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

 

[jmw]

Lorentz;
dangerous words "I can't think of anything you wouldn't be able to learn on your own" I would think that guidance is always a benefit, the learning from the experience and mistakes of others is as vital in mathhs as anywhere else. It is a cosy thing to think that maths is a neat tidy clinical world full of proofs and with no traps for the unwary.

Do they teach you the limitations of the tools you use? How would you know what to look for and where to look for it? Some things you find out about by accident and there must therefore be some things you have not yet discovered that could be important to you. If you teach yourself how much more vulnerable are you?

We are probably all familiar with the cautions when calculating trigonometric functions on calcultors, but it came as a complete surprise to me to discover that the modern PC could be letting us down with hidden consequences of how it works.

For example, in 64 bit computations:

10[sup]16[/sup]=10[sup]16[/sup]+1

This is from a site which I found following links from a fluid dynamics animations site. An accident.
Until now I was unaware of these quirks. I don't recall that much was ever said about this when I was a student. (Computers were fond of 5-hole punched tape back in those days and I am not sure if the plural of computer was viable then)

ARE FLOATING POINT COMPUTATIONS RELIABLE?

or again

IS A COMPUTER A PERFECT COMPUTING MACHINE?

http://www.lactamme.polytechnique.fr/Mosaic/descripteurs/FloatingPointNumbers.01.Ang.html

The suggestion is that we need to be aware of the limitations of the machines which calculate for us.

JMW

http://www.viscoanalyser.com

Eng-Tips: Pro bono publico, by engineers, for engineers.

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

 

[Lorentz]

Hi jmw:

You've raised some interesting points in your post that I will address later today when I have more time.

For now though, I will make the comment that past generations of engineers produced impressive results using only slide rules, so I am not greatly troubled by computers that consider 10^16=10^16+1.

(BTW, how did you get superscripts into your post?)

 

[CajunCenturion]

Click on the link at the bottom on the Post Window, "Process TGML", and it will show all of the available tags and what they do.

 

[mloew]

Lorentz,

Please see point 10 in the FAQ that many members list in their signatures.

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.

 

[jmw]

Good points about slide rules, though I worry about all those computer modelling experiments run as screen savers because of the complexity of the models and the need to run millions of variations at one time.

Why? because the computer has freed us to embark on much more complex calculations than ever before, computations that are far more sensitive perhaps, and we are coming to "trust" computer models as if they were gospel.

I noted that, on the web site that I referenced, different computers can have different errors. In multiple interdependent or iterative functions the potential for error must be increased.

The estimation of errors is very important to engineers but I wonder if we stop before we consider the computer? It would be interesting to know what the NEL have to say about it in their upcoming seminars.

http://www.nel.uk/eventsarticle.asp?ID=108

And I've just now remembered that many process instruments depend on micro-processors for some fairly complex calculations.

Indeed, many modern process instruments are only possible because of modern electronics.

OK, I suspect that in many instruments the magnitude of potential error is probably way below the instrument measurement accuracy but it would be nice to know if we should worry or not as in some areas, the integrity of the software and the calculations is of paramount importance; software used for pharmaceutical applications, for example, fly-by-wire computers etc. (let me just cancel my flight while I wait for some guidance).



In process measurements, we know and expect instruments to have errors and to fail. In critical applications we can reduce the error by running identical instruments in paralel and we cross compare the results.

JMW

http://www.viscoanalyser.com

Eng-Tips: Pro bono publico, by engineers, for engineers.

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

 

[CanEngJohn]

jmw writes

"and we are coming to "trust" computer models as if they were gospel."

Yes. I once had to argue with a designer for two hours that his computer FEA model was wrong.

The FEA was telling him that a square supporting weld was stronger than a circular weld in a torsional fatigue application and that the parent material would fail first.

Reality check anyone? Maybe your model assumptions were wrong?

 

[CajunCenturion]

"and we are coming to "trust" computer models as if they were gospel."

