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





RE: How much math(s) do we really /need/ to learn?
Do you count numerical methods and optimization techniques as part of math or engineering?
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Matthew Ian Loew
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RE: How much math(s) do we really /need/ to learn?
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!
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
In the US, last time I checked, all engineering students must take three semesters of calculus and one semester of differential equations.
RE: How much math(s) do we really /need/ to learn?
Coka
RE: How much math(s) do we really /need/ to learn?
Mike Bensema
www.dutchmenservices.com
RE: How much math(s) do we really /need/ to learn?
I think your first guess is about right.
Steve Braune
Tank Industry Consultants
www.tankindustry.com
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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!
RE: How much math(s) do we really /need/ to learn?
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,
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
SLTG
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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...
RE: How much math(s) do we really /need/ to learn?
Engineers need to appreciate all areas of maths in the beginning and then apply the bits that are relevant to solving real world problems. Very few people can remember much of what they were taught at school a decade ago.
RE: How much math(s) do we really /need/ to learn?
Yes, considerable knowledge of mathematics is essential to an engineer's education- nobody's debating that! But the sheer amount and complexity of the math in our courses of study also seems to be some kind of macho rite of passage for graduates of engineering programs, and even more so for professors of engineering. We keep hearing the same tired argument, "It was basically useless, but it taught me how to think." Well, bully for you!- but there are far better ways to teach engineering students to reason logically and apply their rational analytical skills than by having them perform the mathematical equivalent of running around inside a squirrel cage!
As to the argument that a Bachelor's degree in engineering is just pre-training for an academic Master's or PhD, let's get real- most graduates of engineering do not immediately go on to grad school (thank God!). They go out into industry to serve society- and we have a responsibility to ensure that they know enough about what they'll actually be doing for a living so that they provide a service rather than disservice. That's every bit as important as preparing them for grad-level classes.
Let's be reasonable here: why do we teach analytical integration with the rigour that we do? Much of it has been rendered essentially obsolete by the advent of modern computing technology. It's as if we were still teaching students how to use slide rules- a great way to get them to learn logarithms, but hardly necessary any more despite being an essential tool forty years ago. And yes, I know that analytical solutions are more "elegant" than bashing away at something with Euler's method, and that there are certain types of problems that frustrate the numerical methods- but they're relatively few and far between. It hardly seems logical to continue to beat students' collective heads against that particular wall while leaving important, essential curriculum untaught because there's so little time!
IMHO there needs to be more focus on model-building and the corect use of modern computational methods and tools, and far less on analytical solution of the resulting differential equations. The vacuum created by dropping out one or two courses worth of useless analytical solution-oriented mathematics could easily be filled by other essential course material which the students will actually find useful in their careers. This approach will be far more effective in the quest to build a better engineer.
RE: How much math(s) do we really /need/ to learn?
I couldn't agree with you more. In an ideal world I would have people like you and Greg Locock redesign engineering programs to create a better balance between math and other essential subjects.
In the famous Feynman lectures on physics, the Nobel prize winner cautions students that while math is essential to physics, math IS NOT physics. He does this in the volume introducing electromagnetics. Feynman noted that many mathematically adept people took the approach that since electromagnetics is summed up by Maxwell's equations, they would simply analyze the equations from every angle to learn EM theory. In his observations, people who took this approach rarely contributed much to either the field of physics, or the field of mathematics for that matter.
What Feynman observed in physics students seems to me to be even more pronounced among engineering professors. And IMHO, the first responsibility of engineering professors is to produce competent engineers to serve the needs of society - not to prepare the next generation of graduate students!
Having said all this, I will state that there are times when analytic solutions are valuable, as in confirming or benchmarking numerical codes. No one is advocating removing ALL math from engineering programs, but many have observed (in this thread and others) that the current balance is so math heavy that other essential topics are being neglected.
RE: How much math(s) do we really /need/ to learn?
What math courses have you studied that are not providing
any real world benefit and could have safely been left out
of your degree.
Or what math taught in Eng is of little practical use ??
RE: How much math(s) do we really /need/ to learn?
Some methods are being supplanted by numerical methods. For example, Perturbation theory was at one time required of grad students, but is generally supplanted by numerical methods. Likewise the manual mathematical techniques used by aerodynamicists is supplanted by CFD, and of course the use of finite elements for conductive heat transfer and lineat stress analysis has supplanted manual methods ( infinite series). Galerkin methods are used to solve nonlinear ( or non- self -adjoint) problems in heat transfer and stress analysis. Even the old Codes ( ASME, etc) are beginning to recognize the shift.
