The Should I Become a Mathematician? Thread


by mathwonk
Tags: mathematician
Nano-Passion
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#3043
Apr7-12, 11:09 AM
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I;m taking a calculus II course. Partial fractions seem very unmotivated and ugly to me. But I'm sure there has to be some beauty behind it. Can anyone link me to the underlying theory of it all?
Robert1986
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#3044
Apr7-12, 11:16 AM
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I agree that partial fractions are ugly in the sense that they can be a pain. But, I don't get the unmotivated part. Aren't you decomposing a complicated quotient into the sum of several easier quotients that you can integrate? That is the motivation.

As for underlying theory, I really think it is just algebraic manipulations, like partial fractions or something.
Nano-Passion
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#3045
Apr7-12, 01:20 PM
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Quote Quote by Robert1986 View Post
I agree that partial fractions are ugly in the sense that they can be a pain. But, I don't get the unmotivated part. Aren't you decomposing a complicated quotient into the sum of several easier quotients that you can integrate? That is the motivation.

As for underlying theory, I really think it is just algebraic manipulations, like partial fractions or something.
Well unmotivated because they seem to just come out of nowhere. The book I'm using says do this and this and you will get this. But I don't blame it, deriving it seems tricky-- you need a bunch of clever manipulations that aren't so straightforward.
DrummingAtom
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#3046
Apr7-12, 06:53 PM
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Quote Quote by Nano-Passion View Post
I;m taking a calculus II course. Partial fractions seem very unmotivated and ugly to me. But I'm sure there has to be some beauty behind it. Can anyone link me to the underlying theory of it all?
I agree with Robert1986 that the motivation is simply just decomposing it into a useful form. If you want a more general form of it check out wikipedia:

http://en.wikipedia.org/wiki/Partial_fraction
Cod
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#3047
Apr8-12, 08:16 AM
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Quote Quote by qspeechc View Post
Well, there's no need to put it quite like that

What I meant was, if you think it's really worth it, then I guess I'll save up for Artin, and I'll just have to postpone on getting some other book.

In the mean time I'll take a look at your notes, thanks.
Keep an eye on the price of international editions. They're a lot cheaper and usually contain the same material as their US counterpart.

http://www.abebooks.com/servlet/Sear...ts=t&x=54&y=13
qspeechc
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#3048
Apr8-12, 10:31 AM
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Quote Quote by Cod View Post
Keep an eye on the price of international editions. They're a lot cheaper and usually contain the same material as their US counterpart.

http://www.abebooks.com/servlet/Sear...ts=t&x=54&y=13
Yes, the problem is I'm not in the USA, so the price may be good, but the shipping is dreadful, the first few are all over $40 or $30 for shipping! And then there's import tax, duties, etc., which adds another 40% or thereabouts, so a $60 2nd-hand book (including shipping, I think) comes out at $84 etc.

Also, I've tried a few times to buy from bookseller in India, but they won't ship to where I am.

But thanks for the tip, I'll definitely keep my eye out for a good deal.

I'm in no rush anyway, there are many, many books I'd like to read, and maybe one day I'll get round to Artin (hopefully not too long from now).
homeomorphic
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#3049
Apr8-12, 12:52 PM
P: 1,020
As for underlying theory, I really think it is just algebraic manipulations, like partial fractions or something.
Even I, Mr. Conceptual himself, would agree with that. However, it makes much more sense with complex numbers than real numbers. Maybe people avoid complex numbers because calc students aren't 100% comfortable with it.

Partial fractions just aren't that great of a thing.

I didn't really understand the algebraic tricks when I first saw it, so that was annoying. But after I figured out how to derive it myself, it was somewhat less annoying. It's kind of analogous to multiplying both sides of an equation by something. It just isn't anything to write home about. But it's also not something to get upset about, either.