Anyone see the movie The Net

 

[Tobalcane]

<<< The question is what if you did not study advanced
math in your colledge term.
If your professors taught more practical topics would
you learn the advanced math on your own??>>>

In my opinion the last thing on most college students mind is to learn advance math on there own. When you were eighteen, nineteen, or twenty, were you thinking of advance math? Even if they learn on there own, the understanding would be at a novice level or lower. I feel that to truly understand advance math and apply it in the engineering classes, the college student has to learn it from a professional. Where the student can ask question directly to the professor and to learn the little tricks of the trade. Advance math is like trying to learn auto mechanics. Sure any book can show you how to do a few things, but to truly learn something so that you can repair or fix a car you have to learn from a professional. The professional will teach you what tools to use and how to use them. The same goes for advance math. The professor will teach you what tools to use and how to use them to derive equations and solve problems. Advance math is just that, tools to be used in your engineering classes to solve problems. With out the tools, the job will be very difficult to do.

Well time to go home…

Go Mechanical Engineering
Tobalcane

 

[Lorentz]

Hello All:

CanEngJohn I gave you a star for your last post because it contains a most valuable example:

I once had to argue with a designer for two hours that his computer FEA model was wrong.

The FEA was telling him that a square supporting weld was stronger than a circular weld in a torsional fatigue application and that the parent material would fail first.

This shows the two most dangerous pitfalls of an unbalanced engineering education that has too high of a math content:

1. Though the designer in question was highly trained in math his knowledge of "weld characteristics" was inadequate. Because of this, he could not be trusted to produce a safe design.

2. He argued with you because (like many engineering grads) he assumed that his professors had taught him the most important part of engineering i.e. the math, and he was therefore equiped to figure out the rest on his own.

The designer in question reminds me of a young electrical technologist who almost killed himself at his first job after graduation. The young man had done very well in his classes and was willing and eager to undertake any task given to him. However, his classroom education did not prepare him for work in an industrial environment and while attempting to set up test equipment on live switch gear, he created a ground fault and was nearly blinded by the resulting flash. He left his job soon after for another that allowed him to work at a desk (I think this career move probably saved his life).

It is because of examples like these that I cannot agree with the view that:

It is the job of engineering professors to prepare you for the toughest subjects so the rest can be self taught.

This lets the universities (and colleges) off the hook when it comes to teaching the things engineers should know to protect the public.

 

[Lorentz]

Hello jmw:

I was so pleased with CanEngJohn's example that I nearly went home without discussing your post.

The point I wanted to address was your statement:

I would think that guidance is always a benefit, the learning from the experience and mistakes of others is as vital in mathhs as anywhere else.

I agree that guidance is valuable, but it is also important to examine both the motives and competance of the people who claim to be providing guidance.

For example, life insurance salespeople will try to convince you that they are to be trusted as finacial advisors, but of course they will try to sell you the most expensive policy possible. And they will discourage you from any investments at other institutions since that would not generate commisions for them.

In much the same way universities try to sell as many of their courses as they can. In an earlier post we learned that two semesters of skiing (or other gym) could be counted as credit towards an engineering degree. To me this is an example of how universities squeeze more dollars out of their students by forcing them to take unnecessary extra courses.

And, as maui's post of June 17 points out, there is considerable question as to whether the average engineering professor is even qualified to provide guidance.

Going back to the automechanics example, a professional can train you how to use specialized tools to fix a car. They can only do this if they have extensive knowledge in two areas:

1. What tools are needed, and how to use the tools.
2. How the different automotive systems function and how problems are diagnosed and repaired.

In the case of engineering education, the professors are, at best, addressing the first area.

 

[jmw]

I think we can all agree that education isn't what it used to be.

Education in the UK, and many other places, has lost the plot and for a variety of reasons. Not least, the education system is geared to delivering certificates in return for attendance and fees. Money.

I recently attended a local college for some business start-up courses and was amazed to discover that the final paper is reviewed by the course tutors and given back for corrections if you are likely to fail. In fact, they will practically write your paper for you if you fell asleep too often.

At least in the UK, they are trying to breath life into the aprenticeship schemes again. Work experience is part of many university and college courses where students are "placed" with different industries for learning real skills in the real world.

For those with the gift and the incentive or interest to teach themselves maths, with or without guidance, if it works, fine; but not all people, however good they ultimately are as engineers, can learn without expert guidance.

The best learning environment for an engineer is on the job, especially if mentored by a first class experienced engineer. This also sets us up to know that being an engineer is a lifelong learning experience.

All we can expect of the eucation system is that it teaches student how to learn and enough basic tools for the outside world.



JMW

http://www.viscoanalyser.com

Eng-Tips: Pro bono publico, by engineers, for engineers.

