Random do my math homework for me thread

**Kaylia** · 2012-03-23 02:45

Originally Posted by oldoldman

I have a stupid chemistry question that I just want to make sure I'm getting right. The question is What is the primary natural force that is responsible for Hund's Rule? A) The electrical charge of the electron B) The Heisenberg Uncertainty principle C) ]Magnetism] D) The nuclear mass E) None of these

It's A right? Since it's caused by the repulsion between electrons?

The "electrical charge" is not a force. Heisenberg Uncertainty principle is not a force either. The nuclear mass is not a force. If we want to be nitpick, only "C" and "E" could potentially be right

Secondly, what the fuck is Hund's Rules?

*one wiki later*

There is 3 Hund rules apparently, and all 3 involves differents "force"

#1 pauli's exclusion principles (2 electron can't overlap). It's not a force technically, but it's sometime considered as one (pauli principle)

#2 Repulsion between electron is a force that exists because both electron have an electric charge. However, like I said before, A is not a force, and the question make no physical sense if it's the correct answer (electromagnetism )

#3 Electron spin a magnetic field create a force. (magnetism+spin)

What would I answer? C) or E) are the only correct answer, but C only applies if we are talking about the 3rd laws, E if it's 1st or 2nd. Odd is that your teacher is retarded and meant A) for the second laws, since you mentioned "repulsion".

**oldoldman** · 2012-03-23 03:16

It's a chemistry class so I doubt the prof meant Force in the literal sense.

He probably meant something more like what property of nature.

**oldoldman** · 2012-03-23 03:24

And it's pretty much just the first rule I think.

**oldoldman** · 2012-03-23 03:31

I'm pretty sure it's magnetism, I need to stop doing this shit on so little sleep.

**Woozie** · 2012-03-23 18:04

Originally Posted by Cadsuane

So I'm taking some economics and physics this semestre at a fairly low level and it's really crashing down on me how differently mathematics is approached outside of pure math, which is my major. In particular I remember attending a physics colloquium way back in the fall where this Waterloo physics PhD made some funny remarks about the different ways physicists and mathematicians approach problems, which incidentally is a constant source of jokes from my professors, who apparently have nothing but disdain for this. ie.:

"So the limit of derivatives is indeed the derivative of the limits in this series of infinite functions, provided you have uniform convergence which is a sufficient but not necessary condition. Of course if you did calculus like a physicist, all of this would be entirely too confusing and you'd do it without checking."

I know this is good natured trash talking between departments, but I was thinking about doing a write up or two on an interesting theoretical subject that maybe you guys are already familiar with but maybe were given a very application oriented treatment of, or maybe something weird like Galois groups.

Oh man, I HATE the way physicists do math. To them, it's just a means to an end (and then the ends justify the means somehow). Words like "rigor" and "proof" is like a foreign language to them.

Obligatory Physicists Bill of Rights

Spoiler: show

**Kaylia** · 2012-03-24 00:51

Originally Posted by oldoldman

It's a chemistry class so I doubt the prof meant Force in the literal sense.

He probably meant something more like what property of nature.

I'm aware of this, but he is still doing his students a disservice by giving them confusing questions (and probably theory). I know that many chemistry students have trouble understanding physics concept, but if that's how most teachers are, it's not very surprising. You can't hope to learn a concept when the definition and usage keep changing in different situations.

Originally Posted by Woozie

Oh man, I HATE the way physicists do math. To them, it's just a means to an end (and then the ends justify the means somehow). Words like "rigor" and "proof" is like a foreign language to them.

Obligatory Physicists Bill of Rights

Spoiler: show

Screw you ;( and don't ever walk in the engineering department. Your brain will melt.

Most made me laugh, but there is two that irked me.
#3 I know it's a joke, but we uses complex numbers, group theories and many other concepts. Positive integer (or real number) are generally observable that will be measured.

#7 No way anyone who call themselves physicists would do that. I've seen that hundred of times in the engineering department, but making sure that dimension match is one of the most important things.

**BerenTebogo** · 2012-05-16 16:22

So this semester Numerical Analysis II has been raping me like I was locked in a basement dungeon in Australia. Thankfully, working together with my friends who took the class with me has kept us going and our professor is kind of a softy so we all have A's, but working on this final project, it's become woefully clear that I haven't taken away from this class what I think was intended for us to take away and I'm struggling massively, as are my friends.