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
enviroments in support positions and do not do much
pure design of new products?
Davefitz:
Those items sound a little far from what is commonly
taught in engineering undergraduate programs.
If so my question is what math that appears regularly in
undergrad programs can be done without.
Many engineering programs try to expose you to the things
that need the most explanation. In other words difficult.
They assume the student will pick up a great deal more
knowledge from self study and work experience.
RE: How much math(s) do we really /need/ to learn?
We keep hearing the same tired argument, "It was basically useless, but it taught me how to think."
A generation ago, when people with BA degrees began having trouble finding work, they voiced the same rationalization for the courses they studied.
It seems that the math is not meant to be a working tool, merely a hoop engineering students jump through to prove their intelligence.
It is interesting to note that doctors, dentists and lawyers study little math, yet they are generally considered to be smart, and they are usually employed and well paid (unlike too many engineering graduates of today). I think that one of their key advantages is that their training is highly focused and designed to produce graduates who are useful to society (well, at least doctors and dentists).
I do not advocate simply cutting math courses, rather I would like to see the mathematical examples taught in engineering courses to be based on actual real-world examples of problems working engineers face on a daily basis. Unfortunately, few engineering professors have enough experience to produce such examples, so hypothetical problems are used instead. I believe this is the real reason why their is so much math in most engineering programs.
Next week I'm off to the dentist for my semiannual cleaning and checkup. She is a very good dentist, even though I doubt she still remembers how to solve a quadratic equation.
RE: How much math(s) do we really /need/ to learn?
It is entirely up to you to see the applications of
the math that is taught in engineering classes.
If you doubt that applications exist I suggest visiting
your engineering school library and reviewing some of the
periodicals the ASME or IEEE or many other professional
publications to see that math is used at least to
publish articles.
Engineering professors do not have the time to carry you
through the application of the science
RE: How much math(s) do we really /need/ to learn?
through the application of the science
I am so cynical that I do not believe most of them even know the applications. If you were to give a pop quiz on standard electrical code practices to a group of tenured Ph.D. electrical engineering professors and to a group of apprentice electricians, I am sure the professors would fare quite badly in comparison.
Sorry, but I know too much about college professors to revere them. I would suggest that the readers of this forum would look at their professors in a new light if they would:
1. Read "I. Asimov" the autobiography of the science fiction writer who was also a professor at the Boston University School of Medicine.
2. Rent the DVD of "The Wizard of Oz" and watch closely when Toto pulls aside the curtain.
RE: How much math(s) do we really /need/ to learn?
By the way, it is my understandign that the Wizard of Oz was originanly written as a farce to describe the early 20th centtur debate about the gold standard or currency- and OZ was an ounce of gold, and the yellow brick road was of course the pathway to heaven if we stayed on the gold standard.
RE: How much math(s) do we really /need/ to learn?
I've worked with lots of PhDs in industry who DO have that grounding in reality, and they agree with me about the absurd focus on mathematics. And yes, I've met more than a few industrial PhDs who I WISH were in an academic ivory tower somewhere instead, but that's another story. There's even a joke on the subject:
How many profs does it take to screw in a lightbulb?
NONE- they get their grad students to do it for them, and then write a paper about it listing the prof as co-author!
Although I'm only a chemical engineer, I believe I know enough about "hoop stress" to design adequate hoops for students to jump through in replacement of this ridiculous mathematical "rite of passage". The only difference is that my hoops would teach USEFUL skills on the way through.
RE: How much math(s) do we really /need/ to learn?
Case in point: It happens every few months, where I have to explain "y= mx + b" to a fellow degreed engineer. This is usually in explaining that the spring behavior they are witnessing is exactly as predicted. I try to be gentle, as these people are our customers, but it is difficult to keep a straight face while explaining.
http://www.EsoxRepublic.com
RE: How much math(s) do we really /need/ to learn?
If an instructor of undergraduate fluid mechanics (for example) can't assume a certain level of competence in math, then how can he explain the stress-strain tensor (or a hundred other concepts)? If you can't rely on the math to describe the concept, then the whole exercise becomes arm waving and requiring that students take your assertions on faith--now there are a couple of stinko options.
Math ain't about hoops to jump through, and it isn't simply a tool to teach people to learn concepts (or time management). It is the language we use to describe the world engineers are trying to modify.
