How much math(s) do we really /need/ to learn? 23

[GregLocock]

This is a continuation of a previous thread that was going OT.

At university something like 15% of my course was maths. It was the hardest part of the degree for me (and I was in the top 2-5% in maths at high school).

Since this is an international forum I guess it complicates things, but I'd like to get an idea of how much maths people (a) think should be taught in, say, a decent mechanical engineering degree, and (b) of that what they actually use, and (c) what they wish they had learned but didn't (d) what they had to learn but wish they hadn't.

Here's my (non complete) guess:

(a)

Calculus to say the level of double integrals and surface integrals, Taylor series and so on.

Fourier Analysis

ODEs, preferably a bit more than I did

PDEs, to a very simple level

Stats, sufficient to design experiments and test hypothesese

Complex numbers of course

Trig - I wouldn't get too hung up on trig, just the basics seem enough to me

Matrices with hand worked examples up to say 3x3, or 4x4, inverting, transposing, adding and so on, but not Gaussian elimination or any of the other tricks we needed before PCs

Vector maths (I didn't do enough of this)

Laplace, to a very basic level.


(b)I've used all the above, to some extent, since leaving uni.

(c) Green's function, Bessel functions, more Laplace, more statistics

(d) Lots of matrix stuff and numerical methods. Some of the calculus.

Cheers

Greg Locock

 

[mloew]

Greg,

Do you count numerical methods and optimization techniques as part of math or engineering?

Best regards,

Matthew Ian Loew
"I don't grow up. In me is the small child of my early days" -- M.C. Escher

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[HydroScope]

Well I'm just at the end of my course, All of the above certainly rings a bell. So I guess I can say I definetly did enough of maths and beleive it should be cut down, since you have not meantioned anything above that I haven't heard of, but I may not be completely co-herent in. I am confident that if my career took it on I need to use that maths I could do it. I have a different opinion, I feel most universities are concentrating on too much engineering management!! and push aside the technical aspect. for example in the past mech. eng. students would do all maths over 2 years, we did our over 12 month, Adv. Kinematic and dynamics where core subjects, now electives. In many subjects I did there has been a lot of evidence that particular subjects(topics) are crunched up and not taught well for the benifit of also cramming in the "management" subjects, which in my opinion is a load of #$%$%@#$%$@#%#$.

for example I just complete a subject titled "energy applications". This included "compressible flow", "heat exchanger design" and "turbomachinery" all in one!!. past years would have had 6 cr points allocated for each topic. i.e one subject for one semester for each. What benifit does that have for a inspiring engineer!! some how the justify it by incl. engineering management topics. Engineering communication, Engineering and society, management, technology asessement(thier are others). I learn't very little out of doing these subjects, what I took away (not that useful) should have been condensed into one subject or better still not given at ALL!!

Thus maths and other techinical stuff, some you may never use some of it in your career, but when you got an idea, or somebody tries to sell you a "great idea" and you want to discover whether it will work and what all the limiting factors are. I'ts nice to know you once did something that difficult at uni. and you can figure it out. management skills for engineers can be picked up in the work place as we go. I know my point is valid here as too many students have complained about the manangement aspect, one subject I wrote above is now out of the course with more to follow. But thats not particularly comforting to me whom had to go through it and had other subject suffer from it!

 

[2dye4]

In my opinion no time spent learning math is wasted.
A very important topic now is numerical methods
mainly because you can understand mathematics more solidly
from programming computers to approximate equations.
This is fundamental to the descrimination between a
technician and an engineer. An engineer can be presented
with a problem say of vibration. Then go to his PC and
program a simple application that solves the boundry value
or optimization or convolution problem that gives new
insight into the problem. The field of optimal control
systems will be popular in the future do the embarressing
riches we have in computer power. Advanced math will be
the ticket of entry.
Don't forget it was math that was largely responsible for
winning WWII.

 

[rbcoulter]

In the U.S. you can get an engineering technology (ET) degree that is basically an engineering degree with less math. It is even accepted in most states as sufficient education to qualify to take the PE exam. So I see no need to remove the extra math in the engineering programs since anyone that wants to take less math can get the ET degree.

In the US, last time I checked, all engineering students must take three semesters of calculus and one semester of differential equations.

