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rpg16
rpg16
3:50 AM
yes muad... shoot
:)
only 9 hours later :D
 
 
3 hours later…
Casebash
Casebash
6:45 AM
I wonder if this chat feature will ever take off. Whenever I check out a room, it is almost empty
 
 
1 hour later…
Rahul Narain
Rahul Narain
8:03 AM
@KennyTM It would be nice if we could, though. I hear the MathOverflow mods have made good use of that ability. And at some point Jin is going to get busy making the designs for the other Area 51 sites...
@Chandru1 If the font you're seeing is really that bad, it might be an issue with the particular fonts you have installed on your system. Could you post a screenshot of what the font looks like at your end?
 
KennyTM
KennyTM
@RahulNarain yeah, but SE 1.0 and 2.0's admin structure are fundamentally different.
 
 
1 hour later…
giddy
giddy
9:23 AM
heylo
@Casebash hmm some other SO rooms are quiet too, but the SO tavern always has someone there. Maybe it will take off in time! =)
 
 
4 hours later…
Sachindra
Sachindra
1:00 PM
hey ppl...
is there any way to manually find out whether a number (large enough) is a prime number?
 
J. M.
J. M.
1:15 PM
manually?! apart from trial division, I don't see how.
 
 
1 hour later…
Stefan
Stefan
2:30 PM
hey people
does the mats SE cover stats? such as probability distributions?
hey people
 
J. M.
J. M.
@Stefan: stats.stackexchange.com
 
Stefan
Stefan
shot guy :) its really about how to use the scientific calculator ? u think stats wil accept that?
or anybody else?
i need to calculate the variance of a discrete prob distribution fast, using the stats mode in my scientific calc.
 
J. M.
J. M.
you do not have a manual?!
in any event, I don't think it'd be appropriate for that site either.
 
Stefan
Stefan
well... its tricky.. calculator's manual only covers the basics... and i can't find any buttons that will do it for me
the sum is something like SUM[ ( x - mean )P(X) ]
 
J. M.
J. M.
what particular distribution is this, and what calculator?
 
Stefan
Stefan
2:41 PM
discrete probabilty distribution
and is a SHARP calculator ( standard high school scientific calc )
I can get the mean with SUM[ xy ]
 
J. M.
J. M.
there are a number of discrete probability distributions... maybe you need to look at your textbook for the formulae
 
Stefan
Stefan
i have the formula... and i can do it with a pen and paper. but im writing exam in two days. I'd like to do it on my calculator... will make things really fast
anyway thanks @JM
 
 
1 hour later…
Jonas T
Jonas T
4:05 PM
A chat!
Oh, no users :D.
 
Stefan
Stefan
@jonasT hey guy
 
muad
muad
4:27 PM
 
SkypeMeSM
SkypeMeSM
4:40 PM
Hello
 
muad
muad
hi
 
SkypeMeSM
SkypeMeSM
hi muad are you familiar with convex optimization?
 
muad
muad
SkypeMe, No, I don't know anything about that
 
SkypeMeSM
SkypeMeSM
ok. how about joint and marginal probability distributions?
 
muad
muad
also do not know probability theory
 
SkypeMeSM
SkypeMeSM
4:52 PM
:) ok. never mind then.
 
muad
muad
Why are you interested in these things?
 
Jonas T
Jonas T
5:10 PM
Heh.
Those things are fun!
 
Chandru1
Chandru1
@RahulNarain Dear Rahul, how do i take the screen shots!
@Rahul,Kenny TM: This is how it looks :x)
@Rahul: I would like this to be changed as soon as possible. What are your views on the font. I liked the one which was in the beta
 
Chandru1
Chandru1
5:33 PM
@Rahul: I use google chrome. as my browser
 
Rahul Narain
Rahul Narain
5:44 PM
@Chandru1, that looks like a nice font to me. Sorry, but I can't agree with you. However, since this is a subjective issue that matters a lot to you, I can write a user script you can install on your browser that will change the fonts to sans-serif.
What version of Chrome are you using? Also, it looks like you're on Linux, is that correct?
 
