Why do engineers need mathematics?

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  • #1
matqkks
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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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  • #2
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.
 
  • #3
matqkks
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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.
 
  • #4
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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  • #5
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.
 
  • #6
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.
 
  • #7
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.
 
  • #8
matqkks
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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.
 
  • #9
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.
 
  • #10
Gary_123
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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.
 
  • #11
matqkks
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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.
 
  • #12
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.
 
  • #13
Coin
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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:
 
  • #14
Michael_E
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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.
 
  • #15
matqkks
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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.
 
  • #16
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.
 
  • #17
mcknia07
282
6
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.
 
  • #18
matqkks
280
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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).
 
  • #19
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.
 
  • #20
matqkks
280
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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.
 
  • #21
Gary_123
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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.
 
  • #22
matqkks
280
5
Why can't some engineering students evaluate the integral of 9.8dt but they can easily integrate xdx?
 
  • #23
Jupiter6
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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 that's not in their textbook. The student can only be as good as their teacher.
 
  • #24
Peter Hiatt
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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.
 
  • #25
matqkks
280
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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.
 
  • #26
DavidWhitbeck
351
1
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 that's not in their textbook. The student can only be as good as their teacher.

Excuse me, but this is so typical of an engineering student. Not only do you have to squish your education into four to five years (unlike law, medicine and science), but you still have the gall to complain that you want the general science and math courses (that form the foundation of your upper level course work I might add!) to be specialized for you to care.

Did you realize that cs majors use linear algebra for different applications than ee majors? And what about chem e, do you think they use linear algebra for the same problems? If you teach classes like that as an applications class then every department would need their own. And that is highly inefficient. Besides you will learn the applications in your upper level classes, else why would you have to take it?

You seem to think that the math prof should supply your motivation for taking a math class. No, you are a college student, you are responsible for figuring out why your department wants you to take that class, and what you should learn from it. You need to be self-motivating.

Now you can solve linear systems on graphing calculators, matlab, mathematica, maple, octave etc you don't need a computational grunt work class either. You need to learn the concepts. So even for that interpretation of your "alot of theory" remark, it's still to me pedagogically sound way to teach linear algebra.
 
  • #27
DavidWhitbeck
351
1
The student can only be as good as their teacher.

And this is very important, and I hope high school students and undergrads are paying attention...

This is a typical type of remark that I would expect from a mediocre student (Jupiter I'm not calling you mediocre btw). Good students assume responsibility for their own education. Mediocre and poor students place that responsibility on the shoulders of their instructors.

You will have many classes where the lectures are brilliant and you will learn what you need to... BUT just as often (or perhaps more so) the lectures will not perfectly transmit the material, and most of the learning is done out of class, by your own studying. If you rely on lectures and lecture notes, you will end up not learning the material in many classes. And that is NOT the fault of the lecturer, that is your fault.

Now I'm not saying you can't throw rotten tomatoes at lecturers that do a poor job, but I am saying that you can't hold them accountable for your education.
 
  • #28
matqkks
280
5
First and foremost it is the duty of the student to be motivated in his or her studies but I FAIL to see what is wrong with the lecturer providing some motivation for his/her module. Maybe they are not confident in using the mathematics or don't know where the mathematics is applied. Well if they cannot provide motivation or do not enough knowledge then what are they paid for. It is not good enough for lectures just to stand in the front and do a one way delivery from their notes.
Moreover what is wrong with lecturers showing where particular fields of mathematics is used?
Theory, numerical examples, applications all help students to learn mathematics.
Lecturers should show where linear algebra is used in cs, ee, me, etc.

Excuse me, but this is so typical of an engineering student. Not only do you have to squish your education into four to five years (unlike law, medicine and science), but you still have the gall to complain that you want the general science and math courses (that form the foundation of your upper level course work I might add!) to be specialized for you to care.

Did you realize that cs majors use linear algebra for different applications than ee majors? And what about chem e, do you think they use linear algebra for the same problems? If you teach classes like that as an applications class then every department would need their own. And that is highly inefficient. Besides you will learn the applications in your upper level classes, else why would you have to take it?

You seem to think that the math prof should supply your motivation for taking a math class. No, you are a college student, you are responsible for figuring out why your department wants you to take that class, and what you should learn from it. You need to be self-motivating.

Now you can solve linear systems on graphing calculators, matlab, mathematica, maple, octave etc you don't need a computational grunt work class either. You need to learn the concepts. So even for that interpretation of your "alot of theory" remark, it's still to me pedagogically sound way to teach linear algebra.
 
  • #29
Jupiter6
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If you rely on lectures and lecture notes, you will end up not learning the material in many classes. And that is NOT the fault of the lecturer, that is your fault.

Now I'm not saying you can't throw rotten tomatoes at lecturers that do a poor job, but I am saying that you can't hold them accountable for your education.

LOL...I pay 30K tuition a year, but I won't hold you accountable for doing your job. No wonder our country is failing in the sciences. I agree motivation is important and without it you will not be getting an engineering degree. Yes there are good and bad profs but I feel you missed my point. I never wrote that egr. profs should teach math for me to care about math. I feel egr. profs. teaching math would produce better engineers. Students learn what they're exposed to. Very few students are going to do problems that they are not told to do becuase they're busy doing other stuff. Some of my best professors who taught say, advanced thermo, mechanical vibrations or dynamic systems, didn't even use a textbook. They had their own systems, own notes, own problems, which is why they earned every penny they make. They actually seemed to care.

