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How much numerical analysis do we need?

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Main Question or Discussion Point

for each of these careers: engineer, physicist, mathematician, how much numerical analysis is necessary? is just learning mathematica sufficient? or do you need at least a full class in numerical analysis?
 

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morphism
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The answer of course depends on what you will be doing...
 
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so since i'm unsure whether to go into theory or industry, it'd be best to take as much numerical analysis as possible in undergrad?
 
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But numerical analysis is so boring.
 
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But numerical analysis is so boring.
yea thats why id rather put it off until my last semester of undergrad, so my grade wont matter to grad school admissions

oh i forgot to mention that i'm starting my physics research this summer, and my only programming experience is a class in c++. so would taking a numerical analysis seminar that teaches mathematica be really helpful?
 
for each of these careers: engineer, physicist, mathematician, how much numerical analysis is necessary? is just learning mathematica sufficient? or do you need at least a full class in numerical analysis?
Yes simply because you shouldn't be one of those people that uses canned software without knowing what it's doing. The computer is not supposed to be a magical black box. When you solve a problem numerically, the effectiveness and appropriateness of the algorithm you use is extremely important.

And say you started doing research in an area where you could just use a program developed by someone else... and then later you want to solve a different problem that program can't do? Will you be able to dyi or will you have to hope that you can find another program that you can buy to get the job done?
 
f95toli
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for each of these careers: engineer, physicist, mathematician, how much numerical analysis is necessary?
Of course it depends on what you will be doing, but generally speaking the answer is: a lot.
The problem with problems in the real world is that they are almost never as "neat" as the questions you are asked in courses at university. People tend to forget that analytical solutions to e.g. PDEs are actually quite rare, this is especially true in engineering.
Physicists tend to do a bit of both: we use analytical tools (pen and paper) to understand a problem, usually by making simplifying assumptions (e.g. weak perturbations etc), but when we need actual numbers we often have to use a computer.

However, note that "numerical analysis" can mean different things. As far as I remember we spent most of the time on things like error estimations in my NA course which in retrospect is perhaps good to know but not something I use very often (at least not directly); we learned most of the "practical" stuff -like how to actually solve PDEs etc- in various math courses (e.g. the PDE course was mostly about FEM).
 
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alright, i get the message, we need lots of numerical analysis.

anyways , i'm starting my physics research this summer, and my only programming experience is a class in c++. so would taking a numerical analysis seminar (which only has 1-hr lecture each week)that teaches mathematica be really helpful? if not, i might as well drop the class
 
alright, i get the message, we need lots of numerical analysis.

anyways , i'm starting my physics research this summer, and my only programming experience is a class in c++. so would taking a numerical analysis seminar (which only has 1-hr lecture each week)that teaches mathematica be really helpful? if not, i might as well drop the class
I think that it can be useful. Why don't you ask your adviser?
 
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numerical analysis is fun. i think it's so fun i'm going to drop the physics major and just get a computational science degree.
 

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