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-   -   What is advanced-level mathematics used for? (http://www.physicsforums.com/showthread.php?t=500513)

FishmanGeertz May21-11 12:04 AM

What is advanced-level mathematics used for?
 
I barely understand the bare basics of algebra, my math skills are abysmal. But what applications do advanced mathematics such as stochastic calculus and linear algebra have?

Other than in physics, science, and engineering, what other things can advanced-level mathematics be used for? How about in daily life?

Unrest May21-11 12:24 AM

Re: What is advanced-level mathematics used for?
 
It can enhance your abstract thinking ability.

Not directly useful for anything in daily life.

DivisionByZro May21-11 06:07 AM

Re: What is advanced-level mathematics used for?
 
Quote:

Quote by Unrest (Post 3314007)
It can enhance your abstract thinking ability.

Not directly useful for anything in daily life.

I fully disagree, how do you think barcodes were invented?

A few uses of Linear Algebra:

Codabar system
Digital image compression
Calculating life expectancy
Modelling population growth
Profit maximization
Universal Product Code
Lots more

If you want a thorough discussion of exactly how they are used, then just open up some linear algebra books, or do a Google search.

Higher math isn't just solving puzzles (In fact, that's not really what math is). People don't just do mathematics to improve their thinking abilities; it certainly helps, but it has many applications.

Keep in mind that mathematics need not be applied to anything. Just because you can't use a result of mathematics (at first) for anything practical does not make it useless.

ZealScience May21-11 06:08 AM

Re: What is advanced-level mathematics used for?
 
There is great deal of uses in physics (also era involves some Chemistry) and engineering. In general relativity a lot of linear algebra and calculus is required. In engineering, mostly calculating some basic mechanics problem.

Other than these, Economics uses great deal of calculus to model the market which is very important. You can search more on financial mathematics (not accounting~~boring).

DivisionByZro May21-11 11:12 AM

Re: What is advanced-level mathematics used for?
 
Also, I've heard that matrices can be used to balance out chemical reactions in chemistry. I haven't actually done that myself, but I was happy to know that there was an easier way than what I did in my first year chemistry class!

Unrest May21-11 12:18 PM

Re: What is advanced-level mathematics used for?
 
Quote:

Quote by DivisionByZro (Post 3314304)
A few uses of Linear Algebra:

Oh sure it's useful in all sorts of professions. But not daily life, and many well paid jobs don't need it either.

But the trouble is, when you're 16 you don't quite know what you'll be doing in 10 years time, and by then it's too late to learn so easily.

Samuelb88 May21-11 12:48 PM

Re: What is advanced-level mathematics used for?
 
Everything has its applications. Of course, applications of some fields are more obvious than others.

FishmanGeertz May21-11 07:07 PM

Re: What is advanced-level mathematics used for?
 
What about the use of high-level math in areas other than physics, science, and engineering?

paulfr May21-11 10:57 PM

Re: What is advanced-level mathematics used for?
 
Mathematics models the natural world.
So your question is nearly identical to ......
What use is it to learn English ?

Furthermore, Logic, one of the foundations of Mathematics, is the link between The Arts & The Sciences.
All artforms (nearly) seek to communicate.
How better to make your case than with clear precise easy to understand logic ?
Be it painting, screenplay, poem, courtroom summation or a novel.

Some of the very the best lawyers were good at Math.
That is one of the reasons they excel at the Law.

Mathematics underlies nearly everything you see around you.

But it will not guarantee a good life.
That is the province of religion and moral philosophy.

ZealScience May21-11 11:15 PM

Re: What is advanced-level mathematics used for?
 
Quote:

Quote by DivisionByZro (Post 3314655)
Also, I've heard that matrices can be used to balance out chemical reactions in chemistry. I haven't actually done that myself, but I was happy to know that there was an easier way than what I did in my first year chemistry class!

I think balancing equations is simply simultaneous equations, I mean for rather complicated equations. Matrices are just simple forms of simultaneous equations, they just save your paper and ink. Of course there are many ways of balancing equations, but many of them might not work for all cases.

