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

 

[QCE]

Just because a software package can solve a problem for you doesn't mean you shouldn't understand the math concepts being solved for you. I work in the field with many techs that can operate generators and even test them but ask them how the thing works or what the test is doing and they have not clue or way to express the concepts involved. Pushing the button and getting a number is the only thing most understand.

Math is essential to physics, physics is essential to engineering! Follow the logic?

 

[Maui]

I couldn't help but smile when I read several of the posts above. It appears that several of the engineers out there have a strong disdain for mathematics. And I've seen this both in engineering majors and non-engineering majors alike. Math, in general, is not a subject that everybody looks forward to studying. Most students take those courses in partial differential equations and numerical methods because they are required to take them in order to earn the engineering degree. Others look at mathematics simply as a tool for them to use so that they get the design right, or to determine the correct loading distribution, etc.

The reason that specific math courses are required as prerequisites to taking junior and senior level engineering courses is so that the professor can concentrate his time and effort on teaching you the actual engineering concepts without suffering the additional burden of teaching you the mathematics he needs to use to get there. Several of the above posts cite the fact that engineering professors are not grounded in the "real world", and don't teach students from practical examples that are encountered in an industrial setting. This is, for the most part, a valid argument. The reason that they don't provide such examples is that the vast majority of tenured engineering faculty members have never worked in industry. And they can't teach you what they don't know themselves. So instead they try to teach you what they do know. And this usually revolves around the type of work that they have done in their research. And more often than not this involves the use of some in-depth mathematics.

There is an analogy between the way that I view the mathematical concepts that I have mastered and the ability to speak a foreign language. How well you understand the language determines how well you can communicate your ideas to others. If you don't speak it very well, then you will have a hard time getting your point across to someone else. If you are fluent, then communicating your concepts is much easier.

As an example, over 18 years ago I needed to run an analysis to curve fit some experimental data that I had collected. Since I had to do this several times and fit certain data sets to different functions, I decided that it would be a good idea to write a program that would allow me to type into the program, while it was running, the symbolic form of the curve that I wanted to fit the data to. Then I would enter the data, and the program would display the curve fit. I wrote this program to be general so that it would be able to accept just about any functional form. And it worked very well. Most people today would simply buy a software program to do this, and not have any understanding of how it generated the resulting curve. But these types of software programs were not widely available (if at all) back then, so I had to construct it myself. Without a thorough knowledge of the necessary mathematical concepts, as well as the programming language, I wouldn't have been able to do this.

So what math courses do you need to study in order to earn your engineering degree? That depends upon the engineering discipline. But you can't depend entirely upon your engineering professors to decide this for you. Teaching is usually not their top priority anyway. Their main responsibility is to bring grant money into the university. If they do this part of their job well, then they could be the worst professor in the college, but the Dean will do nothing but praise them. Then again, they could be the best teacher you've ever had, but be denied tenure because they weren't able to attract enough grant money.

Maui

 

[Lorentz]

Hi maui!

There is a lot of reality in your post, just as there is in "I. Asimov" which I think all engineering/science students should read.

BTW, in my early years I was a math/science nerd. I don't have disdain for math, I just feel that there is so much more out there to learn. For instance I think my own EE education was deficient in courses from your specialty.

Have a good weekend everyone!

 

[Tobalcane]

My daughter is three and half years old. When she grows up, I would like here to be well rounded and well informed individual. I feel that is what college is all about. If the university is the parent and the students are the kids, the university wants there kids to be well rounded. The kids may learn something that they think they don’t really need, but like any good parent would say “be prepared for the future”.

In order to understand engineering concepts one must understand physics. To understand physics you have to understand the math. If math is the foundation, then a person who is well rounded in math will have a strong foundation. Even if you think that the math did not help you, all of the engineering concepts you are using now were derived using advanced math (calculus and higher).

When my daughter goes to college, I will tell her to learn as much as possible so she can be prepared for the future.