 

[COKA]

I it not about how many math courses you have to take. It has to do with problem solving skills. Some math courses require different thinking then just basic calculs. If you are "good enough" to get "A"s and "B"s in all your math courses, chances are that you have developed a problem solving skill that will be applied to your job related problems. Over my University years, I developped a method for every math problem: define the unknown, define what known variables are associated with the unknown, brain storm, and do the calculation. A lot of the times I had to go back and re-do the calculation part. What am I doing at work? The exact same thing! Math is the best thing that can happen to any engineering student!

Coka

 

[ischgl99]

For mechanical engineering, I had to take through calc 5 for my degree while all the other engineering disciplines stopped at diff eqs. My complaint with the math was it was too much of memorization learning and not enough application based. I think the math classes can be combined better with numerical methods to give the engineers a better understanding how how the math is applied to real world applications.

Mike Bensema

http://www.dutchmenservices.com

 

[JoeTank]

Mr. Locock,
I think your first guess is about right.


Steve Braune
Tank Industry Consultants

http://www.tankindustry.com

 

[moltenmetal]

In Canada, engineering is still a four-year bachelor's degree. There is too little time to cover all the truly necessary subject matter without cutting something out. And it DEFINITELY needs to be at least one math course, probably two. All that effort just to get us to the state of the art in math circa 1800 is just not time well spent!

Teaching a bachelors-level engineer a good portion of the math I was taught is a totally fruitless exercise. If you want to teach analytical and problem-solving skills, you can do it in a far more RELEVANT way than by beating them over the head to teach them math skills rendered irrelevant by modern computing technology.

What students need is more exposure to setting up mathematical models- the equations and differentials- determining the appropriate boundary conditions, and then applying the correct numerical methods to solve them. Too much effort is spent to teach the tricks of analytical integration. If I EVER need to use the method of Frobenius again, or to find the inverse Laplace transform for a convolution of hyperbolic functions again, or to use the error function again, I can talk to a mathematician and get the advice I need, just like I would seek out the skills of a specialist in any other area of my practice!

Students also need EXPERIENCE. Co-operative experience should be MANDATORY for all professional programs, not just engineering. And most important of all, they need direct experience with DESIGN, with the mentorship of practicing professional engineers rather than just academic professors. Courses provide information only- PRACTICE is what turns that theoretical information into KNOWLEDGE. Skills which are not honed by practice will rust and blunt with dis-use.

 

[Comcokid]

Any decent Engineering BS degree needs the math.

A) Part of the purpose of a BS degree is as a stepping stone to a MS degree, which is then a step in getting a PhD. Advanced math is necessary for any advanced work or research.

B) If you leave school with just a BS, it is true, when you get out of school you will most likely never encounter a use for most of the math you had to take. But then again how do you know just what kind of math you will need during your career?

Today, I would find myself very challenged to do some simple calculus or differential problems. But, having been exposed in depth to the principles, I have no problem explaining to a tech why a fast voltage transition or non-linear junction has harmonics (Fourier) of why FM or PM modulation at a certain modulation index does not work (Bessel).

I would like to get a Masters degree someday, and I know it would be an uphill climb to become proficient at the math again. But at the same time I know the necessity to have the math as an important part of the education.

 

[Lorentz]

Hello All:

Back in the dark ages when I was studying for an EE degree, my professors filled the blackboards (they were black in those days) with integrals and gradients, matrices and transforms, circuit diagrams, block diagrams, pole/zero plots, and ... well you get the picture.

However, there was never any discussion of electrical safety codes, standard construction or manufacturing practices, or even an explanation of the principles of fluorescent lighting (as I said this was the dark ages). My professors seemed to assume that these "minor" gaps would be filled in by senior engineers who were eagerly waiting to mentor a fresh group of EE grads.

On my first job after graduation, I found that most of the senior engineers were busy in "project management" and left the messy work of mentoring to experienced electricians who had been moved in from the field. The electricians reviewed and approved the drawings produced by the rookie EEs.

I came to the conclusion that my professors had focused so heavily on math because it was easy and cheap to teach, and because it was where they excelled, rather than because it was essential to the training of an engineer.

Maybe things have changed since my undergraduate years. I hope so, but many of the postings in this forum lead me to think that it is "business as usual," and employers hire new engineering grads in spite of all their math training rather than because of it.

Have a good weekend everyone!

 

[PSE]

Math provides knowledge of the science behind the engineering, necessary when you truly have to probe deeply into a problem to look for subtleties. The "practical" side of engineering seems less taught in the classroom and more so by those first months/years on the job where the real world intrudes on perfect theoretical models.

