Why do engineers need mathematics?

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Main Question or Discussion Point

Paul Erdos said mathematics is like a machine which converts coffee into theorems and proof.
Marcus in his book "Finding Moonshine" says mathematician is a pattern searcher.
Lord Kelvin asked the question, whom do you call a mathematician?
He answered a mathematician is a person who finds the integral of e^(-x^2) from plus infinity to minus infinity as easy as you find 2x2=4.
Is this what mathematics is about?
Why is mathematics taught at university not related to the engineering course we study?
Mathematics seems to be an abstract idea which does not overlap with our engineering course.
Shouldn't it be taught in an engineering context?
 

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russ_watters
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Why is mathematics taught at university not related to the engineering course we study? Shouldn't it be taught in an engineering context?
I don't know where you go or what year you are in, but I needed all the math I got. There are, of course, some theoretical topics in math that you don't use but need in order to learn topics that you will need.

Sorry, yes, engineers need math.
 
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Yes I think we do need mathematics but it the never seems to have any engineering flavour to it. I would like it to be taught in context so that we see the relevance.
 
Hootenanny
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Yes I think we do need mathematics but it the never seems to have any engineering flavour to it. I would like it to be taught in context so that we see the relevance.
I have taken many applied mathematics courses, which definitely have an engineering flavour, fluid mechanics, classical mechanics, continuum mechanics ... etc.

Of course, pure mathematics or statistics courses are going to have very little, or no engineering applications within the taught material itself. However, you don't have to look far for applications of the methods or theorems developed in pure mathematics.
 
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Astronuc
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Engineering is applied physics and the best engineers have a good grounding in the maths and physics. Mathematics is the language of physics, and to a large extent engineering.

If one just wants to plug numbers into formulae, that's little more than being a technician.

Certainly it helps to have mathematics (applied math) taught within the engineering context, but there are physical principles which are best understood with a reasonable amount of mathematical rigor.
 
Hootenanny
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Just adding to what Astronuc said, the courses I mentioned above may seem like very 'pure' mathematics courses to an Engineering major since they still employed a high level of mathematical rigour (as one would expect from the Applied Mathematics Dept.). However, to me personally, it was very easy to see the applications of the methods that were being taught.

Even in Engineering, sound mathematical rigour and method is required to model situations which may at first seem counter-intuitive.
 
quadraphonics
Why is mathematics taught at university not related to the engineering course we study?
Mathematics seems to be an abstract idea which does not overlap with our engineering course.
Shouldn't it be taught in an engineering context?
It sounds to me like you've never taken an upper-division engineering class. Most of those are more-or-less applied mathematics. This is even more so at the graduate level.
 
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I was not talking about fluid mechanics, circuit analysis, mechanics etc where I see the relevance but the mathematical methods courses which seem to teach engineers in a very abstract sense. Rigour is important but I would like to see an application of engineering of the mathematical topic taught.
 
quadraphonics
I was not talking about fluid mechanics, circuit analysis, mechanics etc where I see the relevance but the mathematical methods courses which seem to teach engineers in a very abstract sense. Rigour is important but I would like to see an application of engineering of the mathematical topic taught.
Well, as an engineer who skipped those mathematical methods classes in favor of actual "pure" mathematics courses, I can't say I share your need to have an immediate application presented in the class. The expectation is presumably that you'll find your own applications, or already have some in mind when you sign up for the class. More generally, it's important to have a strong background in math so that you'll be able to read math publications down the line when you run into problems that require math you weren't taught in class. Again, these publications typically will not emphasize any engineering applications; putting math to work is *your* job.
 
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An excellent book which teaches mathematics in an engineering context is:
Engineering Mathematics through Applications by K. Singh.
It also has complete solutions online to all the problems in the book.
I don't agree that it is the student's job to find the relevant engineering application of the mathematics topic.
 
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Thanks

An excellent book which teaches mathematics in an engineering context is:
Engineering Mathematics through Applications by K. Singh.
It also has complete solutions online to all the problems in the book.
I don't agree that it is the student's job to find the relevant engineering application of the mathematics topic.
Thanks for this Gary. I have found book on Amazon and like the positive reviews.
 
rbj
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Why is mathematics taught at university not related to the engineering course we study?
Mathematics seems to be an abstract idea which does not overlap with our engineering course.
Shouldn't it be taught in an engineering context?
i don't agree with either of these premises. mathematics as taught in the university is related to the engineering we study. it does overlap with the engineering courses. and it is also taught in the engineering context.

as to the title question: "Why do engineers need mathematics?" - it's so that when we turn the knob, we turn it far enough and do not turn it too far.
 
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I was not talking about fluid mechanics, circuit analysis, mechanics etc where I see the relevance but the mathematical methods courses which seem to teach engineers in a very abstract sense. Rigour is important but I would like to see an application of engineering of the mathematical topic taught.
I don't know how things work anywhere else, but at the college I attended the engineering-relevant mathematics courses were very much geared to practical applications and were carefully tailored to transmit those skills which would be of direct use in future engineering courses. This was actually a bit frustrating to me as I was not in the engineering program and a more abstract approach would have been of more use to me personally! :) The balance between applications and theory is always a tricky one, and I imagine each institution is going to handle that balance differently.