I think the discrepancy lies on who would benefit from the advance math. Technicians would not benefit from advance math. Designers would not benefit from the advance math. Analysis would benefit from advance math. People on the cutting edge of engineering concepts (not design) would benefit from advance math. So depending on the job you got when coming out of engineering college and forward will dictate on how much math you will be using. But, the bottom line is that the university made you a well rounded engineer so that you can tackle any task that you are charged with. If you find your self doing analysis or cutting edge engineering concept, you have the university to thank for the foresight.

Well time to go home…

Go Mechanical Engineering
Tobalcane

 

[GregLocock]

I disagree with the thrust of your argument. I can (and do) teach myself maths, just as I can teach myself electronics, or thermodynamics. The university course should get its graduates to the point where thay can learn for themselves, NOT spoon feed advanced maths down their throat, to the exclusion of a thorough grounding in some other engineering related field.

I'm not saying that we shouldn't have had maths courses, I just had the feeling that there was an undue emphasis on tricky, pure, maths, at the expense of other things which might have been more useful.

Cheers

Greg Locock

 

[Tobalcane]

<<< I'm not saying that we shouldn't have had maths courses, I just had the feeling that there was an undue emphasis on tricky, pure, maths, at the expense of other things which might have been more useful.>>>

In a way I do agree with you, but at the same time being well rounded in math (even knowing the tricky pure math) for a young student who will be taking some intense engineering class (and if the student decided to go after their masters later) where they have to “derive” key equations in class and on exams will more benefit than hasten. When the professor starts deriving equations (they might use tricky pure math), the student has to know the math beforehand or the student will miss an import point of how the final equation was developed. That is probably why some engineering colleges are going to a five year program where the college is tacking on some real world design classes, but even there the emphasis is still have the students prove their engineering concepts mathematically. This is something like a prelude to a masters program.

Personally, the class that should be cut out should be some of the “non-core” classes such as art, psychology, and maybe gym and put in more “hands on tech/hardware” oriented classes. Something were the student can put down their calculator and pick up a screw driver, break a machine down, understand, and then put it back together.


Go Mechanical Engineering
Tobalcane

 

[Lorentz]

the class that should be cut out should be some of the “non-core” classes such as art, psychology, and maybe gym

Things must have really changed since my undergrad days, I have never heard of "gym" classes in any engineering program. Is this now common?

 

[Tobalcane]

Well in my undergrad we had to take one or two gym classes, made no sense. For me I took two semesters of skiing.

 

[Tobalcane]

Come to think about it...I was able to get away with taking gym as an elective vs a requirement.

 

[buzzp]

I had to take a year of gym and all the other BS elective courses. These are a waste of time for sure.

 

[Lorentz]

I find these "gym" requirements to be incredible.

Electricians and technicians sneer at university graduates who have never heard of a "hi-pot" test (and would probably kill themselves without the tradespeople to show them how to safely test a high voltage cable), yet two semesters of skiing (or equivalent gym courses) are considered an essential requirement to the training of engineers.

Do universities also require students in medicine, law, dentistry etc. to fill a gym requirement?

 

[GregLocock]

Here's my classes from the first two years

mechanics
structures
maths
electronics
electrical
materials
thermo
surveying
soil mechanics
drawing and design
comms theory

Third year

mechanics
structures 1
structures 2
surveying
maths

Not much fat to cut out, is there? There was an optional non-examined course in the first year called the "engineer in society" which I ignored.


Cheers

Greg Locock

 

[2dye4]

You can not learn enough in a engineering program to
be effective when you graduate. It is the job of
engineering professors to prepare you for the toughest
subjects so the rest can be self taught.
It is argued that there is no application for the math
that is taught in engineering courses.
The recent autonomous robot challenge sponsored by
DARPA is an example of new applications of engineering.
How much math do you think the applicants to this contest
used in their algorithems to guide their vehicles??

You must learn the common knowledge on your own.