Chandru1
Chandru1
@Rahul: Yes i am using linux fedora and latest version of chrome
thanks a lot rahul
Please write a script so that the fonts are like the one in the beta stage.!
Wait i shall check the version and tell u
google chrome 7.0.517.41
@Rahul: Eagerly awaiting your response!!!!!!!!!!!!
 
KennyTM
KennyTM
6:05 PM
@Chandru1 have you installed the font "Georgia"?
 
Chandru1
Chandru1
Yes, its already installed
 
Rahul Narain
Rahul Narain
6:26 PM
@Chandru1: If you have Georgia installed you shouldn't be seeing that font! It's probably not installed properly; can you check? I'll whip up the user script anyway some time today or tomorrow when I have time -- please don't await it so eagerly! :)
 
Chandru1
Chandru1
@Rahul: Yes rahul! its not installed.
@Rahul: I was under the impression that its a default font! which comes
So how to install it
@Rahul: For the user script: OK, take your time!
@Rahul: Now its even worse after installing georgia. Anyhow write the script and inform me
 
giddy
giddy
6:48 PM
hello!
anyone there
 
KennyTM
KennyTM
7:11 PM
@Chandru1 That can't be right. Are you installing the correct Georgia font?
 
Chandru1
Chandru1
@Kenny TM: Yes, its looking fine now. the thing is i forgot to install Georgia bold font. Once i installed it everything is fine.
 
KennyTM
KennyTM
@Chandru1 ok.
 
Chandru1
Chandru1
@Kenny TM: The MATH.SE site is looking much better now. phew...
@Kenny TM: I don't understand why JIn is doing things which are not needed. The upvote symbol which used to be one triangle up was far better, the 2 triangles isn't looking good!
 
KennyTM
KennyTM
@Chandru1 the old themes are for beta sites only. you should have voiced out earlier if you find the arrows don't look good. (i think it's fine.)
 
Chandru1
Chandru1
7:30 PM
@Kenny TM: What i am saying is, this site had that single arrow when it launched. the double arrow is not looking good! See as a visitor i am making a request, thats all. Its all upto you now.
 
muad
muad
8:19 PM
hi giddy
Hi Weltschmerz
 
Weltschmerz
Weltschmerz
Hey.
 
muad
muad
That's interesting, that you switched from physics to mathematics
I read on your profile
 
Weltschmerz
Weltschmerz
Yeah. Physics seemed too constrained for me.
 
muad
muad
what mathematics are you currently interested in?
have you ever had classes called applied mathematics? I've wondered what the difference is between applied mathematics and physics
 
Weltschmerz
Weltschmerz
Hm, what mathematics... I don't know, I'm learning the basics. I like everything.
 
muad
muad
8:30 PM
cool :)
 
Weltschmerz
Weltschmerz
I suppose that applied math is different from physics in that the arguments are based more on math itself. I mean, it's still math. Whereas with physics it's a different line of reasoning.
Also physicists tend to be very sloppy in their math and I found that very annoying.
 
muad
muad
Weltschmerz, it's not very rigorous as a mathematics undergrad
 
crasic
crasic
physics isn't applied math for the same reason that theoretical physics isn't pure math
You're end goal is to produce a repeatable prediction or explanation of an observable phenomena, Yes you typically use math as your primary tool to achieve that goal.
 
muad
muad
crasic, that is a nice way to put it
 
Weltschmerz
Weltschmerz
Yes. In mathematics you're not bound by that.
 
crasic
crasic
8:36 PM
Your*, Essentially, the focus of your work, for the most part isnt the math itself. It would be like calling demography a sub-branch of statistics
There are subfields that muddy the waters, string theory for one.
 
