I thought I would include it here in my blog. The responses are quite interesting. I just pasted them in as is, so there might be some grammatical or logical errors. That is just what makes it interesting. The original website was at https://www.physicsforums.com/threads/what-is-advanced-level-mathematics-used-for.500513/
So, here is what people had to say:
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?
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It can enhance your
abstract thinking ability. Not directly useful for anything in daily life.
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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.
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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).
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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!
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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.
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Everything has its
applications. Of course, applications of some fields are more obvious than
others.
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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 art forms (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.
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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.
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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?
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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?"
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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.
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Cryptography is a pretty
big one.
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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!"
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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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*Science *Physics
*Engineering *Computer programming *Genetics and other fields of biology
*Chemistry *Business accounting/finance and economics But people other than
physicists, scientists, and engineers wouldn't have any real use for any
advanced maths.
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I believe that
advanced-level mathematics (especially pure maths) is for fun and for
appreciating the beauty. I am currently at high school and love learning math
(college-level math), but find the maths at high school very dull and boring.
The current education system just turns maths into a very systematic work. For
example, when we learn Pythagoras Theorem, after teaching the theorem itself,
we are told how to (1) Find the length of the hypotenuse if the sides are given
(2) Find the length of one side when the hypotenuse and one of the sides are
given while the teacher can just let us find the way of doing it ourselves with
the original theorem. Even with the exercises provided, the questions are
divided into parts about the first type of problem and second type of problem.
It is just plain stupid (sorry for being a bit too rude).
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Finance, cryptography...
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There is a method to
this madness. True you can derive these different formula's from the original
theorems each and every time you need to use them. But, you will need to apply
these things from time to time as you move into higher level work and it's helps
if you have a lot of these very basic things like trig formulas memorized (at
least somewhat memorized) such that you don]t have to go back and derive them
each and every time you need them. Of course there is nothing wrong with
learning how to use the theorems and understand their meanings to derive the
formulas or, given a formula prove it's validity based on the theorem(s). When
i was in high school (and freshman college) many of the more fundamental
courses omitted the proofs or simply glossed over them. But I never felt
comfortable, I always preferred working through the proofs and, thinking of
other approaches I could take to them.
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You must distinguish
between these two questions: "What do people often use advanced
mathematics for" and "What can advanced mathematics be used
for". People who have training in advanced mathematics, and a certain
knack for applying it, can apply it to almost any subject, even art and
literature. Statistically, the people who know advanced mathematics tend to be
engineers, physicists etc. so that's where you most often see advanced
mathematics applied. If an artist or literary historian happened to be an expert
in differential equations, they might well be able to apply it to their field
of study. However, they might not find many of their peers able to understand
or appreciate their work.
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Because of it's
sometimes mind-boggling complexity and difficulty, it is difficult to wrap your
mind around that level of math without having to have an IQ of 140+ Math is
despised by most high school and college students. Only the people with high
IQ's (a tiny percentage of the population) tend to excel in, and take further
interest in it.
