How do mathematicians and engineers differ in their work and training?

[supernova1203]

How do they differ?

Not just in the training they receive, but also the kind of work they do?

I imagine mathematicians work more so in theory, proofs, logic etc etc where as engineers don't do that sort of stuff?

 

[fss]

Engineering is much more real-world applicable.

 

[supernova1203]

in other words you don't have to worry too much about proofs and pure mathematics?

 

[Shackleford]

in other words you don't have to worry too much about proofs and pure mathematics?

You don't have to worry at all about proofs and pure mathematics. However, you better know how to use the mathematics in formulating and solving problems.

 

[supernova1203]

You don't have to worry at all about proofs and pure mathematics. However, you better know how to use the mathematics in formulating and solving problems.

Yes :)

 

[Angry Citizen]

You should be able to do at least some proofs. I'm an engineering major and I'm proving stuff in my calc III class. I'll probably be doing some proofs in linear algebra as well. You shouldn't be afraid of proofs. They do help you understand the mathematics, even from an applied standpoint.

 

[panzival]

I'm almost done my first year in engineering and there's been very little proofs. My profs will do the proofs but I haven't had to do any myself, except in Linear Algebra. And even there it's usually just 1 question each assignment and test.

 

[Shaun_W]

You should be able to do at least some proofs. I'm an engineering major and I'm proving stuff in my calc III class. I'll probably be doing some proofs in linear algebra as well. You shouldn't be afraid of proofs. They do help you understand the mathematics, even from an applied standpoint.

I disagree. I don't see the point in proofs for an engineering student.

 

[wisvuze]

Uh.. what part of being an engineer gives you a free ticket to be ignorant of the very tools with which you use to solve all your problems??

 

[chiro]

How do they differ?

Not just in the training they receive, but also the kind of work they do?

I imagine mathematicians work more so in theory, proofs, logic etc etc where as engineers don't do that sort of stuff?

Pure mathematicians usually work with things that are abstract and are concerned about how rigorous and concise their arguments are to establish proper conclusions about their results.

Engineers on the other hand work with things that are extremely specific and applied.

One important thing to mention is that the models that engineers use are very very precise and factor in as many assumptions as it needs to help create something that will not only work, but work under any conditions that it must work under: nothing is taken for granted.

With some areas of applied mathematics, this is not necessarily a prerequisite. Say someone is doing research into some applied area to come up with baseline assumptions: they may do some analysis and come up with a set of compact assumptions (minimal set of assumptions) that describe a lot of the behavior of some phenomenon but don't account for more detailed behaviors.

In the above case, the applied mathematicians are not making the kinds of assumptions a typical engineer may have to do, but then again they are not designing things like roads or bridges that could, if done under bad assumptions, cost real lives and a lot more real money.

Also it should be pointed out that no field is one that is static. Most problems that exist are ones that don't have textbook solutions, or even frameworks for analyzing these problems. They are dynamic and you will no doubt at one point face a problem that may not have a full solution. To solve these kinds of problems, you use your experience (and others as well) to break your unfamiliar problem down into something that becomes familiar in some sense.

Engineers need to understand assumptions, and assumptions are written in the language of mathematics, and if you want to change or create new assumptions, you will have to do the kind of thing that mathematicians do in the context of your domain (engineering).

 

[Shaun_W]

Uh.. what part of being an engineer gives you a free ticket to be ignorant of the very tools with which you use to solve all your problems??

The bit where you can solve all your problems without knowing the proofs behind the maths used to express your problem.

 

[clope023]

Uh.. what part of being an engineer gives you a free ticket to be ignorant of the very tools with which you use to solve all your problems??

The part where it's not necessary in any way, shape, or form to know the proofs behind the math you're using to apply it.

 

[EntropicLove]

So what *exactly* is an applied mathematician then? Is there such an actual label or do you just apply math to a certain area then call it that?

Mix of mathematician and engineer?

 

[clope023]

So what *exactly* is an applied mathematician then? Is there such an actual label or do you just apply math to a certain area then call it that?

Mix of mathematician and engineer?