That being said, a huge percentage of engineers never use any math beyond algebra after graduation. In Oil & Gas Production (not necessarily refineries), engineering is all about economics (run inside a packaged program) and project management. I was once in a discussion that required an analysis of the assumptions behind Bernoulli's equation, so I derived it on my board and we analyzed each of the assumptions that went from one step to the next. At the end I didn't erase my white board. I had so many other engineers ask me "what the heck is that?" that I put a sign on it "can you name these equations?"--none could although each one of them used programs based on that equation every day.
David Simpson, PE
MuleShoe Engineering
www.muleshoe-eng.com
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.
RE: How much math(s) do we really /need/ to learn?
Pure math is a poor tool to teach people how to solve engineering problems- there are far better ways, and more relevant problems...
It is only a poor tool when we are not taught how to bridge the pure math to the practical application.
I develop and use mathematical models about 1 to 2 times a month for a variety of problems I have on the manufacturing floor. Some involve predictive maintenance, some involve dynamic force loading on wear components that are wearing too fast (and no I do not have FEA at my disposal to help me with those). While I don't differentiate and integrate too often (second moment of area being the odd exception) I still use a lot of the anylytical tools and basic linear and nonlinear equations which I pulled from my education.
Also I had training on how to move from theory to practical. We called it modelling. It started with third year Heat Transfer which presented this in smashing fashion. Every example in class and every homework assignment was a perfect cylinder or a perfectly insulated something with a theoretical heat source.
Then the tests and exam were written .. A neighbor's well freezes up in January. To supply him with water you hook up a 50' hose between the two houses ...(data on temp and hose specs etc ..)... calculate the minimum flow rate required to ensure the water does not freeze while travelling between the two houses. Or Calculate the temperature setting for a thermostat in a toaster given that the toast is considered perfect when the surface temerature of the toast has reached ...
We very quickly learned how to model. I came to appreciate this when I got to industry and wished it was done for more subjects and courses in my degree than the three which did focus on models. No one can get enough practise or be too good at modelling.
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
Some math skills are like those of the slide-rule users or buggy-whip makers of days gone by- essential at the time, but rendered pointless by modern technology- and in my engineering education, those made up AT LEAST a full course, probably two, of the mathematics I was taught. Let's stop teaching these less-than-useful skills when they're, say, 20 years obsolete instead of waiting 50+ years.
Instead, let's teach students how to build mathematical models from the differentials up, then solve them using the best available tool- whether that be the analytical approach for the simplest problems, or a spreadsheet and Euler's method for slightly more complex ones, or a more complex mathematical software package for the tougher ones. Then let's teach kids how to parameterize and error-check their models, so they have some sense whether or not the computer is spewing bovine solid waste instead of useful information.
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
Math is essential to physics, physics is essential to engineering! Follow the logic?
RE: How much math(s) do we really /need/ to learn?
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
RE: How much math(s) do we really /need/ to learn?
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!
RE: How much math(s) do we really /need/ to learn?
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
RE: How much math(s) do we really /need/ to learn?
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
RE: How much math(s) do we really /need/ to learn?
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
RE: How much math(s) do we really /need/ to learn?
Things must have really changed since my undergrad days, I have never heard of "gym" classes in any engineering program. Is this now common?
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
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?
RE: How much math(s) do we really /need/ to learn?
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
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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
www.dutchmenservices.com
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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??
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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?
RE: How much math(s) do we really /need/ to learn?
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:
1016=1016+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
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.
RE: How much math(s) do we really /need/ to learn?
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?)
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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
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.
RE: How much math(s) do we really /need/ to learn?
"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?
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
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
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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
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.
RE: How much math(s) do we really /need/ to learn?
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
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
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
www.kitsonengineering.com
RE: How much math(s) do we really /need/ to learn?
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
RE: How much math(s) do we really /need/ to learn?
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
RE: How much math(s) do we really /need/ to learn?
RE: How much math(s) do we really /need/ to learn?
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
RE: How much math(s) do we really /need/ to learn?
I know I had said farewell in another thread, but I found something so juicy at www.nspe.org that I just had to fit in one last post. Check out:
http://www.nspe.org/forum/frames.asp?ResponseID=69...
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!!
RE: How much math(s) do we really /need/ to learn?
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.
RE: How much math(s) do we really /need/ to learn?
Quite correct! Thats perhaps why there is so much of challenge, fun, excitement and risk in engineering in contrast with accounting.
I feel there are always going to be those who will do anything to become an engineer and even if they get the "treatment" Mike got, they will overcome it. I can feel with Mike, but his experiences are his own and not of engineers.