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The Should I Become a Mathematician? Threadby mathwonk
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#3043
Apr712, 11:09 AM

P: 1,306

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?



#3044
Apr712, 11:16 AM

P: 828

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. 


#3045
Apr712, 01:20 PM

P: 1,306




#3046
Apr712, 06:53 PM

P: 661

http://en.wikipedia.org/wiki/Partial_fraction 


#3047
Apr812, 08:16 AM

P: 308

http://www.abebooks.com/servlet/Sear...ts=t&x=54&y=13 


#3048
Apr812, 10:31 AM

P: 792

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). 


#3049
Apr812, 12:52 PM

P: 1,260

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. 


#3050
Apr812, 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.



#3051
Apr812, 07:12 PM

P: 1,742

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.



#3052
Apr812, 09:04 PM

P: 216




#3053
Apr812, 10:06 PM

P: 274

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. 


#3054
Apr912, 07:34 AM

P: 216




#3055
Apr912, 09:46 AM

P: 137

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 


#3056
Apr912, 11:37 AM

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P: 9,481

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.” '



#3057
Apr912, 06:15 PM

P: 604

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 


#3058
Apr912, 06:49 PM

P: 1,260

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. 


#3060
Apr912, 10:01 PM

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P: 9,481

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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