Math thread! Come in and have some pi...

[Muckle_Ewe]

Instructions...


Download this add-on for firefox.

Latex Composer
https://addons.mozilla.org/en-US/firefox/addon/4082/

For the unaware, Latex is a universally used typesetting software for maths documents.



Now look at the very bottom right of your browser.
Should be a small round symbol thing like this ---> .
Clicking this brings up the compiler.

Now you can enter code that produces math output.



Now posting the code here won't convert it into math output since this site doesn't have Latex installed but...
If you just copy and paste the code here, others can again copy and paste it into the compiler to see your formulas and what not.

So folks... Whats your maths experience? Area of interest etc!

For me,

Dynamical system, methods of integration, asymptotic methods and maths biology are my areas of interest. Just graduated 2 weeks ago. Feels good man... Going for a masters now as well.

\Gamma(z) = \int_0^\infty t^{z-1} e^{-t}\,dt

[moosecakes4all]

Biological math? Sounds interesting mayne! Aware me.
Just finished Calc 1 last semester with an A, going into calc 2 this fall. Really enjoyed it.

[Muckle_Ewe]

Biological math? Sounds interesting mayne! Aware me.
Just finished Calc 1 last semester with an A, going into calc 2 this fall. Really enjoyed it.

Being from UK I'm not quite sure what Calc 1 and 2 are... Perhaps an example of what's in it?

As for maths biology...

It's basically a combination of dynamical systems and differentiation.

I wouldn't have thought you would have covered dynamical systems yet but...

From wiki

The dynamical system concept is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ******t space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each spring in a lake.


So basically how stuff changes as parameters change.

Like populations. And you find limiting populations, where any more people/things introduced into the environment will cause them to die out due to resources etc.


Stuff like that!

[moosecakes4all]

Ahh, i see, i see. Totally different than what i thought it would be lol.
Calc 1 and 2 are just basically single variable calculus.

[Muckle_Ewe]

Ahh, i see, i see. Totally different than what i thought it would be lol.
Calc 1 and 2 are just basically single variable calculus.

Bump before I sleep...


I need to start properly looking at multivariable calc. Solid at single var but never really gave multi a thought. Greens theorem and what not...

Ah well...

Gonna start looking at some n-body stuff when I get up tomorrow.

[Muckle_Ewe]

hello all. took calc 1 but never learned partial derivative needed in my advance econ class...


lets say I want to take the partial derivative of 15y + Sqrt(x)

with respect to X... would I get 7.5x^-1/2

and then with respect to Y... 15y + ? ughhh confused

Treat the y as a constant when you partial diff with respect to x and vice versa.

So for x it would be 1/2x^-1/2

For y it would be 15.

I literally just said I'm not great at multiple calc but I think that's right.

[turkey_server]

masters in pure math. working on my phd dissertation in geometric topology now.

[Spaghettii]

hmm i like where this is going

[Alephz]

hello all. took calc 1 but never learned partial derivative needed in my advance econ class...


lets say I want to take the partial derivative of 15y + Sqrt(x)

with respect to X... would I get 7.5x^-1/2

and then with respect to Y... 15y + ? ughhh confused

The fundamental idea of partial derivatives is any function which isn't being partially derived is treated as a constant.

eg, supposed a function such as

f(x) + f(¬x) --- (¬x == not x).

the partial derivative treats f(¬x) as a constant, so, the partial derivative of the function becomes

f'(x)

remember the derivative of any constant is 0.

So going back to your question, observe that your function has two parts

15y = f(y)
sqrt(x) = x^1/2 = f(x)

so the partial derivative d/dx of 15y + sqrt(x) = d/dx f(y) + f(x) = f'(x) = 1/2 x ^(-1/2)

[Muckle_Ewe]

masters in pure math. working on my phd dissertation in geometric topology now.

Christ I hate topology, and pretty much all pure math to be honest, except number theory. What exactly is your diss on? Is geo top the title of it or is a specific part of that?

[wingman11]

Being from UK I'm not quite sure what Calc 1 and 2 are... Perhaps an example of what's in it?

As for maths biology...

It's basically a combination of dynamical systems and differentiation.

I wouldn't have thought you would have covered dynamical systems yet but...

From wiki

The dynamical system concept is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ******t space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each spring in a lake.


So basically how stuff changes as parameters change.

Like populations. And you find limiting populations, where any more people/things introduced into the environment will cause them to die out due to resources etc.


Stuff like that!

calc 1 is differential, calc 2 is integral

[turkey_server]

Christ I hate topology, and pretty much all pure math to be honest, except number theory. What exactly is your diss on? Is geo top the title of it or is a specific part of that?

geometric topology is a pretty big field. i'm still 2 years away, so right now i just read a lot of literature (there's no textbooks at this point... just papers) to try and learn the material. focusing primarily on coxeter systems, mostly just because that's what my major advisor is interested in, lol.

[Muckle_Ewe]

Could someone show me, step by step, taking the partial derivative of the Cobb-Douglass function? Need to learn it for econ..

Y = AK^a L^1-a

a = alpha.

With respect to K, and then respect to L.

I know what the derived functions should look like, but can't figure out the steps. How do you take a partial derivative when there is not an actual number involved, like alpha, above?

When differentiating with respect to K here (for example), treat everything else as a constant.

So just remember the rules...

If f(x) = x^k

Then f'(x) = kx^(k-1) (see here http://en.wikipedia.org/wiki/Derivat...tary_functions)

In the K case, it would be.

Y = AK^a L^1-a

Derivative with respect to K is...