 

[Tobalcane]

Lorentz,

I think in most undergrad (bio med / doctors, pre-law / lawyers) degrees you have to take electives and one course would be gym. Other courses would be art, photography, history…etc. I don’t know any engineering programs that did not have any electives. That is why my position is to cut down on electives and put in tech/hardware classes instead.

On a word on skiing, skies are engineered too; there are different shapes, stress, bending moments, coefficient of friction, coefficient of thermal expansion, materials…etc. A skiing enthusiast who first got their spark from a ski gym and then graduated from an engineering college would have the potential to design better skis for the sporting world; just because on an off chance the person took a gym class.

2dye4,

On the autonomous robot challenge sponsored by DARPA, I am sure that system from the chassis down to the circuit card assembly was analyzed mechanically. Some wear along the line each part was thoroughly analyzed and tested to guarantee that it can perform under the extreme conditions. So, there must have been a mechanical engineer who looked at the random vibration, both conduction and convection thermal issues (radiation if the CCA was in a hermetic seal unit), dynamic stress, fatigue analysis…etc. All of this would have used advance math in the software and hand calc to correlate. This is standard for military application. The government has very intense specifications that the defense company has to demonstrate. And the way the defense company demonstrates (before initial build) is through mind blowing analysis with a lot of advance math.

 

[ischgl99]

<<I had to take a year of gym and all the other BS elective courses. These are a waste of time for sure.>>

I took German in college for some of my electives, graduated and worked for a german machinery company, spent a year working at the factory in Germany and am now fluent. This elective separated me from all the other candidates and got me the job. They are not all BS.

The more practical experience taught in collge the better, even for those going onto grad school. A good example of what should be taught is this

http://emat.eng.hmc.edu/classes/e119/minilathe.htm

Mike Bensema

http://www.dutchmenservices.com

 

[Lorentz]

You must learn the common knowledge on your own.

Well, two things I'll say about that:

1. The "common knowledge" is often what the public expects engineers to know in order to protect life and property.

2. A lot of that "common knowledge" is not easily derivable from pure mathematical analysis. It is often the result of years of accumulated experience and testing, plus analyses of past failed designs (some of which were disasters).

I think that both engineering students and the public have a right to expect more from engineering professors than just math courses.

 

[2dye4]

Lorentz:
I agree with both of your statements.
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??

 

[flamby]

I will differ and say it is not the job of professors to prepare you. Their job is to guide and help you to prepare yourself and if you don't, you fail more than they do (many students do fail). Most of the learning, in college or out of it, is a person's own achievement though there are many aids, friends, teachers and mentors.

Our colleges & universities taught us the art of learning, competing with our friends and enjoying the overall process of earning knowledge. Is gave us a confidence that prepared us for the world. THIS is what education is all about. Whether the maths was more or less would not matter 10-20 years down the road if you have the basics right and the ability to learn.

 

[Lorentz]

Hello 2dye4:

If your professors taught more practical topics would
you learn the advanced math on your own??

I think that math is just about the easiest subject you can learn on your own. With a pencil, pad and a library card you can safely teach yourself just about all the math you'll find in a typical university program (and if you have access to a computer, I can't think of anything you wouldn't be able to learn on your own).

You can of course also teach yourself elementary auto mechanics from a number of good do-it-yourself books and have the satisfaction of changing your car's spark plugs, and brake pads etc. But you will only be an amateur unless you receive training from a trade school that will teach you to work with the specialized equipment real professional mechanics use. If you try to work on your car's suspension springs or air conditioning you will probably injure yourself - and the do-it-yourself books warn amateurs not to attempt work that should be left to trained professionals.

To me the question is not "would I?", rather "why would I?". Knowing what I know now, I would avoid most of the courses I took as an undergrad. To me they seem like amateur applied math courses rather than professional engineering courses.

 

[Lorentz]

Hello flame:

I'm afraid you and I will just have to agree to disagree on the responsibilites of engineering professors.

BTW, have you changed jobs yet, or are you still an outsider in that uncomfortable family-owned-business?