The idea of engineering profs. teaching math is not my idea alone. There are plenty of univeristy officials who think this way as well. You will see more and more of it in the future. The phrase "a student can only be as good as their teacher" implies that students are a relfection of their professor. A good or bad professor will produce good or bad students accordingly.
 
  • #30
DavidWhitbeck
351
1
LOL...I pay 30K tuition a year, but I won't hold you accountable for doing your job.

I've heard that snotty comment before. When I was a TA a student walked into my office expecting immediate help when it wasn't my office hours. His rationalization was because he paid 20K a year, he should expect help from me whenever he wanted. I told him that if he paid ME that 20K a year, I would help him day or night, but that was not the case and I told him to get out.

Whether you realize it or not faculty, postdocs and grad students receive a substantial amount of their financial support from grants outside of the university, and much of the money that you are paying the university is not going to them. So stop thinking of them as your indentured servants. They have a duty to teach you to the best of their abilities, but your sense of entitlement is misplaced.

Very few students are going to do problems that they are not told to do becuase they're busy doing other stuff.

And those students deserve poor grades. Just because your friends and acquaintances have poor study habits and don't have the common sense and maturity to make their education their #1 priority while they are in college doesn't mean that they are on the right path.

You notice the few that do take the time to study properly outside of class, and you will see the people that will be taking the good jobs while you are stuck wondering why your Dilbert-esque attitude landed you a boring, underpaid job.

A good or bad professor will produce good or bad students accordingly.

And I'm telling you that is wrong. The best students ALWAYS master the material regardless of the quality of the instructor. Only the mediocre ones will find their performance reflected in the quality of the instructor.
 
  • #31
matqkks
280
5
Of course cannot expect instant help but he can expect the lecturer to reply to emails and keep to appointments.
If maths professors cannot teach engineering mathematics in an engineering context then you will find more and more engineering professors teaching mathematics. It is a lazy way out to use their mathematics techniques (or methods) notes for engineering classes as well as their maths classes.WAHT IS WRONG WITH TEACHING IN AN ENGINEERING CONTEXT?
 
  • #32
Jupiter6
131
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I've heard that snotty comment before. When I was a TA a student walked into my office expecting immediate help when it wasn't my office hours. His rationalization was because he paid 20K a year, he should expect help from me whenever he wanted. I told him that if he paid ME that 20K a year, I would help him day or night, but that was not the case and I told him to get out.

Again, nobody said anything about profs. having to spend unscheduled time with students. You keep bringing up things that have no relevance to the original post.

Whether you realize it or not faculty, postdocs and grad students receive a substantial amount of their financial support from grants outside of the university, and much of the money that you are paying the university is not going to them. So stop thinking of them as your indentured servants. They have a duty to teach you to the best of their abilities, but your sense of entitlement is misplaced.

The only thing I felt I was entitled to in school was a capable professor.

You notice the few that do take the time to study properly outside of class, and you will see the people that will be taking the good jobs while you are stuck wondering why your Dilbert-esque attitude landed you a boring, underpaid job.

I'm not sure if you are referring to me or not, but my BSME came with honors and a fine job.

And I'm telling you that is wrong. The best students ALWAYS master the material regardless of the quality of the instructor. Only the mediocre ones will find their performance reflected in the quality of the instructor.

Sure, 2 out of 30 students will do well regardless of the professor. Hell, 2 out 30 people in any class could have bought the Schaum's outline and taught themselves. If that's really how you feel, I would not want you teaching my class. Every point you have mentioned has cast you as part of the problem...e.g. depend on the textbook, blame the students, who cares about application, I'd rather be researching. For some reason, I highly doubt you pursued engineering in school, otherwise you'd feel differently.

Back to the original context arguement. Students learning linear algebra have no idea what eigen values are used for until two years later. If they were taught the application in conjunction with the theory, things would go smoother becuase there is an end result. The same is true for diff eq. being taught a year before systems or vibes. It's almost like teaching someone how to play piano without a piano in the building. It actually takes longer to teach, because it's just BS in one ear and out the other, and no results. Of course, math professors are interested in job security but that's their problem.
 
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  • #33
matqkks
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Good posting Jupiter6! I agree with all your points on this issue of teaching.
 
  • #34
Peter Hiatt
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I remember a student signing up for a class that was closed. There were similar classes available with other professors but this student tried to BRIBE the guy to get into the better professsor's class. Get real. Better professors do make better engineers.
 
  • #35
epenguin
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Sounds like you want a "Mathematics for Engineers" or similar title book.

I once wrote a spoof book review of an imaginary book with that kind of title which I described as "Another volume in the 'Something For Somebody' series offering second-rate accounts of subjects for somebody not really interested."

And there is something in that.

On the other hand it is true in some of the sciences students are floored by mathematics which is quite easy and which they have even done a few years earlier at school. That is they cannot understand or recognise say problems or manipulations of equations of, say for example chemical or biochemical kinetics when they could easily have dealt with the same equation if it had been excercise 6 of Chapter 7 in their school math book. That is because when they did the math they never thought or were told that what they learned had any application outside the schoolroom or that it meant anything.
 
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