I think the motivation in calculus is also to write things in a form where they can be integrated.
synkk
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#3050
Apr8-12, 01:33 PM
P: 216
Does university reputation matter? I have an offer from a top 20 world university, and top 10 UK universities to study mathematics, but also one which is closer to home, but has less reputation? I'd prefer to go to the one with the lower reputation, as i'd like to stay at home, but I'm not sure if I should just suck it up and go to the one who should give me more career prospects. After graduating I plan on going onto actuarial, or investment banking jobs, or perhaps graduate work, if i'm good enough.
Locrian
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#3051
Apr8-12, 07:12 PM
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With a very few exceptions at the very top or bottom, I would say university reputation does NOT matter going into actuarial work. Actuarial work is not like law where only going to the top few schools makes it worth the price.
synkk
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#3052
Apr8-12, 09:04 PM
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Quote Quote by Locrian View Post
With a very few exceptions at the very top or bottom, I would say university reputation does NOT matter going into actuarial work. Actuarial work is not like law where only going to the top few schools makes it worth the price.
Any ideas about investment banking? I've looked at the alumni of the less reputable school and it appears some people have gone onto investment banking, however it was from an economics degree. Though I do read around a lot on economics and I've interned at an investment bank, I don't think think I'd be able to do the degree (I'm not an essay person). Searching around, it does seem that investment banks do seem to go for target schools, however I'm not quite sure.
DeadOriginal
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#3053
Apr8-12, 10:06 PM
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Quote Quote by synkk View Post
Any ideas about investment banking? I've looked at the alumni of the less reputable school and it appears some people have gone onto investment banking, however it was from an economics degree. Though I do read around a lot on economics and I've interned at an investment bank, I don't think think I'd be able to do the degree (I'm not an essay person). Searching around, it does seem that investment banks do seem to go for target schools, however I'm not quite sure.
If you don't graduate from a target school and you didn't have any outstanding internships that allowed you to network extensively your chances of going into investment banking are against you no matter what you studied.

On the other hand, I wouldn't do actuarial science to try to get into investment banking. Actuaries are focused in insurance. If you want to get into investment banking, the CFA exams will serve you better.
synkk
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#3054
Apr9-12, 07:34 AM
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Quote Quote by DeadOriginal View Post
If you don't graduate from a target school and you didn't have any outstanding internships that allowed you to network extensively your chances of going into investment banking are against you no matter what you studied.

On the other hand, I wouldn't do actuarial science to try to get into investment banking. Actuaries are focused in insurance. If you want to get into investment banking, the CFA exams will serve you better.
I wasn't planning to do actuarial science to go into investment banking. Thank you.
IGU
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#3055
Apr9-12, 09:46 AM
P: 102
qspeechc -

Jacobson's Basic Algebra I is available in a Dover edition. It's probably the level you're looking for and around $12 new at Amazon. Less dense than Lang, more extensive and a step up in depth from Herstein's Topics in Algebra.

It is somewhat dry, meaning you have to supply the enthusiasm.

-IGU-
mathwonk
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#3056
Apr9-12, 11:37 AM
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qspeechc: To put it another way, recall the famous quote: 'when asked how he had managed to make such progress in mathematics despite his youth, Abel responded, “By studying the masters, not their pupils.” '
dkotschessaa
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#3057
Apr9-12, 06:15 PM
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Quote Quote by Nano-Passion View Post
Well unmotivated because they seem to just come out of nowhere. The book I'm using says do this and this and you will get this. But I don't blame it, deriving it seems tricky-- you need a bunch of clever manipulations that aren't so straightforward.
This might make you hate them more, but whenever I get stuck on something like this I always like to know something of the history of it. The first known use of partial fraction decomposition was by Isaac Barrows, in his proof of the integral of the secant function: http://en.wikipedia.org/wiki/Partial...in_integration

Following on the advice of Mathwonk to make your own exercises, (way early in this thread) this is another place where this is useful. Take something like [5/(x+5)] * [8/(x^2+2)] or something like that. Multiply it all together, then try to decompose it again. Maybe integrate it before and again afterwards to show yourself how everything fits together. Then make more complicated problems.

If you're a real math geek this will actually start to become enjoyable...

-DaveK
homeomorphic
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#3058
Apr9-12, 06:49 PM
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If you're a real math geek this will actually start to become enjoyable...
Perhaps, but I wouldn't want anyone to get the impression that you have to like that sort of thing to do math. It's much more interesting than that, thankfully. I'm sure there's a place in math for those who are thrilled by things like partial fractions. But there's a place for those who are not thrilled by them.

Partial fractions? Just learn them so you can get a good grade and be better at integration and then move on to better things. It would be much more interesting to design some Turing machines or figure out how to do some ruler and compass constructions. Something that has some intellectual content to it.
dkotschessaa
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#3059
Apr9-12, 08:33 PM
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Homeomorphic, you are correct. That pretty much just came out wrong.
mathwonk
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#3060
Apr9-12, 10:01 PM
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I agree with dkotschessaa that partial fractions is just a way of reversing adding fractions. it may seem more natural when you study complex analysis and poles and laurent expansions.

as a general rule, there is nothing at all that has no value and no interest, it is just being taught that way. I have a friend who is really really smart, and every time i say to him that something is rather boring or uninteresting, he ALWAYS says back: well what about this?..... and it becomes fascinating......


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