háj!<div><br><div>ájszink ájvill csúz dö förszt van...</div><div><br></div><div>tenkjú, Norbert! :)</div><div><br></div><div>Viktor<br><br><div class="gmail_quote">2010/7/18 Pintye Norbert <span dir="ltr"><<a href="mailto:norbert.pintye@gmail.com">norbert.pintye@gmail.com</a>></span><br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">Hello!<br>
<br>
I have already attended all of these lectures, so I'm going to write a<br>
short (as you have probably realised, english) description about them.<br>
(Of course in my viewpoint.)<br>
<br>
Theoretical Computer Science: If you would like to learn more about<br>
Turing Machines, computational complexity (e.g. P, NP, Recursive<br>
Algoritms), and Lambda Calculus, this is the right course for you. You<br>
could use the book "Ivanyos, Rónyai, Szabó: Algoritmusok", it covers<br>
all of the topics mentioned except the part Lambda Calculus, but I<br>
have a good (english) note about it. There were homeworks at each<br>
week, none of them from the unsolvable "Oh my God" kind. There were<br>
two tests, the first one was harder, but the final grades were shaping<br>
pretty well.<br>
<br>
Albebraic and General (or Common?) Combinatorics: This was the one I<br>
liked the least of all. It covers symmetric polynomials, Young<br>
Tableaux (plural form of tableau) [a special king of tool providing a<br>
convenient way to describe the group representations of the symmetric<br>
and general linear groups and to study their properties], Matroid<br>
Theory and Hyper Graphs. The were three lecturers, three tests (not of<br>
the easiest kind). I think in defult of time we just blocked in these<br>
topics.<br>
<br>
Commutative Algebra and Algebraic Geometry: ho-ho-ho, my personal<br>
favourite (and good enough for my MSc Thesis :)). I do not recommend<br>
this for *you* despite it seems paradoxical, but I have a good reason.<br>
It uses and requires lots of algebra that I'm sure you (and everybody)<br>
have not learnt enough yet (and mind that you are studing applied<br>
mathematics). Of course the lecturer tries to stop this gap. So, in<br>
deed, if you are capable to learn 3x more than before, and interested<br>
in a very dynamic and diversified science, (and if and only if this is<br>
the case), then you're welcome to subscribe. For the sake of clarity,<br>
it is still possible to have very good results. By the way, Algebraic<br>
Geometry is concerned with the relationship of Algebra and Geometry<br>
(not surprisingly). It takes a set of polynomials (in fact a radical<br>
ideal in a polynomial ring) and defines geometric objects (in fact<br>
closed sets and hence topology) as the common zero locus (root) of<br>
them. Then it defines maps (in fact polynomial rational maps of some<br>
kind) on geometric objects and morphisms between them, and studies how<br>
they interact. As a goal, it turns out that we can do the whole thing<br>
not only with ideals of a polynomial ring but with any ring endowed<br>
with an identity element. Ok, ok, you may say, but what's the point?<br>
Why is it interesting? Well, if you're interested in cryptography,<br>
elliptic curves are part of this science. For example one may show<br>
that the points of these curves form an additive (abelian) group. Etc.<br>
<br>
Representation Theory: Discover it yourself :). Beside Group Theory,<br>
now I feel I know nothing about math. It covers Group Actions, Lie<br>
Groups, Lie Algebras, and the representation of Lie Algebras. An<br>
algebraic object is just too abstract that no one (not counting the<br>
fanatics of algebra) can deal with it, so after representing it in an<br>
appropriate (handy) structure (like a group of automorphism), one can<br>
deduct more about its behaviour. You could find out more about the<br>
group structure of manifolds (continuous group actions) and the<br>
tangent space at a particular point of them. As before, hardly algebra<br>
(and topology) oriented, but the representation part is easy. I<br>
enjoyed the lessons.<br>
<br>
Differential Geometry and Topology: I think it's not your cup of tea.<br>
Tensor products, sheaves and Cohomology Theory of Vector Bundles of<br>
Differential Forms (in fact only sections of them). If you have not<br>
learnt much topology before, it will be completely strange and<br>
uncomprehending. If you want to learn Algebraic Geometry, it is<br>
useful. Also this is the case if you are interested in differential<br>
forms (e.g. Special Relativity Theory and Maxwell's Equations). Just<br>
to know that your thursday starts with 4 hours of this intensive<br>
lesson (with exercises) is a nightmare, believe me, so I'm not that<br>
shallow to recommend, but If you are still capable, just subscribe and<br>
blow your mind, because it has some really interesting parts.<br>
<br>
That's all folks!<br>
<br>
For further questions please feel free to contact me.<br>
<br>
Wish the best, gruff<br>
<br>
2010/7/18 Viktor Szabó <<a href="mailto:szaboviktor1988@gmail.com">szaboviktor1988@gmail.com</a>>:<br>
<div><div></div><div class="h5">> Sziasztok!<br>
> Egy kérdésem lenne Felétek így a nyár kellős közepén: az alábbi három tárgy<br>
> közül egyet föl kell vennem (mert eddig csak 3 témakörből választottam<br>
> tárgyakat, de 4-ből kell) :<br>
><br>
> Elméleti számítástudomány<br>
> Algebrai és általános kombinatorika<br>
> Kommutatív algebra és algebrai geometria<br>
> Reprezentációelmélet<br>
> Differenciálgeometria és topológia<br>
><br>
> Szerintetek melyiket lenne érdemes, Ti melyiket ajánlanátok leginkább?<br>
> (Nehézség, számonkérés, oktatás érthetősége szempontjából stb.)<br>
> Előre is köszi a segítséget!<br>
> Viktor<br>
</div></div>> _______________________________________________<br>
> Mat06 mailing list<br>
> <a href="mailto:Mat06@lists.math.bme.hu">Mat06@lists.math.bme.hu</a><br>
> <a href="https://lists.math.bme.hu/cgi-bin/mailman/listinfo/mat06" target="_blank">https://lists.math.bme.hu/cgi-bin/mailman/listinfo/mat06</a><br>
><br>
><br>
_______________________________________________<br>
Mat06 mailing list<br>
<a href="mailto:Mat06@lists.math.bme.hu">Mat06@lists.math.bme.hu</a><br>
<a href="https://lists.math.bme.hu/cgi-bin/mailman/listinfo/mat06" target="_blank">https://lists.math.bme.hu/cgi-bin/mailman/listinfo/mat06</a><br>
</blockquote></div><br></div></div>