Going to preface this with my knowledge going in:

Never used MATLAB before this course, limited general programming knowledge. Still consider myself very weak.

Never used LATEX before this course, am now a LATEX master.

Very familiar with PDEs, comfortable working with them in all manners up until now, numerical analysis of PDEs is new to me. Finite differences methods make 100% sense for me with pen + paper, coding up those finite differences methods is a challenge.

I do not, in any solid way, understand the application of differentiation matrices in matlab for finite difference methods.

I have no idea how to call CHEBFUN in a code and have it do things I need it to do.

-----

That said, I have googled, I have read PDFs, and papers, I own 2 MATLAB books, I have LeVeque's Finite Difference book that I won from a conference actually. I have admittedly slouched this semester compared to others, and haven't hit this stuff as hard as I should, and that sucks, but it is what it is.

I'm pretty sure I can adapt the code I have from the previous project for the simple time-step solutions for the project, but I'm a bit confused on how to change the differentiation matrix that I have from Ut = Uxx heat equation to Ut = Ux (even though it's simpler). I also don't really know how to make a plot of the error between time-stepped solutions for various methods vs. the exact solution.

Need just worlds of help with CHEBFUN.

----

I get all of this stuff conceptually, trading accuracy for computational speed, stable methods vs. unstable methods, deriving local truncation errors and stability conditions, I'm fine with that. Pen and paper and I'm good to go. Put me in front of MATLAB and I become useless.

I can provide .m files that I have coded up and etc. Most of you are friends with me on fb so we can discuss further there, but if anyone is willing to skype a bit, converse on fb, or send me some links they find helpful I would love you forever. I'm not used to being this stumped with math.

**Woozie** · 2012-05-16 16:33

It's been almost 2 years since I've done any numerical stuff, and about 2 and a half since I've used matlab. I probably wont be much help without first spending a few hours looking at my old work to remember stuff, which I wont have time to do today.

**BerenTebogo** · 2012-05-16 16:35

That's fine, if anyone isn't pretty damn familiar with Matlab already I don't want to push anyone to go relearn shit, but I figure there must be a few people around here (engineers?) who might know what is going on.

It's funny, now that I think about it, none of you are really computational or numerical specialists huh?

**Woozie** · 2012-05-16 17:14

I'm starting my physics masters very soon so I'll need to relearn matlab anyways. I just wont have time to for at least a few more days.

I originally did like three and a half years of numerical research and no other type of research, so I guess I was kind of a specialist. But apparently three years isn't much, because after only two years of pure theoretical math research I've forgotten a ridiculous amount of important stuff. Ironically, I probably will go into applied math as a career for the sake of getting a better job (that's right, I'm joining the dark side

) which is more reason I need to relearn all of this stuff anyways.

It's kinda frustrating because theoretical math is so much fun and solid state physics/optics/other stuff that's immediately useful to the world. I'm always at the top of my class in theoretical math classes but in applied math, I actually had to get help from my own students (my students from Advanced Calc/"introductory analysis" who happen to also have taken numerical methods). So to go to applied math means I'm going to my second weakest field (experimental physics being my weakest because of my lack of motivation for it). In the end, I'll probably be happy as long as I'm using both math and science in my career, even if it's not physics at all (like bioinformatics). But to be able to study theoretical particle physics or cosmology or something related to Real Analysis/Functional Analysis/PDEs or even analytic functions/complex variables would be paradise.

On one occasion, I told a professor I've known since high school that I'm considering going into applied math and he strongly discouraged me from doing it. He's kinda like a father figure to me and he knows me really really well and he knows my strengths, weaknesses, and interests. Knowing all of this, he'd much rather see me in theoretical math than applied math despite the big difference in job opportunities because the differences in my abilities and interests are that big. And he's not biased towards theoretical math. He's an applied mathematician himself (and was my professor for numerical methods).

When I told the physics professor who knows me best that I was considering experimental physics, he also strongly discouraged it despite the difference in job opportunities. He's a computational guy himself though. He encouraged me to try an experimental route at my REU because he knew that once I got some experience with experimental physics, I'd realize that it wasn't for me. And he was right. I typically love all of science even though I like some way more or way less than others. Experiments is pretty much the only thing about science that I do not like at all whatsoever (ironic, since that's the most important part of science. To me, experiments isn't much different than cooking, but I love cooking so I don't know why I dislike experiments). I'd rather go into a field that doesn't do science at all than go into a career where the majority of my work is performing experiments.