Weltschmerz
Weltschmerz
Well, string theory hasn't made any experimental predictions yet. It works above the physical theories that do make predictions.
 
crasic
crasic
Its something in between, they are to impractical to be fully accepted into physics, and too sloppy to be in the math department
 
Weltschmerz
Weltschmerz
So I'd say string theory is, for one, a lot like mathematics. I don't know anything about it, anyway, so this may be bullshit.
 
muad
muad
I think you must be an expert in quantum mechanics to do string theory
 
crasic
crasic
And group theory
 
Weltschmerz
Weltschmerz
8:39 PM
And a lot of other stuff, I hear.
 
crasic
crasic
In any case, as a physics major I can attest to sloppy math
Which is why I'm doubling in math, so that I can force some rigor into my life
 
robinhoode
robinhoode
Since the room has turn to this topic, I had a question that was on my mind a while back but never bothered to ask: Suppose I wanted to skip the silly intro physics text books and get into some semi-serious / intermediate physics. What math plus what physics books would get me there?
 
crasic
crasic
Depends on where you want to start
 
Weltschmerz
Weltschmerz
Good thing you can double. Over here you have to start all over from scratch. They don't even validate your old math courses.
 
robinhoode
robinhoode
The lack of preciseness in my intro course annoyed me really, really badly.
 
crasic
crasic
8:42 PM
There are plenty of good Classical mechanics books, that ignore newton and force diagrams completely
 
Weltschmerz
Weltschmerz
Good question, robinhoode.
 
robinhoode
robinhoode
Every fact about the real world was left to my intuition. Made me want to puke
 
Weltschmerz
Weltschmerz
Look up Arnold's book on mechanics.
MAthematical methods of mechanics, or something like that, is the title.
 
crasic
crasic
I would advice against jumping into more advanced topics like QM
 
muad
muad
robinhood, lol
 
crasic
crasic
8:42 PM
Not because they are mathematically difficult
But its hard to appreciate the results without the intutition of a classical system
 
robinhoode
robinhoode
@crasic Understandable
 
Weltschmerz
Weltschmerz
As for QM, if you know some functional analysis, you can understand it very well.
 
Jonas T
Jonas T
Landau has a nice little book ab out mechanics too.
 
crasic
crasic
It would be like taking abstract algebra and never learning how to factor polynomials
 
muad
muad
@robinhood: Since you have programming skill you should also look at this book: mitpress.mit.edu/sicm
 
crasic
crasic
8:43 PM
Landau is...
Wel...
He is a good reference
not a great textbook
 
robinhoode
robinhoode
@muad Yeah, I saw that book but wasn't ready at the time. Perhaps now or very soon
 
Weltschmerz
Weltschmerz
crasic, or it could be that it's even better to be introduced to QM right away. It's not so hard for a mathematician to accept that there are only probability densities associated with the positions of particles in space.
 
muad
muad
robinhood, there is one difficult piece of mathematics
 
crasic
crasic
The point is, if you have no idea what angular momentum means in the physical sense
 
Weltschmerz
Weltschmerz
Landau's textbooks are very good for theoretical physicists but the arguments that involve mathematics are very sloppy and heuristic.
 
crasic
crasic
8:45 PM
How can you begin to internalize the quantized version of it
 
muad
muad
robinhood, but if you know any functional programming you will understand it better than a mathematician
 
crasic
crasic
Or even spin for that matter
 
Weltschmerz
Weltschmerz
crasic, that's my point. It's like studying metric spaces before topology. Do you really need them? You'd be stuck imagining open sets as balls for the rest of your life.
 
robinhoode
robinhoode
@muad I boil a lot of mathematics down to functions and objects. I don't know if that's a good or a bad thing. Just what I do.
 
Chandru1
Chandru1
@All: Good night everyone, its 2 A.M in India, and i am feeling tired!
 
muad
muad
8:46 PM
bye Chandru
 
Weltschmerz
Weltschmerz
Same thing for classical vs. quantum mechanics. I don't know, it's a thing of personal taste I suppose, but I'd much rather be introduce to QM concepts first.
 
crasic
crasic
I disagree
but I'm in physics
so I may be biased
 
Chandru1
Chandru1
@Muad: Bye!!!!!!!!!!
 
muad
muad
@robinhood, I am talking about the "action" - which is a functional. The mathematician is too shy to write (A -> B) -> C but that's what it is.
 