Also, matrices are very useful in doing statistics, though I haven't learn much of statistics, I heard of something called covariant matrix that is used for complicated systems. And statistics can be applied to many areas. May be you can look more on that.

yenchin May22-11 12:19 AM

Re: What is advanced-level mathematics used for?
 
This article on mathematics education (and so-called applications of math in real life) is a good read:
http://www.maa.org/devlin/LockhartsLament.pdf

Somewhat long, but well worth the time.

DivisionByZro May22-11 06:53 AM

Re: What is advanced-level mathematics used for?
 
Quote:

Quote by Unrest (Post 3314711)
Oh sure it's useful in all sorts of professions. But not daily life, and many well paid jobs don't need it either.

But the trouble is, when you're 16 you don't quite know what you'll be doing in 10 years time, and by then it's too late to learn so easily.

How does that even matter? Just because some random CEO doesn't use his knowledge of basket-weaving doesn't make basket-weaving useless. That's a really poor argument. Why does everything have to be immediately useful in daily life, and by daily life, I assume you mean eating, breathing, sleeping, and no more.

It seems to me that you think that if you don't use something every day, or can't use it to make lots of money, then it's useless. As said many times in this thread, mathematics is all about logical and abstract thinking; it's basically a form of creativity. Now tell me, how useless are the former?

micromass May22-11 07:31 AM

Re: What is advanced-level mathematics used for?
 
When people ask me what the use is for mathematics, I always respond with the following poem by Morris Bishop:

There's a tiresome young man in Bay Shore.
When his fiancee cried, "I adore
the beautiful sea".
He replied, "I agree,
it's pretty, but what is it for?"

LCKurtz May22-11 07:02 PM

Re: What is advanced-level mathematics used for?
 
Another interesting read is Underwood Dudley's article:

http://www.public.iastate.edu/~aleand/dudley.html

Anonymous217 May22-11 07:56 PM

Re: What is advanced-level mathematics used for?
 
Quote:

Quote by DivisionByZro (Post 3315796)
How does that even matter? Just because some random CEO doesn't use his knowledge of basket-weaving doesn't make basket-weaving useless. That's a really poor argument. Why does everything have to be immediately useful in daily life, and by daily life, I assume you mean eating, breathing, sleeping, and no more.

It seems to me that you think that if you don't use something every day, or can't use it to make lots of money, then it's useless. As said many times in this thread, mathematics is all about logical and abstract thinking; it's basically a form of creativity. Now tell me, how useless are the former?

He never said higher math was useless in the general context, simply useless in daily life. There's nothing wrong with the validity of his statement since we take the meaning of "useless" in every day conversation as "generally useless" rather than "completely useless". However, there are few professions that are useful in daily life, such as cooking, etc. so the statement, although basically true, is misleading.

gb7nash May22-11 08:55 PM

Re: What is advanced-level mathematics used for?
 
Cryptography is a pretty big one.

yenchin May22-11 09:16 PM

Re: What is advanced-level mathematics used for?
 
Quote:

Quote by micromass (Post 3315838)
When people ask me what the use is for mathematics, I always respond with the following poem by Morris Bishop:

There's a tiresome young man in Bay Shore.
When his fiancee cried, "I adore
the beautiful sea".
He replied, "I agree,
it's pretty, but what is it for?"

I prefer this:

A math professor, a native Texan, was asked by one of his students: "What is mathematics good for?"
He replied: "This question makes me sick! If you show someone the Grand Canyon for the first time, and he asks you `What's it good for?' What would you do? Well, you kick that guy off the cliff!":biggrin:

Unrest May22-11 09:25 PM

Re: What is advanced-level mathematics used for?
 
Quote:

Quote by DivisionByZro (Post 3315796)
As said many times in this thread, mathematics is all about logical and abstract thinking; it's basically a form of creativity. Now tell me, how useless are the former?

Yes, I was one of those people who said that. But I think the OP was concerned about direct applications. Like when you would want to sit down with a pen and paper to write an integral or perform a matrix operation. For most people the answer would be never in their life.

Us mathy types would think about it all the time when we hear news stories or write on internet forums, but that's not normal people. If you aren't inclined to analyze things for fun, then knowing how to integrate won't make you do it.


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