Edit: On topic, I think Kaylia is pretty familiar with numerical stuff but apparently he's banned. Are you friends with him on Facebook? Paul can probably help you too. I have no idea what Paul actually does but since he's an engineer he probably knows a lot more numerical stuff than Kaylia, Miz, or me.

**BerenTebogo** · 2012-05-16 17:25

Kaylia doesn't have a FB. I'm hoping Paul shows up lol

**Eliseos** · 2012-05-16 18:14

I don't think I'd be of much use here. I haven't used Matlab in over a year and that math sounds pretty above my head

I can take a look at it later and look through some old notes.

**BerenTebogo** · 2012-05-16 18:39

Thanks a bunch, let me know on fb when you're free.

**Mizango** · 2012-05-16 18:50

@@ MATLAB can eat penis.

**Yugl** · 2012-05-16 18:57

Check Byrthnoth; he may know how to operate the program even if he does not know advanced mathematics (I assume the former is more important for now and you can figure out the rest once you have the basics).

**Byrthnoth** · 2012-05-18 04:25

Nope. I know how to use MATLAB pretty well but only in the most basic ways because I'm self-taught and haven't had a math course since single variable calculus freshman year (which was a shitty rehash of my Calc BC class in High School). PChem taught me some more math (by necessity), but I wasn't supposed to have to learn it so my knowledge of it is sketchy.

Can anyone tell me if this probability equation is correct?
http://www.bluegartr.com/threads/103...79#post5216879

The system works like this:
1) Everyone has a chance of getting an item every time the monster is killed (~1%)
2) If someone that already has the item gets a second one, they can make a "Slip" that goes in to the loot pool and is free lottable.
3) If you get 3 Slips you can redeem them for the item.

The equation is trying to show the odds that you will complete your armor through Slips instead of just by getting the drop, because these Slips are R/Ex so getting 2/3 and then the armor wastes the two you have. I get that the odds are astronomically low for most reasonable cases, where you can expect that about half the alliance just does the fight for the rare item and will lot a slip.

**Woozie** · 2012-05-18 12:50

I happen to be on my way to campus, so I'll give that to my combinatorics professor if I see him. Otherwise, I'll try to figure it out later.

**Woozie** · 2012-05-18 15:41

Edit: I want to first mention that, as it turns out, my combinatorics professor rarely does counting problems and he said he'd need review before he can fully answer this. But this is what happened so far:

Your odds of completing a piece with slips after your kth battle would be P(getting three slips in k battles and not getting an item in k battles). P(A&B) = P(A)+P(B)-P(AUB) where "U" means union "&" means intersection. So the probability of completing a piece after your kth battle is

P(getting your third slip in after that battle)+P(having gotten zero items after k battles)-P(Getting your third slip on that battle AND getting zero item drops).

This is the statement of the problem as I gave it to my combinatorics professor.

In this game, a group of n people battle a monster. After the monster dies, each individual has a 1/100 chance of battle armor appearing in their inventory. If a person who already has battle armor obtains a second one after a battle, a coupon appears in the loot pool and everyone can lot on it, all with an equal chance of winning the lot. A person with three coupons can redeem it for the piece of armor. A person cannot win more than three coupons total, ever, and a person with a piece of armor cannot win coupons, and any coupons this person has will disappear. Any person with battle armor can produce a coupon regardless of whether the armor was obtained from battle or obtained from redeeming a coupon.

A "winner" is someone who got their armor by random chance at some point (not by redeeming coupons). Everyone else is a "loser"

Is that an accurate statement of the problem? Here are the assumptions I made (which I need you to correct before I continue working on this problem):

(1)Group composition does not change from battle to battle. The first battle has n people and every subsequent battle has those same n individuals. These individuals only battle has a team and do not go off and do "side battles" in their free time. Without this assumption, I can't do the math.

Here's an example of what I'm trying to avoid: On your first battle, no one gets an item. Between your first and second battle, every individual goes off and does battles with various pick up groups/guilds/clans/whatever. The probability of coupons being produced on your second battle will depend on how many if your teammates obtained armor in their side battles, which depends on who they fought with, how many battles they did, how many people on those teams already had armor, etc, etc. I will not have all the necessary information to do the math in this case.