AaK^(a-1)L^(1-a)

(To view a better version paste the below code into the add-on compiler from the first post)

A \alpha K^{\alpha-1} L^{1-\alpha}

[Alephz]

free bump

[leafs43]

The farthest I ever got was the 2nd semester of differential equations.

Both I thought were pretty easy compared to the hell that is Calc II.

Calc II largely is dependent on the teacher teaching it. My first time attempting Calc II we had a new teacher to the university from Harvard and he wrote the text book. This guy had crazy ridiculous standards. He didn't even give partial credit on tests. It was either all right or all wrong. I am so glad I dropped that class and made it up over the summer.

[st_jimmy]

Anyone understand how fractional derivatives work? I heard this was possible, but I'm unable to visualize or wrap my mind around it at all

[leafs43]

Anyone understand how fractional derivatives work? I heard this was possible, but I'm unable to visualize or wrap my mind around it at all

Isn't that just differential equations?

Prolly not stuff like dy/dx but very similar. Maybe more proof based?

edit: I googled it, it's pretty much the same as differential equations.

[st_jimmy]

Isn't that just differential equations?

Prolly not stuff like dy/dx but very similar. Maybe more proof based?

edit: I googled it, it's pretty much the same as differential equations.

You can make fractional differential equations I guess, but as far as I know fractional calculus isn't covered in a regular differential equations class. I'm taking diffy q's in the fall so I guess I will find out then

[Akar]

Anyone understand how fractional derivatives work? I heard this was possible, but I'm unable to visualize or wrap my mind around it at all

They won;t cover it... actually I am not even sure they cover it in any undergrad course.

How they work is:

Suppose you want to take the derivative of a function f, call it Df.
Then D is an *operator* that maps a function f to another function Df.
We write this as f --> Df, kinda.
If you want to find a 1/2 derivative, then the idea is to find an operator H such that
H^2= H H = D. Then applying H to f to get f --> Hf we would say that Hf is the half derivative of f.


actually just wiki it, they have latex and explains it pretty well

[Lookitskeith]

subbed on this bish! Will be using this for Finance next semester, and then for grad school! If anyone needs help writing papers that's my specialty!

[lyrics312]

way over my head

[Muckle_Ewe]

Any of you maths folk ever done any sort of orbital dynamics?

I'll be doing a lot of that next year, what kind of maths should I be looking into?

Thinking...

Differential equations, dynamical systems, finite methods to solve ODEs?

[charity4thepoor]

masters in pure math. working on my phd dissertation in geometric topology now.

mirin

i have taken thru calc 3 , ODE, linear, and number theory. doing vector analysis, PDEs and foundations of math in the fall. pretty excited bout it. so interesting

[9987]

Latex has to be supported by the forum to actually use it.

[Muckle_Ewe]

mirin

i have taken thru calc 3 , ODE, linear, and number theory. doing vector analysis, PDEs and foundations of math in the fall. pretty excited bout it. so interesting

Ah cool. How's number theory going? I found it mind boggling but ended up doing pretty well in it. What's in foundations of maths, epsilon-delta proofs?

Latex has to be supported by the forum to actually use it.

Yeah, but! Read my OP again. It's a add on that lets you preview latex within firefox. Download the add on, type up some math in it, then paste the code for it here. Others can then copy and paste the code into the add on to see your formulas.

[charity4thepoor]

Ah cool. How's number theory going? I found it mind boggling but ended up doing pretty well in it. What's in foundations of maths, epsilon-delta proofs?

foundations of math is essentially learning different techniques of proofs and when to use which ones. number theory was good man finished with an A-. was harder for me at the beginning because i have never had a proof-based class before that, but i got it down by the end.

[gatovolador]

Math undergrad, focused a lot on stochastic models and computer engineering. Wrote compilers for a few years and am now getting a masters doing computational linguistics (more probabilistic models).

[moosecakes4all]

Ill be posting alot more in here in the next three weeks Im sure, once I start Calc. 2. Can't wait for it.

Any of you math brahs looked into Physical Chemistry? Its intense.

[Muckle_Ewe]

Math undergrad, focused a lot on stochastic models and computer engineering. Wrote compilers for a few years and am now getting a masters doing computational linguistics (more probabilistic models).

Fuuuuuuuuuuuuuu stoch mods brings back bad memories.

Had a stoch mod course 2 years ago. Lecturer was diabolical. Just strolled into class and started writing up matrices and recurrence relations. No headings or examples so no one had any idea what we were doing.

Gave us 12 tutorial questions all year (as a comparison, the next smallest amount by a class was 52, Algebra gave out 16-20 practice/tutorial questions per week). Told us past papers would be nothing like exam (which they weren't), didn't give us practice papers etc...

Exam came. All questions were on stuff we grazed over briefly and had no practice on (anyone who has done maths knows doing 100s of Qs is the way to learn stuff...)
As a result, over half the class got less than 40%. Myself included, however they had to give a lot of us credits since everything was scaled down so much.

A lot of the concepts seemed pretty interesting though! Markov chains and the like, just that class dampened my potential enjoyment of it.

[Heisman2]

Ill be posting alot more in here in the next three weeks Im sure, once I start Calc. 2. Can't wait for it.

Any of you math brahs looked into Physical Chemistry? Its intense.

I was a chem major... physical chemistry doesn't use math that is very complicated. It's intense because there are a ton of different formulas to know (for basic classes) and as you go up in it you start incorporating a lot of quantum mechanics. In terms of the actual math used, though, it's not that complex; just a lot of different things.