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 Posted: Fri Jan 04, 2008 3:25 pm
Yeah, I just thought it would be kewl. I remember the first lecture of my first college analysis class was just "Here's how to construct our common numbers from the natural ones." Since then, I keep noticing how much I take for granted in proofs, and how little the various fields of math can be kept separate.
A logic tree for physics would be easier, if you assume all of the math to be true. A logic tree for any scientific discipline would be similarly awesome.
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Posted: Fri Jan 04, 2008 7:25 pm
Actually, the bottom would look absolutely terrible, since mathematicians are very, very careful to never actually define what a set is. As long as we don't make a tree, we can say that mathematics works; once we make the tree then the lack of a foundation becomes a bit obvious.
But yeah, the construction of numbers is really awesome. I'm almost done introducing my batch of 9th graders to the p-adic numbers.
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Posted: Tue Jan 08, 2008 1:41 am
Today I was accused of being too intellectual. Naturally, I tore the person apart (verbally).
That was fun, but in retrospect maybe I should have thought it through a bit more. Upon rereading the post, I found a couple typos that really shouldn't be there.
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Posted: Tue Jan 08, 2008 5:51 am
Heh, typos in my posts stay where they are, as most of my posts are done with a Wii remote and it takes 3 hours to actually submit anything.
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Posted: Thu Jan 10, 2008 11:05 pm
Layra-chan Actually, the bottom would look absolutely terrible, since mathematicians are very, very careful to never actually define what a set is. As long as we don't make a tree, we can say that mathematics works; once we make the tree then the lack of a foundation becomes a bit obvious. I find when i try to explain this to most people, they get rather upset. The worst part is when i try to explain it to a math teacher, as it seems few math teachers actually understand math. (I would be interested to see someone attempt to make such a diagram incorporating non-standard analysis.)
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Posted: Fri Jan 11, 2008 7:49 am
I have the complete Hilbert program tucked away in my desk. I'll let you see it for 1,000,000,000 gold.
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Posted: Sat Jan 19, 2008 12:18 pm
Whoo! I'm done with finals! Now for a week of waiting for my girlfriend to finish finals, followed by a week of nothing.
Curse you, Elias Stein. Curse you and your making the complex-analysis-for-math-majors class half analytic number theory. Curse you for making "Prove the prime number theorem" one of the questions on a 2-hour final.
The other question that ticked me off was:
Let f be holomorphic in the upper-half plane. Prove that if
1) f(z+2) = f(z)
2) f (-1/z) = f(z) and
3) f is bounded
then f is constant. Deduce the four-squares theorem.
Whatever. It's over, and I'll never half to look at analytic number theory again. On to real analysis and more geometry!
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Posted: Sun Jan 20, 2008 7:33 pm
Bleargh Maths.
For my masters the head of department said I need to learn a bunch of undergrad modules or I'll "flounder". Trying to absorb the latter half of an undergrad maths degree in a couple of months is not fun. Induced Homomorphisms and simplicial complexes are not as riveting as they sound.
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Posted: Tue Jan 22, 2008 8:04 am
Morberticus Bleargh Maths. For my masters the head of department said I need to learn a bunch of undergrad modules or I'll "flounder". Trying to absorb the latter half of an undergrad maths degree in a couple of months is not fun. Induced Homomorphisms and simplicial complexes are not as riveting as they sound. Yeah, algebraic topology can be kinda boring sometimes. It's all just diagram chasing anyway. [EDIT] Algebraic topology is also a lot of nonsense. Abstract nonsense, but nonsense nonetheless. As far as I can tell, it's a study in how non-intuitive a representation you can make for a sphere. I hate simplicial sets.
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Posted: Mon Feb 25, 2008 8:39 pm
My trap has caught no flies. I think I just wasted 20,000 gold. Quote: [EDIT] Algebraic topology is also a lot of nonsense. Abstract nonsense, but nonsense nonetheless. As far as I can tell, it's a study in how non-intuitive a representation you can make for a sphere. I hate simplicial sets. Yeah I'm not a fan. Only learning about it for some functional analysis course.
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Posted: Thu Feb 28, 2008 11:18 am
I hate real analysis. I want to kill it with a hammer.
It's just that the grader is so harsh. The class average on this last problem set was less than half. The sets are ridiculously hard, too. The last one took me over 30 hours, only to get 14/30.
Kill with a hammer.
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Posted: Thu Feb 28, 2008 11:11 pm
Is it just me, or is pointless geometry awesome, in both the colloquial and the formal sense?
Oh god, my head hurts.
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Posted: Sat Mar 01, 2008 1:53 pm
Layra-chan Is it just me, or is pointless geometry awesome, in both the colloquial and the formal sense? Oh god, my head hurts. Praytell, how does one construct a pointless geometry?
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Posted: Mon Mar 03, 2008 11:35 pm
Swordmaster Dragon Layra-chan Is it just me, or is pointless geometry awesome, in both the colloquial and the formal sense? Oh god, my head hurts. Praytell, how does one construct a pointless geometry? Instead of dealing with points as the basic object, one considers regions, with an idea of inclusion (making the regions a partially ordered set) to link the sets together; alternatively, one can use the idea of connection (not the diff. geom connection) instead of inclusion, in that two regions are connected if they have a subregion in common. It's closely related to pointless topology, which is topology without the notion of point; instead it just looks at the lattice generated by union and intersection of open sets. Both of them are terribly strange, although neither are as strange as their underlying ontological foundation, mereology.
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Posted: Thu Mar 06, 2008 9:23 am
I guess this is pseudo-random, so I will post it here. Layra, what do you think are the best entry-level books in these fields?
Real analysis
Point-set topology
Algebraic topology
(Less entry-level) Lie groups and Lie algebras
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