/sci/ - Science & Math

>>5419436
Mhm, set membershit vial \in is natural. I wouldn't dismiss it. But then, as a physicist, I kind of see the mere "existence" of cardinal numbers of all sorts as acciendent of set theory, merely emerging from it's structure. On the other hand, I really how associativity (of function like objects) is implemented in the axioms of a category. This makes me somehow feel that some version of a category-like approach might be well suited for an introduction to higher mathematics.
I also think with investigations model theory*, we are long beyond the level of hyper-abstraction, of which the Kolmogorovs and Arnolds of this world were afraid of.

*I love how algebraic logic
http://en.wikipedia.org/wiki/Algebraic_logic

must really be a hands on subject, given the fact that there is abstract algebraic logic

http://en.wikipedia.org/wiki/Abstract_algebraic_logic


:D

>>4950042
Differential geometry and Roger Moore

I don't care about the money and have a four year full ride. Most exciting, malleable, and satisfying bachelors of science?

You mean the main result of Gödel ((In-)Completesstheorems)?
Or do you want to know something about the foundations of mathematics in general, first order logic and set theory, etc.?

A comathematician is a device for turning cotheorems into ffee.

or

Q: What do you get when you cross a chicken with an elephant?
A: The trivial elephant bundle on a chicken.

or

Q: How do you tell an extroverted mathematican from an introverted one?
A: An extroverted mathematician stares at your shoes when talking to you.

http://www.youtube.com/watch?v=BipvGD-LCjU

>>4388221
Ain't that right, brother.

I'm bored, let's talk about some QFT...

>I can only recommend textbooks because that's what I've used, but here are some suggestions:

>* Gravity: An Introduction To General Relativity by James Hartle is reasonably good as an introduction, although in order to make the content accessible, he does skip over a lot of mathematical detail. For your purposes, you might consider reading the first few chapters just to get the "big picture" if you find other books to be a bit too much at first.
>* A First Course in General Relativity by Bernard Schutz is one that I've heard similar things about, but I haven't read it myself.
>* Spacetime and Geometry: An Introduction to General Relativity by Sean Carroll is one that I've used a bit, and which goes into a slightly higher level of mathematical detail than Hartle. It introduces the basics of differential geometry and uses them to discuss the formulation of tensors, connections, and the metric (and then of course it goes on into the theory itself and applications).

oh, and this

http://en.wikipedia.org/wiki/Swampman

Doing what in Wien?
(Quantum Optics is big, te Statistical Physics team is good)

>>4026216
:D

@topic:
>Society and it's business value real intelligence too lowly
I don't know that seems to be self-comfortless to me. Teamwork is clearly the better, that is more effective, way to achieve scientific breakthroughs most of the time. Now you are maybe above average intelligent and you think this makes you better then clever social people - but if you're honest, then they are "the better people" and your kind of intelligence isn't the relevant thing. Then it's just "fair" that the autistic brainiac gets the goodies. Just as fair as if the opposite was the case. Why should the non-intelligent people suffer, so to speak?

Constructive threads?
On my /sci/?!