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marshall
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25 Feb 2012, 6:48 pm

I'm bored.



ruveyn
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25 Feb 2012, 7:03 pm

marshall wrote:
I'm bored.


Poor baby.



Tollorin
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25 Feb 2012, 7:12 pm

No, but I wish I was to understand more advanced stuff in science and physic.


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Fatal-Noogie
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25 Feb 2012, 8:33 pm

I'm not bored, but I need a break...

What do you think is the most inherently frightening branch of mathematics? :chin:

For me, I think maybe systems of non-linear equations,
followed by Laplace and Fourier transformations.
(That's as far as I got in my mechanical engineering training.)


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AstroGeek
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25 Feb 2012, 9:56 pm

I enjoy math, but I prefer physics.



marshall
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25 Feb 2012, 10:16 pm

Fatal-Noogie wrote:
I'm not bored, but I need a break...

What do you think is the most inherently frightening branch of mathematics? :chin:

For me, I think maybe systems of non-linear equations,
followed by Laplace and Fourier transformations.
(That's as far as I got in my mechanical engineering training.)


Differential equations is one of the more ugly branches of mathematics. At least on a rigorous theoretical level. I mean, it's fun looking at numerical solutions to non-linear systems on a computer but actually proving things about non-linear equations is next to impossible.

As for the most frightening, I'd have to vote for tensor calculus. The traditional definitions and notation are abhorrent. If you've had to take a fluid dynamics course you'll understand the horror of being introduced to tensor notation. Tensors simply do not make sense the way fluid dynamics people talk about them in their wretched introductory texts.



dancing_penguin
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26 Feb 2012, 2:14 am

marshall wrote:
Differential equations is one of the more ugly branches of mathematics. At least on a rigorous theoretical level. I mean, it's fun looking at numerical solutions to non-linear systems on a computer but actually proving things about non-linear equations is next to impossible.


Oh, I spent the bulk of my productive time this reading week (ending tomorrow :( ) trying to study differential equations for a mathematical physics course. And yes, it is very hard to read the textbook, which is theory (the book skips a lot of steps, which makes reading the book a sort of puzzle).

I like math much better when there are things to see.


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heavenlyabyss
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26 Feb 2012, 4:48 am

marshall wrote:
Fatal-Noogie wrote:
I'm not bored, but I need a break...

What do you think is the most inherently frightening branch of mathematics? :chin:

For me, I think maybe systems of non-linear equations,
followed by Laplace and Fourier transformations.
(That's as far as I got in my mechanical engineering training.)


Differential equations is one of the more ugly branches of mathematics. At least on a rigorous theoretical level. I mean, it's fun looking at numerical solutions to non-linear systems on a computer but actually proving things about non-linear equations is next to impossible.

As for the most frightening, I'd have to vote for tensor calculus. The traditional definitions and notation are abhorrent. If you've had to take a fluid dynamics course you'll understand the horror of being introduced to tensor notation. Tensors simply do not make sense the way fluid dynamics people talk about them in their wretched introductory texts.


Yes, even Einstein found tensor calculus to be difficult. He even had to ask for assistance with it when he was proving his theory of relativity.
http://isaacmmcphee.suite101.com/the-ma ... ity-a43491



marshall
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26 Feb 2012, 11:26 am

heavenlyabyss wrote:
marshall wrote:
Fatal-Noogie wrote:
I'm not bored, but I need a break...

What do you think is the most inherently frightening branch of mathematics? :chin:

For me, I think maybe systems of non-linear equations,
followed by Laplace and Fourier transformations.
(That's as far as I got in my mechanical engineering training.)


Differential equations is one of the more ugly branches of mathematics. At least on a rigorous theoretical level. I mean, it's fun looking at numerical solutions to non-linear systems on a computer but actually proving things about non-linear equations is next to impossible.

As for the most frightening, I'd have to vote for tensor calculus. The traditional definitions and notation are abhorrent. If you've had to take a fluid dynamics course you'll understand the horror of being introduced to tensor notation. Tensors simply do not make sense the way fluid dynamics people talk about them in their wretched introductory texts.