This said off the top of my head I would tend to respond to "Why do engineers need mathematics?" with "So that they can use Matlab." :smile:
 
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Why is mathematics taught at university not related to the engineering course we study?
Mathematics seems to be an abstract idea which does not overlap with our engineering course.
Shouldn't it be taught in an engineering context?
No, it shouldn't be taught in any particular context. Mathematics is a common derivative of all other forms of language, in that it precisely describes relationships between objects, whether they're abstract concepts or features of physical objects. Often the abstract and physical overlap and so you just never know what part of mathematics you'll need and so you have to study as much of it as you can. You can't get it all, of course, but at least you need to be able to find what you're going to need later in your professional life. The broader the base you can achieve now the better off you'll be later.
 
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I disagree with the concept that engineering mathematics should not be taught in context. Maybe it occurs because some lectures lack confidence in using applications.
If I was on a mathematics programme then I would accept that it does not need to be taught in an engineering or physical science context. However on an applied programme such as engineering or physical sciences the mathematics should be taught in context so that we can see the use of mathematics.
 
FredGarvin
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Does a kid in his freshman or sophomore year really not know what mathematics is for? The way myself and most people I know went through college learned the theoretical stuff first and then learned to apply it. I can understand throwing in examples along the way to say "eventually you will see this in a fluids topic or the like." Heck. Now that I think about it, we were learning derivatives at the same time we were learning Newton's laws of motion in freshman physics classes.

The thing is, those core math classes have to applicable to all engineering students. It would be difficult to impossible to tailor math classes to one particular major. There would be way too many math classes for the university to teach. The ones they can teach have to teach everyone. From there you go off and learn how to apply what you learned.
 
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Engineers do need math, it is the basic concept behind everything that we will have to do, It's like this...we will need to know how things work in order to fix them, which, in most cases, will involve a great deal of math. It's like we have to know the skills and will also have to have the brains behind what we do. You can't really do one without the other.
 
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Why just bolt on the applications of mathematics examples? They should be an integral part of the learning process. For example when solving simultaneous equations they are always in the unkowns x, y and z. Why can't they be in i1, i2 and i3 where the i's represent current?
We are always integrating things like x but not 9.81dt or cos(omega*t).
 
minger
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Because if you were representing the unknowns as currents, then any reasonable person would ask why this holds true. Why can we solve for currents in that way? Then you have the problem of teaching a little bit of electrical engineering.

However, if you just teach the basics of it, then whether you get into circuits, or machine design, you know how to solve the problem once you find that you need to solve a system of equations.

It might be nice to have instead of Calculus II for Engineers to have, Calculus II for Mechanical Engineers who with to have a future in Fluids, but that's just a little unreasonable.
 
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Its good enough just to say that from a particular circuit we obtain the following
equations rather than developing Kirchhoff's laws and then solve the equations. You can point out that you will obtain such equations in their cicuit analysis module.
You are not missing anything if you place i's as the unknowns.
As for other engineering disciplines you can also give examples from these fields in the text or exercises so they are at least comfortable with these symbols. There is nothing wrong with adding x, y and z as unknowns as well.
This general approach will work to motivate students if they see the relevance.
 
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Engineering Mathematics

What is the point of calling it engineering mathematics if we are going to do a mathematics techniques course? There is nothing wrong with applying engineering examples from the start and not just tag on a couple at the end which is useless.
As for the fields of engineering you can apply examples from mechanics, electrical principles, control theory, etc in the same topic. PLace some in the text and the remaining as exercises for the student. This as been done well in the book
Engineering Mathematics through Applications.



Does a kid in his freshman or sophomore year really not know what mathematics is for? The way myself and most people I know went through college learned the theoretical stuff first and then learned to apply it. I can understand throwing in examples along the way to say "eventually you will see this in a fluids topic or the like." Heck. Now that I think about it, we were learning derivatives at the same time we were learning Newton's laws of motion in freshman physics classes.

The thing is, those core math classes have to applicable to all engineering students. It would be difficult to impossible to tailor math classes to one particular major. There would be way too many math classes for the university to teach. The ones they can teach have to teach everyone. From there you go off and learn how to apply what you learned.
 
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Why can't some engineering students evaluate the integral of 9.8dt but they can easily integrate xdx?
 
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I agree with matgkks to some extent. There are too many math professors who have no idea what engineers do. More and more schools are starting to teach linear algebra and diff eq. to engineers in the engineering buildings rather than in the math department. This is because of (undergrad) students who learned a lot of theory but had no idea how to apply it. By the same token, too many math profs. would be hard pressed to actually apply math to a real world problem thats not in their textbook. The student can only be as good as their teacher.
 
The engineering courses are usually arranged to coincide with the math courses that are helpful to them as your years in college advance. Advanced math was often taught by engineers in specific areas. Unfortunately, at my school, the first two years of the various math courses were usually taught by grad students. They had even less interest in engineering use than the professors. I remember one bright grad student was Chinese and could not be understood by the students (his speech, not his math) so they went enmasse to the dean and he was replaced by a professor. The professor told them 1/2 would flunk and the highest grade would be a "c". The professor did not lie. He got even with those students, But believe me, after the class was over, they got even with him, too.
 
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It is unprofessional of the professor to punish students who had a genuine reason to complain. Even if it was not genuine the professor should be thinking that he is contributing to a students future not producing nots and bolts.


The engineering courses are usually arranged to coincide with the math courses that are helpful to them as your years in college advance. Advanced math was often taught by engineers in specific areas. Unfortunately, at my school, the first two years of the various math courses were usually taught by grad students. They had even less interest in engineering use than the professors. I remember one bright grad student was Chinese and could not be understood by the students (his speech, not his math) so they went enmasse to the dean and he was replaced by a professor. The professor told them 1/2 would flunk and the highest grade would be a "c". The professor did not lie. He got even with those students, But believe me, after the class was over, they got even with him, too.
 
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