They analyze problems in physics and engineering from a mathematical point of view, usually with applied analysis, calculus, linear algebra, and differential equations, and statistics. They tend to study things like fluid mechanics, control theory, finance, etc.

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

 

[Shackleford]

They analyze problems in physics and engineering from a mathematical point of view, usually with applied analysis, calculus, linear algebra, and differential equations, and statistics. They tend to study things like fluid mechanics, control theory, finance, etc.

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

Yeah. I've thought about going the Applied Math route in grad school.

 

[Integral]

The bit where you can solve all your problems without knowing the proofs behind the maths used to express your problem.

Sure you can, just don't be surprised when situations arise which your tool box of math equations doesn't come up a correct solution. The trouble is they will give a solution, but it does not have to be right.

 

[HallsofIvy]

I disagree. I don't see the point in proofs for an engineering student.

That reminds me of a young woman who asked me why she had to learn all the "mixture problems" we were doing at the time in the University's required math elective. I asked what she was majoring in and she answered "Nursing". I said, "Well, there it is- medicines are typically mixtures that have to be done very precisely!".

Her response was, "Nurses don't mix medicines, they get them from the Pharmacy already mixed". There was nothing I could say to that- if she honestly believed that she should learn only those specific jobs that a nurse is expected to do and NOT anything that might be related, then she has far too narrow a view of what a nurse or anyone should learn.

An engineer is constantly solving problems and many of those problems are mathematical. Yes, there are often cut and dried methods for solving those problems but if your goal in life is to ONLY work on an engineering job where all things are cut and dried, then I have nothing to say to you.

But a good engineer should look forward to dealing with problems where he must go beyond not only what is "cut and dried" but even beyond what is already known. He must be able to recognize situations where the methods he has learned before do not work,understand why they do not work, and he must be able to devise new methods that will work.

All mathematical methods of solving problems are based on "proofs" and having seen proofs, he will understand where those methods break down and why they break down (or, perhaps more realistically, know enough to go back to the texts books or talk to a mathematician) and see how to change the methods to make them work in this particular situation.

 

[DrummingAtom]

An engineer is constantly solving problems and many of those problems are mathematical. Yes, there are often cut and dried methods for solving those problems but if your goal in life is to ONLY work on an engineering job where all things are cut and dried, then I have nothing to say to you.

But a good engineer should look forward to dealing with problems where he must go beyond not only what is "cut and dried" but even beyond what is already known. He must be able to recognize situations where the methods he has learned before do not work,understand why they do not work, and he must be able to devise new methods that will work.

All mathematical methods of solving problems are based on "proofs" and having seen proofs, he will understand where those methods break down and why they break down (or, perhaps more realistically, know enough to go back to the texts books or talk to a mathematician) and see how to change the methods to make them work in this particular situation.

I know others have mentioned this lately but we need a like button for posts like this. Thanks for insight.

 

[Stephen Tashi]

Engineering is a more recognized and protected as a profession than mathematics. For example, laws may require that the frameworks of public buildings be designed by engineers. A company competing for a government contract involving electronics will want to show that it employs people trained as engineers. Outside of academia, few mathematicians have the job title of "mathematician". I doubt there are many laws or contracts that require that a qualified mathematician be part of a process. If you count "statistician" as being a mathematician, that profession is somewhat recognized as a profession and the services of a statistician might be mandated in certain kinds of contracts.

 

[EntropicLove]

Engineering is a more recognized and protected as a profession than mathematics. For example, laws may require that the frameworks of public buildings be designed by engineers. A company competing for a government contract involving electronics will want to show that it employs people trained as engineers. Outside of academia, few mathematicians have the job title of "mathematician". I doubt there are many laws or contracts that require that a qualified mathematician be part of a process. If you count "statistician" as being a mathematician, that profession is somewhat recognized as a profession and the services of a statistician might be mandated in certain kinds of contracts.

Thank you for mentioning that--Very good point.

 

[vish_maths]

Hi :) i would love to comment on this. The majority of people would agree , Mathematics is the queen of all sciences. And engineering just happens to be it's budding child which can never do without it's mother :) period :)