I am not sure that there is one answer to Greg's post as the amount of math used by someone on the job changes with the nature of the job. I have used everything from simple geometry and trig, through statistics, and higher end calculus (multi-dimensional, complex and fourier). It all depended upon the job and problem at the time. Is too much math taught? I do not think so. While "unused" tools can get rusty, at least you will have it available if/when needed. Might need a little cleaning up though.

Regards,

 

[davefitz]

I think the math courses serve several good purposes, one of which is to give the student sufficient tools to allow him or her to prove to themselves that the engineering formulas and methods later learned are based on firm foundations and are not simply methods learned by rote and adopted by tradition.

One problem with the one-size -fits all math courses is that the students are taught the mathematical basis of all engineering and science avenues of study, and they are not tailored to their individual paths of study. For example , a civil engineer does not need the same course content needed by an EE or nuclear Eng or a physicist. I think at least half of the math curriculum can be safely skipped if it were tailored for the individual engineering curriculum.

 

[moltenmetal]

Just to be clear: eng students need math, and lots of it- they just need at least one or two courses worth REMOVED from the course of study I took. There's plenty of stuff they need to know MORE than how to do advanced analytical integration.

 

[SLTG]

I think math is pretty important in engineering degree. I didn't use any of it to be honest, but It tought me on how to think logically and solve problem effectively.

SLTG

 

[buzzp]

As mentioned, the math is part of the learning process. If you understand the math and develop your understanding of some system or process based on the mathematical model you will develop a great intuition for the project. Granted, the math adds confusion but in order to develop the understanding in your field you must understand the relationships involved. Relationships have traditionally been shown using math (I don't know of another way). A lot of careers paths may not require mathematical calculations of such magnitude (if they do you can get out your HP).

Someone already mentioned that there are programs developed for teaching using less math, in the eletrical area, this is generally the BSEET (electrical engineering technology).

I think college teaches you the basics but more important, it teaches you to work through problems in an efficient manner using physical relationships and find solutions to difficult problems - this is engineering.

 

[BML]

In my opinion, the math is needed. I took math through Calc IV, Diff Eq, Linear Algebra. I needed one more class to get a minor in math. Do I use it now? Not much. But as a few people mentioned, it is part of the learning process.

Someone else mentioned engineering being a "4-year degree". I took 5 for mine. The engineering degree requirements at my school automatically started with at least 6 more semester hours required than a standard degree (134 vs 128). Some went as high as about 140. The point is that we need to take the time to educate and train people the proper way (theoretical, application, and hands-on) rather than try to spit out graduates in 4 years.

Just my $0.02.

 

[CajunCenturion]

I think that purpose of most Engineering programs is preparation. Preparing you to meet the challenges that you will come across during your engineering career. Some of the challenges may require the use of advanced math, and so it is the university's responsibility to help prepare you for that by, at a minimum, exposing you to the advanced maths. You may go through your life never using it, but the student who sat next to you may be using it every day.

 

[CanEngJohn]

About 15 years ago when I was working through first year I remember looking ahead at the loads I had and cringing. I was heading into 4 full year math courses plus two stats and numerical methods and a 4th year course which was 50% mathematics behind design. (I wound up taking an elective on compressible flow that was even more math).

All worked out I spent 1/3+1/4+1/5+1/8 of my degree dealing with pure mathematics. (This worked out to roughly 20%.) And I still have hit mathematical concepts which I did not learn in those courses (Anyone want to know what the symbol is for a 4 dimensional Laplacian?). What it did do was allow me to understand modeling concepts so well that it is easy for me to create simple and effective models when I need to and justify the assumptions. It also threw enough homework at me to learn how to time manage at least to a fundamental level.

The key thing to remember though is we do not learn mathematics at University because Engineers use mathematics. We learn it because we might need a concept down the road and when that happens we have to have some experience to draw on in order that we may be successful learning the concept at that point. Arguably 90% of the knowledge we need to be successful comes post degree. But 75% of the tools, methods and thought processes we need to be successful come from our education (and not just in school). In the case of Engineers, Mathematics is probably one of our best learning subjects.

 

[Gauss2k]

It's a little off the subject but; Personally I see my degree as a place where I learned how to learn. They throw so much stuff to learn as fast as possible (and several times, we know it will not but usefull in the future) that we develop the ability to compute the infos very fast and look for the missing datas.

Later, on the market, when we face something that is not familiar, we can seek the needed information and learn it fast to go through almost anything.

We can't expect them to show everything or just what every individual student need...