(2)There is only one type of armor and therefore there is no need for a person to have multiple pieces (what I'm assuming is that there's only one piece of armor that you would want coupons for and that a person with this armor will not want or need coupons but still have a chance of producing coupons.

In reality, this is what I'm actually assuming: For each type of armor that the monster drops, each of them have a probability of 1/100 and are independent of each other [so that getting one piece after a battle doesn't change your probability of getting other pieces in that same battle. If I have a 1/100 chance of getting "battle boots" and a 1/100 chance of getting "battle helmet", then me obtaining battle boots after a battle does not mean I cannot also get a battle helmet after the same battle, nor does it change the probability of me getting a battle helmet], and each type of armor has a different coupon ("battle boots" cannot be obtained with "battle helmet" coupons. Battle boots coupons are produced when a person with battle boots obtains a second pair of battle boots). If this is true, then assumption (1) basically holds for each individual item and my math could be interpreted as "the probability of getting battle boots" or "the probability of getting a battle helmet" but not "the probability of getting any piece of battle gear".

(3)Individuals are "moral". No one is going to roll on a coupon if they do not need it. For example, if five coupons are produced after a battle and I win all five, I will pass two of them (at random) and keep three. People with armor do not lot, and people who win a number of coupons that puts them above three total will pass a sufficient amount so that they have exactly three. Saying that coupons disappear upon getting the items was just a way of saying "people will not redeem coupons upon getting a piece of armor". Of course, that assumption is unnecessary since you'll stop lotting coupons after getting the armor and hence it's impossible to get three coupons if you already have the armor.

(4)Every single individual has a 1/100 chance of getting the armor in their inventory. (the other possibility is that there's a 1/100 chance of it appearing in the loot pool and all n people have to fight over the same piece).

(5)Every single individual starts out without having armor (this is for simplicity. We could have a situation where, for example, 1/3 of the people already have the armor. It shouldn't be too much different than starting at zero. If we can solve one of the situations we can probably solve the other)

(6)Every individual wants and can use the armor (the situation gets tricky otherwise, because if we do not assume this, then we have people who can produce coupons but cannot cast lots on coupons. Saying that one person does not want the armor is not the same as saying that one person already has the armor because in the former case the person cannot produce coupons [yet] and in the later they can. I'm not sure how much more or less complicated this makes things. It could be that it's not that much more complicated all)

This problem reminds me of the Putnam exam lol. Please correct any bad assumptions I've made. The conclusion that we came up with is that this is way too complicated to do by hand for a large number of people n. So instead, our goal was to find an expression of the average number of coupons you'd have after your kth battle. So we'd have a number of the form E(c)=f(n,k). This is as close to a "solution" that we expected to find. We don't expect to be able to solve this equation for k (that is, we wont be able to say f(n,k)=3, solve for k, and then have an exact amount of battles you'd have to do on average to get 3. The expressions we came up with were too complicated to worth trying to solve).

Here's some of the conclusions we drew:

We think it would help to bring as many people as possible, but we couldn't verify this. The number of people does not change the chances of being a winner or a loser, but it does increase the number of coupons produced. Of course, you're rolling against more people for the coupons but we still think that, over time, it will help more since there's a limit to the number of coupons a person could ever want and many people will never need this limit. Of course, people with armor technically have no incentive to go to battle if my assumptions are correct.

The probability that you're a loser after k battles is

http://latex.codecogs.com/gif.latex?1-(99/100)^k

The expected number of losers after k battles is

http://latex.codecogs.com/gif.latex?(1-(99/100)^k)n

We then incorrectly said that this is the number of people you'd be rolling against. In reality, some of the losers may have redeemed a set of coupons by now.

The probability of a person being a second time winner after your kth battle is easy to find. In order for this to occur, the person needs to win once in the first k-1 battles, and then to win on the kth battle. The probability of 1 win in k-1 battles is

http://latex.codecogs.com/gif.latex?...\frac{1}{100})

and the probability of a win on the kth battle is 1/100. So the probability of being a second time winner is

http://latex.codecogs.com/gif.latex?...rac{1}{100})^2

We incorrectly deduced that this would be the probability of each individual producing a coupon. This is wrong because you do not have to be a second time winner to produce a coupon. You could be a first time winner who redeemed a set of coupons before your first win.