Yes, even Einstein found tensor calculus to be difficult. He even had to ask for assistance with it when he was proving his theory of relativity.
http://isaacmmcphee.suite101.com/the-ma ... ity-a43491


I bought a book on differential geometry for self-study but haven't found the inspiration to really dive into it. The more modern treatment and notation makes the concepts more precisely defined than they were in Einstein's time but at the same time it adds a lot more work. But you get to see a neat generalization of stuff like "directed surface area elements" to higher dimensional spaces.



ruveyn
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26 Feb 2012, 11:58 am

heavenlyabyss wrote:

Yes, even Einstein found tensor calculus to be difficult. He even had to ask for assistance with it when he was proving his theory of relativity.
http://isaacmmcphee.suite101.com/the-ma ... ity-a43491


Einstein's mathematical friend Besso clued Einstein in on the work of Riemann and Levi-Cevita.

ruveyn



marshall
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04 Mar 2012, 12:04 pm

I guess despite the supposed stereotype there aren't a lot of aspies who love math. Right now I'm trying to self-teach myself axiomatic set theory.



anxiouspoet
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04 Mar 2012, 3:55 pm

marshall wrote:
I guess despite the supposed stereotype there aren't a lot of aspies who love math. Right now I'm trying to self-teach myself axiomatic set theory.


I'm a math senior who just got accepted to a PhD school in pure math. And I guess there are times when me and math are on good terms when we're not having lovers' quarrels.
By "learning axiomatic set theory" do you mean learning ZFC (zermelo-fraenkel set theory with axiom of choice) and learning how to construct basic mathematical objects? That's fascinating stuff the first time you see it. It really helps build philosophical skill and faith in math to judge itself critically.

It can also be mind-bending to really examine those different levels of infinity. Not to mention when you get into constructability of universes, inner model theory, and forcing etc.etc.



marshall
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04 Mar 2012, 8:34 pm

anxiouspoet wrote:
marshall wrote:
I guess despite the supposed stereotype there aren't a lot of aspies who love math. Right now I'm trying to self-teach myself axiomatic set theory.


I'm a math senior who just got accepted to a PhD school in pure math. And I guess there are times when me and math are on good terms when we're not having lovers' quarrels.
By "learning axiomatic set theory" do you mean learning ZFC (zermelo-fraenkel set theory with axiom of choice) and learning how to construct basic mathematical objects? That's fascinating stuff the first time you see it. It really helps build philosophical skill and faith in math to judge itself critically.

It can also be mind-bending to really examine those different levels of infinity. Not to mention when you get into constructability of universes, inner model theory, and forcing etc.etc.

I have an undergraduate degree in math and MS degree in atmospheric dynamics / climate. I've only taken a few graduate level applied math courses that were related to atmospheric science (yucky stuff on PDE's and numerical methods). My interest in foundation math is more a self-study hobby.

I bought a book on ZFC set theory (the original print was from 1960 so it's a little dated) and didn't really like how it developed the axioms in a rather confusing way. I didn't like how the book talked about "proper classes" on an informal/intuitive level without really explaining them logically, other than showing how treating them as ordinary sets leads to various paradoxes. I came up with my own notation to try and work out some problems then when looking on the internet discovered that what I came up with was very similar to single-typed NBG notation where the distinction between sets and proper classes is that sets can be members while proper classes can be subclasses of other proper classes but never members.



Fatal-Noogie
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04 Mar 2012, 8:35 pm

marshall wrote:
I guess despite the supposed stereotype there aren't a lot of aspies who love math.

Huh? Why do you say that? Is it from the responses on this thread?
It might be a little sparse/apathetic here, but I don't think this is a fair sample size.

(For the record, I LOVE math.)


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modustollens
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05 Mar 2012, 12:51 am

I like math, but not the "learning by induction" kind (like DEs). I like understanding math. I am not as advanced as set theory yet.



Reindeer
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05 Mar 2012, 3:45 pm

Well I LOVE physics and I am currently reading physics/mathematics at my college :)
But I am better af physics than just pure mathematics >.>


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