Weltschmerz
Weltschmerz
crasic, because actually the spin of a particle has nothing to do with it spinning, I'd say just go straight to the mathematics of it.
 
crasic
crasic
8:47 PM
Because in the end, you are not dealing with abstract mathematical concepts, but with a physical system, and the lack of physical intutition may hinder you in understanding or exploiting that system experimentally
 
Weltschmerz
Weltschmerz
again, I'm just answering the question about how a mathematician should be introduced to physics, not how a physicists must approach QM.
 
crasic
crasic
Of course it isn't spinning, but spin behaves like angular momentum
 
Weltschmerz
Weltschmerz
You're right there, crasic.
 
muad
muad
Weltschm, metric spaces are basically nice topologies
 
crasic
crasic
Which is why the picture is a useful one
 
Weltschmerz
Weltschmerz
8:48 PM
That's why I'm clarifying, what the question was.
 
crasic
crasic
Then yes, I would say you are right
If a mathematician wants to learn what we are all about, and bang his head repeatedly over the sloppiness of the math, go straight to QM
 
muad
muad
I am reading Dirac - Principles of Quantum Mechanics
 
crasic
crasic
At least classical mechanics is fairly rigorous in terms of classical (newtonian) analysis.
 
Rahul Narain
Rahul Narain
@Chandru1, looks like you're satisfied with the look of the site now. Phew, less work for me! :)
 
muad
muad
crasic, I am a big of nonstandard analysis in physics
 
Weltschmerz
Weltschmerz
8:50 PM
I remember studying QM, I came across a couple of good sources that actually cared to explain in detail the bridge that can be built between the two languages - physical (Dirac's brackets) and mathematical (L^p spaces and so on) - of QM.
 
muad
muad
a lot of "plausible" arguments become mathematical derivations
 
crasic
crasic
Sakurai?
 
Weltschmerz
Weltschmerz
nop. Zeidler, applied functional analysis.
 
muad
muad
Weltschmerz, as far as I can tell - the hilbert space is (a,b) and the Dirac is <b|a>
 
crasic
crasic
Its a grad textbook, but it jumps straight into the vector space picture
 
muad
muad
8:51 PM
not a really hard connection to make :p
 
Weltschmerz
Weltschmerz
There's a book by a Russian mathematician, Fadeev, titled "Quantum Mechanics for mathematics students". I don't think it's been translated, though.
 
Jonas T
Jonas T
Don't read Conway.
 
crasic
crasic
Some of the later developments of classical mechanics become to eerily approach QM. Like Hamiltonian mechanics and then, more recently analysis of stochastic systems
 
Jonas T
Jonas T
There is also an AMS book about QM.
amazon.com/… this one
 
muad
muad
what is analysis of stochastic systems?
 
Jonas T
Jonas T
8:53 PM
Stochastic analysis? No, it is about SDEs and SPDEs.
 
crasic
crasic
Its a classical non-deterministic system
 
Weltschmerz
Weltschmerz
crasic, like not the initial conditions of the system are given, but probability densities for them?
(it's the only way I can imagine a non-deterministic classical system)
 
muad
muad
Wiener process
In mathematics, the Wiener process is a continuous-time stochastic process named in honor of Norbert Wiener. It is often called Brownian motion, after Robert Brown. It is one of the best known Lévy processes (càdlàg stochastic processes with stationary independent increments) and occurs frequently in pure and applied mathematics, economics and physics. The Wiener process plays an important role both in pure and applied mathematics. In pure mathematics, the Wiener process gave rise to the study of continuous time martingales. It is a key process in terms of which more complicated stochas...
I read about this in Norbert Wieners biography - he was able to prove some of the conjectures about idealized brownian motion using Lebesgue integral theory
One of them being that it is a non differentiable curve (a.e.) - and it says that you need a different type of calculus to do differential equations with this type of curve involved for that reason
What does this apply to? kinetics of gases?
 