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

 

[GregLocock]

I disagree that you can't teach yourself advanced maths.

To pick on an obvious example, at uni we covered the basics of Fourier series analysis, by hand calculation. Hah, neat, I thought (and easy).

In the years since I have taught myself enough signal analysis to be involved in specifying signal analysis equipment from the ground up, writing signal analysis programs for use in production environments, etc etc. I wouldn't claim to know /everything/ about frequency analysis, by any means, but I know several hundred times more about it than when I left university. No one 'taught' me as such, it was all from books and thinking.



Cheers

Greg Locock

 

[Lorentz]

Hi Greg:

And it is entirely possible that you may have more current knowledge then some students who are being "guided" by burnt-out tenured professors.

In my final year as an undergrad, I took a course in sample data control systems where the professor used only his hand written notes (no text book) to teach us about Z-transforms and zero order holds and such. He also taught a technique for checking system stability that involved the evaluation of high order determinants. It was so awkward, I was convinced you would be better off just solving for the system poles directly.

A couple of years later, I took a course in digital filtering taught be a professor who DID have a current text book. He referred to an optional section which explained a much simpler stability test - about as simple as performing synthetic division.

At first I was glad to see how the science had advanced so quickly, but I became outraged when I checked the references to see when the new test had been developed. It turns out that the control's professor had been teaching a method that was 15 YEARS out of date! I assume that the notes he used were the ones he took when he was completing his own Ph.D.

Whenever I hear the argument that engineering professors only have time to teach the math so that their students will then be able to teach themselves, I think of that professor and wonder why HE was not able to teach HIMSELF.

 

[RDK]

Threads like this one miss the real reason for attending university.

It does not matter what course of study you take, engineering, business or law for example.

The purpose of an engineering education is not to teach you to be an engineer. The real purpose of an engineering education is to teach you to think like an engineer. Change engineering to law or business in the above sentence and the same logic applies.

You can never be taught everything. All you can be taught is how to think your way through typical and atypical types of problems that you will face in practice.

Engineers always think in terms of if-then-else. It is a very linear and logical thought process.

While you may get some useful knowledge along the way in your studies and you may acquire some useful analytical tools as well what is happening to you at university is not the transfer of knowledge from your professors to you but a moulding of your thought processes so that you will think and react like an engineer when you start working. Taking advanced math courses is a good way to do this.

Do you really expect that you will be sent back to school every time technology changes or to you expect that you will go back to first principles and work your way through the new technology by thinking like an engineer?

In my university education I majored in hydrology. I actually worked in this field for 6 months and then started field construction. I have been there for over 27 years. I was not trained to be a structural engineer but have done structural calculations (usually as a sanity check on the designs of others) I had little training on electrical design but can discuss these issues with electrical engineers and not embarrass myself too much. I was never trained in mechanical design but can do heat load calculations, again as a sanity check on the designs of others.

I can do this because of experience and by returning to my basic roots as an engineer and applying engineering logic to the problem and using first principles.

Once you think like an engineer the real teaching of becoming an engineer starts and this is after graduation.

In Canada to become a pharmacist takes 30 days work experience after graduation. To be a lawyer takes one-year post graduation experience to be an engineer takes 4 years.

Where did you actually expect that you would become an engineer? At school or out in the trenches with mud on your boots?






Rick Kitson MBA P.Eng

Construction Project Management
From conception to completion

http://www.kitsonengineering.com

 

[GregLocock]

When did I become an engineer?

Hmm.

That is a fascinating question.

Not when I was making steam engines on a lathe at home.

Not when I was fixing my motorbike

Not when I was attending lectures at uni.

Not even when I was doing labs.

I think the defining moment for me was when I was in business with a friend of mine from university, and basically I realised that if I did not change the machine then nothing would change. I was 26 then.

Ever since then I've preferred to smash up the status quo, and try to redesign things from a fundamental assessment of the requirements.



Cheers

Greg Locock

 

[HgTX]

Various thoughts:

1. I went to two different engineering schools. The first didn't require differential equations for all engineers (though my guess is it did for certain majors). The second did.

In civil engineering there's only one diffEQ that I've ever seen. I can't see sitting through an entire class just to know how to derive that one equation--especially because even if one doesn't know how to come up with it, one can certainly verify it.

