lists.math.bme.hu/cgi-bin/mailman/listinfo/mat06
> >
> >
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