Jonas T
Jonas T
The theorem?
In SDEs you integrate wrt brownian motion.
 
crasic
crasic
Weltschmerz, No, even knowing the initial conditions doesn't give you a predictable outcome.
 
Weltschmerz
Weltschmerz
9:08 PM
Why, crasic?
 
crasic
crasic
The crazy thing is that you would think that maybe there are hundreds of IC's, but there have been physical stochastic processes that have a handful (3 or 4) initial conditions and still don't behave deterministically, and they are classical interactions
 
muad
muad
what physical processes do these SDE and SPDE come up naturally?
 
crasic
crasic
Why? Thats the reason the field exists. I'm not to knowledgable about it. Jonas seems to know something about stochastic analysis and maybe can answer better.
@ muad Brownian motion is the simplest one
or at least, a simple one
 
Weltschmerz
Weltschmerz
No uniqueness theorems there?
 
muad
muad
I tried to read Eiensteins paper on the derivation of the size of the atom but I could not follow it X)
he is using Brownian motion
 
robinhoode
robinhoode
9:18 PM
Has anyone tried typing up math notes, with lots of Latex equation, and putting them up online? Is there any good software for that? I know there is Latex to HTML, but wondering if there was something web-based, perhaps, so I could maintain it while on campus or at home.
 
crasic
crasic
There is a google docs project that allows for live tex collaboration
 
muad
muad
robinhoode, jsMath and LaTeXMathML are adequate.
 
crasic
crasic
Here is the link docs.latexlab.org
 
robinhoode
robinhoode
@crasic I believe that's still in beta, though..
@muad I think I might go with jsMath & Drupal.. Seems like the least maintenance for what I'm after
 
Jonas T
Jonas T
Why not MathJax?
 
crasic
crasic
9:25 PM
Well, its a google doc and its open beta, your files won't be lost, but it might not render correct all the time.
 
Weltschmerz
Weltschmerz
hey guys, see you later.
 
muad
muad
bye Weltschm
 
robinhoode
robinhoode
@JonasT What's the difference?
 
muad
muad
yes MathJax is like a new version of jsMath
 
Jonas T
Jonas T
It looks more advanced to me (and newer)
 
muad
muad
9:26 PM
it's better to use MathJax
 
robinhoode
robinhoode
Nice, thanks guys.
 
crasic
crasic
Personally I use svn and then just publish pdf's
 
muad
muad
I write all my notes on paper :P
 
robinhoode
robinhoode
@crasic Yeah.. this is really just for my own benefit, but I figure I want to let Google index them like regular pages so someone might get some use out of them. Not sure
 
crasic
crasic
Oh notes? yeah
My algebra prof doesnt have a textbook
He writes up notes every week and hands them out to us
 
robinhoode
robinhoode
9:30 PM
@muad Paper notes are not searchable :P
 
crasic
crasic
then proceeds to lecture directly, from them.
Not true! livescribe.com
It was annoying at first, but now I appreciate having his whole lecture on a piece of paper that I can follow
 
muad
muad
$$ \sqrt[3]{2} $$ - looks like we don't have LaTeX in here
 
crasic
crasic
$\latex$
yep
 
muad
muad
:(
 
crasic
crasic
Speaking of Euler
Anyone partake in project euler?
 
muad
muad
9:37 PM
I played it a few years ago but didn't do very well
 
crasic
crasic
There is a guy on there that does every problem in x86 assembly
Personally, that seems excessive, but it forces him to come up with algorithms that don't rely on big libraries.
 
muad
muad
yes there are some really interesting characters there
 
Jonas T
Jonas T
Hmm, what problems did that guy solve in asm?
I want to check them.
 
crasic
crasic
Almost all of them
I haven't gotten too far, but definately the ones on the first page
And then the random ones I did later also had him use asm if I recal
 
Jonas T
Jonas T
Heh.
 
robinhoode
robinhoode
9:47 PM
So what do you guys do to pay the rent? Or are you in school?
 