2. On the other hand, the second program discontinued dynamics for CivE's right after I took it. When I think about it objectively, I guess I really can't see much of a use for it, but for reasons I can't put my finger on I don't like that deletion. Maybe I'm just being sentimental. I don't think I've used a thing from it, either on the job or in grad school.

3. My second-year calculus classes were cross-listed between the math and engineering departments. They were specifically meant for engineers--math majors took different classes. And yet the profs of these supposedly engineer-tailored classes couldn't always tell us what real-world problem the math they were teaching us could be used to solve.

4. Understanding basic calculus is really handy--how to derive the various equations, rather than just "plugging and chugging". However, it's really easy to get through calculus classes without any of that problem-solving understanding, just use each formula as a black box for a particular type of problem. So I really don't think a math course is where you want to turn to learn creative problem-solving.

5. I agree that more numerical analysis, modeling, etc., is a good idea. Knowing the math to do all those computery things by hand doesn't help you unless you run the occasional hand calc to check, and that's not doable for many real-world problems. On the other hand, knowing how not to do something really stupid in setting up one's model? Priceless.

Hg

 

[makeup]

Maths is a lovely subject, it is key to everything that we do no matter what it is. If you cant quantify it mathematically then it has no purpose. The problem is that most of us are employed by people who for some reason ask for a degree and when we get there we find that we dont use anything that we have spent 4-5 years learning. So we tend to get this idea that we dont need it. Another point is I totally agree that computers do it easier but they also rely on humans to input data and if you cant reason with the result then youre stuffed. Remember not all results are in a figure format, some are symbolic or may involve derivatives that can only be solved by using alternative methods. So in my view if you cant handle maths you cant deliver a completed job.

 

[2dye4]

The key to this question is can you make a profitable
career in engineering without knowing advanced math.
Of course most people can have wonderfully productive
careers without knowing the basics of how things work.
But to deny the central neccesity of advanced mathematics
for engineering is folly. Just because most of you do not
use it in your jobs does not make it a faulty benchmark
for entry into our profession. Please examine the history
of development of some our greatest achievments and you
will find math at the heart. On the other hand if you
do not think you need the advanced math you probably
don't

 

[Lorentz]

Hello Everyone!

I know I had said farewell in another thread, but I found something so juicy at

http://www.nspe.org

that I just had to fit in one last post. Check out:

http://www.nspe.org/forum/frames.asp?ResponseID=6982&TopicID=10&ModeId=0

and read the predicament of one Mike Chaffin, a widower with children and a B.Sc. in Math who is considering transitioning into either engineering or accounting. He meets considerable resistance and announces his final decision in his 8/20/2004 post "Not looking good":

"After many months of inquiry, I have come to one conclusion...I should not get involved in engineering...accounting will be my path.

Engineering degrees and laws have absoutley no logic or cohesion in their applications. So many laws, so few choices.

I really wanted to get involved in this field, but I cannot in good concience put my and my childrens future in the hands of such a tenious and uncertain field.

I might add that the professors that I spoke with did not help much and seemed to actually oppose my entry into their programs. They seemed to despise my BS in math, and told me that I would have to take all my math classes over starting with pre-calcalus. After working with mathematical applications and statistics for 6 years, I cannot conceive that they can take this approach. I basically found that it has more to do with my tuition fees than knowledge. They want me to take my classes over just so the univeristy can collect more tuition, it has nothing to do with educating students!!

Boy, if everyone that wants to get involved in engineering gets the treatment that I have gotten, there will be no engineering graduates in the years to come.
Mike"

And with that folks, I wish you all Goodbye and Good Luck!!

 

[btrueblood]

Greg,

I got my MS in Aero engineering years ago. To get it, I had to take 3 semesters of "Applied Math". On more than one occasion during those semesters, I'd throw up my hands, and refuse to do the homework set, deciding I'd rather take a "B" grade (by getting a lower score on the final) than study something I'd "obviously" never need to know again.

I've had quite a few occasions where I got proven wrong. Memorably, I never studied Bessel functions (went out drinking beer the night before the midterm on that section). Absolutely miserable score on the midterm, but passed the class with a "B". About 9 months later, my first job out of school, had to analyse the combustion stability of a rocket engine, using guess what kinds of functions to model the acoustics? ARGGGH! (And I'd sold the damn textbook, at a lousy discount, to buy more more beer too!).

You just never know what you're gonna see...

Ben T.