From here, we said that the expected number of coupons produced on the kth battle is therefore

http://latex.codecogs.com/gif.latex?...rac{1}{100})^2

which is wrong because the preceeding equation is wrong. The expected number of wins is the expected number of coupons divided by the expected number of people rolling. If we divide my last equation by my number for the expected number of losers after k battles, we get the expected number of coupons obtained (but ignoring the fact that more coupons can be produced because of first time losers who redeemed previously, and that the number of people you're competing against is smaller because some losers have the armor already). Basically we sum that over k=1,2,3,4,....N (but not 1 because no coupons can be produced in the first battle) and you have an expression for the amount of coupons after k battles. From here, you can see which battle will produce more than three coupons.

To answer your question directly (i.e. to see the probability of getting a coupon after the nth battle, you need to find the probability of producing 1 coupon times the probability that you'll win a lot against the people who need it, plus the probability of 2 coupons being produced and the associated probabilities of winning 0, 1, or 2, plus the probability of three being produced, etc. You need to take that to the maximum number of coupons that can be produced, which by itself would be hard to figure out (e.g. you can't just say that after 15 battles, all n-1 teammates may have produced 14 coupons because if that were the case you would have redeemed your slip a long time ago). Also, it gets weird to figure out the probability of actually winning. If 5 coupons are produced and there are 10 people you're competing against, you cannot claim that you have a 1/10 chance of winning each. That's because if one person wins all 5 he only takes three. If a person with two coupons wins more than one, he only takes one. You'd have to figure out these things out and then find the probability of winning exactly 1, the probability of winning exactly 2, etc. This is going to turn out to be a big, complicated sum.

After realizing this, my professor and I both concluded that trying to solve this by hand when computers are available makes about as much sense as doing long division with quadruple digit numbers by hand when calculators are available. If my assumptions are correct, I'll run a simulation and can figure out the expected number of battles before you win the armor (by either method) and probably answer some other questions about this as well (and it will get me reaquainted with matlab).

**Byrthnoth** · 2012-05-18 19:44

You're majoring in Math or Physics, I take it? xD Precise determinations are kind of a giveaway!

I'm a biologist primarily, and thus I love simplifying assumptions. Try these on for size!

Assumption A) I'm not sure if you included this, but I probably should have specified that I'm willing to assume a constant group composition. So you have a constant 6 people that can produce slips, 9 people that want slips, and 3 people that came because they just came and can't jack off for another 20 minutes. Groups typically do runs of 4~6 fights, so the odds of someone switching from the lotting or fapping to slip producing within a run are low enough to be neglected.

Assumption B) It's probably also acceptable to neglect the probability of creating 2+ slips in the same fight, if you are unwilling to use average yields.

Spoiler: show

So, this is how I thought it through:

Spoiler: show

**Woozie** · 2012-05-18 20:48

Just finished my Masters in math this past semester and started my Masters in physics, lol. How far along are you in bio? What do you plan to do? When I was trying to figure out career stuff, a lot of people told me to consider bioinformatics. Apparently it's a huge field with lots of job and for good pay. I've always liked biology anyways so doing bio+math for the rest of my life would be nice even if that wasn't my original goal.

Somehow, by the time I saw my professor the word slips had become "coupons" in my mind lol

I think I see what you're saying here. All of the complicated situations I described have such a low chance of happening that they can be ignored. So in that case, everything you posted seems to be correct. Well, I'm confused about one part

(Odds of getting 3 slips in N runs) :: On average, this will be (p*S/K)^3 = G. Because it is an average, that includes trials where multiple ones can drop. Alternatively, we can neglect those trials (Assumption B) and use the first term above to calculate this. The same disclaimer applies below.

You're saying that for sufficiently small N, we may as well only consider the probability of producing one slip per run, right? In that case, shouldn't you get pS(1-p)^(S-1) as

Let h= pS(1-p)^(S-1)/K (so this is the probability of getting a slip in a given run)

Then the probability of getting three slips in N runs should be h^3(1-f)^(N-3)*(N choose 3)
So the probability of getting three slips in N runs and not getting an armor is h^3(1-f)^(N-3)*(N choose 3)*(1-p^n)

For small enough N. Even with N=10, the probability that someone else will get a slip and then produce a slip and that you'll win said slip is a little under 1/8000 with your group composition if I did my math correctly (which I probably didn't, but the chances definitely small, as you pointed out, so ignoring this possibility makes sense. I don't know why I didn't think of that myself. I've been doing math too long; physicists are much better at ignoring quantities that get in their way than mathematicians lol).

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