crasic
crasic
I'm in school :D
 
robinhoode
robinhoode
I do web software for a small company in NYC.
 
crasic
crasic
I work in a lab on campus, but that pretty much just pays for groceries
It's not the money I tell myself, its the papers!
 
robinhoode
robinhoode
I'm not too thrilled with it.. Thinking about breaking into actuarial science / statistics.
 
crasic
crasic
Sounds perfectly intolerable :D
I don't have the mindset to be an actuary
 
robinhoode
robinhoode
9:50 PM
Neither do I. But I need a back up plan if I can't get into grad school.
 
crasic
crasic
I just read this gem for "counter-examples to relativity"
Minkowski space is predicated on the idea of four-dimensional vectors of which one component is time. However, one of the properties of a vector space is that every vector have an inverse. Time cannot be a vector because it has no inverse.
Where are you going to school now?
 
robinhoode
robinhoode
I'm at a liberal arts school in Philadelphia. I'm trying to transfer to the local technical college but no luck so far. Will probably have to try again in January.
 
muad
muad
Whoever wrote that probably doesn't care about Clifford algebras
 
crasic
crasic
I don't think they care much about anything
counterexample #9 is : The action-at-a-distance by Jesus, described in John 4:46-54.
2
 
robinhoode
robinhoode
Omg.. that's hilarious
 
crasic
crasic
9:54 PM
@robinhoode don't worry about it. There is a grad student in my lab that dropped out of HS to get a GED then went to a liberal arts school in S.C. and now is a grad student at UC Berkeley
The sad thing is that the person who wrote the article wrote it because somebody at some point told him that moral relativism is related to relativity
He has no trouble with QM, but disproving relativity is a means to disprove liberal pseud-science
 
muad
muad
crasic, that was a huge concern when Einstein first developed his theory
 
crasic
crasic
moral relativism?
Its like saying that science and pseudo science are related because they both have science in the name
#32 is the barn and ladder paradox
Apparently the person who wrote it had enough time to read about the paradox, but not about its resolution.
In any case
Americans are funny funny people
 
muad
muad
"Prior to relativity, philosophers such as Aristotle, Kant, and Mill argued that there was an absolute truth and an absolute way of approaching various aspects of life" - scienceinsociety.northwestern.edu/content/articles/2008/…
"However, now armed with relativity, facts are no longer absolute, but instead dependent upon your viewpoint, your own "philosophical" inertial reference frame"
 
crasic
crasic
Philosophers can say whatever they want, the point is that moral relativism should not reflect on the hard science behind relativity
 
muad
muad
Obviously Newton developed his theory of physics in line with the Christian philosophy of "Do unto others as you wish they do unto you" in mind
LOL
 
crasic
crasic
10:03 PM
In any case, i find it surreal that as scientist and mathematicians sit and ponder the universe, there are people out there who fight over our conclusions about the world
 
muad
muad
Newtons 3rd law "The mutual forces of action and reaction between two bodies are equal, opposite and collinear"
 
Jonas T
Jonas T
Uh, those counterexamples are on conservapedia?
Is that a serious site?
 
crasic
crasic
Yes
In the sense that those people believe what they say
Look at the comments
Read the relativity page and read the talk page
 
Jonas T
Jonas T
Damn.
 
crasic
crasic
Yep
 
muad
muad
10:13 PM
"After Albert Einstein came up with the theory of relativity people in the social sciences such as the German sociologist Max Weber, again applied the concept of relativity to concepts such as morality. Thus appeared the concept of moral relativism in which morality simply becomes what a particular society believes is moral." - mypracticalphilosophy.com/shelp/moralrel.htm
 
crasic
crasic
10:29 PM
I just realized that 6 months worth of an algebra course is contained in 2 chapters of Cohn
 
muad
muad
what algebra are you doing?
 
crasic
crasic
Abstract, in the american sense
So groups+rings+fields
We did vector spaces last semmester
 
muad
muad
you can teach yourself Galois theory
it is great fun
 
crasic
crasic
I'll look into it
Group theory is great fun
Especially from the physics stand point
 
muad
muad
I don't know any applications of group theory in physics
 
crasic
crasic
10:35 PM
Particle physics is a study in representation theory
Spin 1/2 is SU2 symmetry of a particle
 
muad
muad
well I suppose Lie groups in the classical mechanics, Noethers theorem
 
crasic
crasic
Its less, the abstract results of group theory, and more practical applications and representations
For example, nutty result
Take the pauli spin matrices (representation of SU2)
multiply by i
and you get the generator for the quaternions (and also the group of unitary quaternions)
 
muad
muad
that sounds a lot like the quantum logic gates
 
Jonas T
Jonas T
11:12 PM
Why are there so little nice analysis questions on math.se?
 
J. M.
J. M.
11:22 PM
and too many number theory ones. :)
 
Jonas T
Jonas T
Yeah.
 
J. M.
J. M.
I don't think I've ever seen a day where the front page didn't have at least two number theory questions.
which leads me to my conjecture: with the current setup of m.se, getting high rep requires above average competency in number theory
and it is of note that a number of highly-rated answers are answers to number theory questions
Personally, I'm not complaining, but it sure is funny.
 
Jonas T
Jonas T
Yes! How is that possible?
Are there that many number theorists or that many number theorists on the internet... Or maybe it is a hard subject.
But then again, some analysis subjects are hard as well.
 
J. M.
J. M.
Well definitely it is not a question of difficulty
and "hard" is an understatement, I'd use "intricate" :D
 
Jonas T
Jonas T
Hmm, yes.
 
muad
muad
11:36 PM
I would post analysis questions regarding fractals but I couldn't even get started -_-
 
J. M.
J. M.
Yeah, sometimes the difficulty in asking questions is in choosing the right words to use.
on second thought, I suppose that applies to answers too.
 
muad
muad
I meant more that I couldn't even get into the basic books on it
 
crasic
crasic
I think the reason number theory is popular on the internet is because its tenable even to the non-professional mathematician
It's studying properties of a natural number system, even amateurs can come up with fairly deep observations.
 
muad
muad
one thing I wonder about number theory is how do you solve a new equation?
 
crasic
crasic
what do you mean?
 
J. M.
J. M.
11:50 PM
but first you have to come up with the equation...
 
muad
muad
it seems like any equation I can solve, say congruences or pell or whatever.. it's been done to death - and the equations nobody solved are way too difficult for me
 
J. M.
J. M.
in any event, solving Diophantines in general is hard.
At least for me, it isn't obvious that you can use a CF to solve Pell.
that things are neat and easy with CFs is an "after the fact" observation.
"I think the reason number theory is popular on the internet is because its tenable even to the non-professional mathematician" - so is geometry, but surprisingly enough, you don't see that much geometry questions. :)
 
crasic
crasic
CF?
 
J. M.
J. M.
continued fractions
 
crasic
crasic
right
I suspected as much
 
muad
muad
11:55 PM
crasic, the idea is that - to solve x^2 - 2y^2 = 1, well you find a good approximation x/y to sqrt(2)
if x/y is close to sqrt(2) then sometimes we might have x^2 = 1 + 2 y^2
what's really cool is that Baker used the same idea on the cubic version to bound integer solutions of a cubic
I just read about that thing recently so I am still thinking how neat it is
 
crasic
crasic
Not a big fan of Number theory
I'm taking a class on it right now.
 
J. M.
J. M.
when I read about that sort of thing, I wonder more about what s/he saw that made him/her come up with it.
 
crasic
crasic
I think algebra is by far my most enjoyed subject covered in math.
Its abstract, and not as computationaly daunting as geometry or analysis
 
muad
muad
J. M. - yes I get far too distracted with that when I read Gauss
 
J. M.
J. M.
eh, Gauss is weird in so many ways. :D
 
crasic
crasic
11:59 PM
Thanks for the Euler translations BTW, great stuff
 

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