RoopinderTara
Mechanical
I wrote this after hearing David Cullimore speak at a Solid Edge conference. Youngest keynote speaker I've ever seen. He designs and races electric cars. He couldn't pass calculus so has no engineering degree.
Eng-Tips is the largest engineering community on the Internet
Intelligent Work Forums for Engineering Professionals
-
Congratulations waross on being selected by the Eng-Tips community for having the most helpful posts in the forums last week. Way to Go!
Math a rite of passage for engineers- but should it be? 4
- Thread starter RoopinderTara
- Start date
- Status
moltenmetal
Chemical
I think we could drop at least two math courses from the 4 year chemical engineering curriculum if we were careful, replacing the instructional time with things of far more practical value to Bachelors graduates. We could drop one course in a heartbeat and lose absolutely nothing of use. But that would leave what, five or six 1-semester math courses? Still the biggest focus in the program. Right now, we spend all that course time to bring students to the state of the art of mathematics circa the year 1730 or so. Teaching analytical integration in depth, particularly of partial differential equations, is a waste of instructional time in my opinion. But all that said, I do think a fundamental knowledge of calculus is REQUIRED LEARNING for engineers. If you can't set up differentials and at least solve them by finite difference approximation, you lose useful access to so many subject areas important to engineering that you'd be severely hamstrung.
Math is an integral part of learning to be an engineer for some good reasons grounded in understanding the subject matter in other courses and being able at the end of it all to apply the principles to new situations. However, it is also true that it is used as an artificial intellectual hurdle- that's really what the analytical integration is used for in my opinion. I'd be perfectly happy to throw that elitist attitude in the garbage along with the course material which is of little to no practical use for MOST practicing engineers. If I ever need to use the method of Frobenius or to use Laplace transforms again, I'll be perfectly happy to hire a mathematician- same as I would do with numerous other specialist disciplines.
Math is an integral part of learning to be an engineer for some good reasons grounded in understanding the subject matter in other courses and being able at the end of it all to apply the principles to new situations. However, it is also true that it is used as an artificial intellectual hurdle- that's really what the analytical integration is used for in my opinion. I'd be perfectly happy to throw that elitist attitude in the garbage along with the course material which is of little to no practical use for MOST practicing engineers. If I ever need to use the method of Frobenius or to use Laplace transforms again, I'll be perfectly happy to hire a mathematician- same as I would do with numerous other specialist disciplines.
Amusing, but irrelevant, article. Bill Gates, Steve Jobs, and a large number of people became successful without college degrees, and presumably, without the math. But, as the last couple of paragraphs in the article show, he can't even do calculus, or much trig presumably, so he can't do or understand ANY analysis of his designs, and has to rely on someone else who did grind through the math classes to do that work. Which is OK, the world needs visionaries and geniuses, but to conflate his innate intuition with something that should be emulated is a silly notion.
MM's comments also reveal another fallacy, which is that you know in college what you want to do with the rest of your life, and therefore can meaningfully decide what knowledge to learn, and the bottom line reality for many, is that it's not so at all. The math. and science, background gives you the freedom to do more than just being a button pusher. Hiring a mathematician, or even a consultant, is fine when you're flush with money and time, but most projects are not that way, and hiring someone who knows nothing about your project and your requirements every time a math problem comes up is death by a thousand cuts. Moreover, the rejection of math likely condemns most people to a pigeon-hole for the rest of their lives, which may be perfectly fine for some people. But, there are lots of people for which doing no more than what you basically did upon graduation is not the life for them; they want to grow and expand their responsibilities and challenges. THAT requires the math and science background that the article blithely considers to be irrelevant.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529
MM's comments also reveal another fallacy, which is that you know in college what you want to do with the rest of your life, and therefore can meaningfully decide what knowledge to learn, and the bottom line reality for many, is that it's not so at all. The math. and science, background gives you the freedom to do more than just being a button pusher. Hiring a mathematician, or even a consultant, is fine when you're flush with money and time, but most projects are not that way, and hiring someone who knows nothing about your project and your requirements every time a math problem comes up is death by a thousand cuts. Moreover, the rejection of math likely condemns most people to a pigeon-hole for the rest of their lives, which may be perfectly fine for some people. But, there are lots of people for which doing no more than what you basically did upon graduation is not the life for them; they want to grow and expand their responsibilities and challenges. THAT requires the math and science background that the article blithely considers to be irrelevant.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529
The lack of a degree is usually a show-stopper for future employment.
I forgot to mention one other thing, which is that not having the theoretical background makes it pretty hard to convince co-workers and investors that you know what you're doing. If you have the chops, you can kill it a few times, and your word will be golden thereafter. Without the chops, everyone will be wondering if the next time is when you get it all wrong and crash and burn.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529
I forgot to mention one other thing, which is that not having the theoretical background makes it pretty hard to convince co-workers and investors that you know what you're doing. If you have the chops, you can kill it a few times, and your word will be golden thereafter. Without the chops, everyone will be wondering if the next time is when you get it all wrong and crash and burn.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529
-
2
- #6
Inane article.
Calculus is not a "gate keeper".
It's a prerequisite because it is the mathematical foundation for so many of the fundamentals of physics and engineering.
If you can't do calculus then you won't be able to understand the next 3 years.
The Cullimore kid is undoubtedly smart. I bet he is fully capable of understanding calculus, but that he was crippled by bad teachers.
I college girlfriend of mine, studying computer science, was struggling with calculus because the teachers were teaching by rote.
I explained in about 10 minutes what the physical meaning of a derivative and an integral were to her and the light bulb came on in her head. "Holly crap, that's really useful! Why aren't they teaching that in the class?"
Calculus is not a "gate keeper".
It's a prerequisite because it is the mathematical foundation for so many of the fundamentals of physics and engineering.
If you can't do calculus then you won't be able to understand the next 3 years.
The Cullimore kid is undoubtedly smart. I bet he is fully capable of understanding calculus, but that he was crippled by bad teachers.
I college girlfriend of mine, studying computer science, was struggling with calculus because the teachers were teaching by rote.
I explained in about 10 minutes what the physical meaning of a derivative and an integral were to her and the light bulb came on in her head. "Holly crap, that's really useful! Why aren't they teaching that in the class?"
moltenmetal
Chemical
MintJulep's response is mint in this case. The kid is smart, and no doubt fully capable of learning the subject matter if it were taught properly.
That said, some of the advanced math taught in engineering programs is superfluous and is there as an intellectual hurdle rather than as a useful tool. That should change, but won't, until people other than those with PhDs set the curriculum at the Bachelors level.
That said, some of the advanced math taught in engineering programs is superfluous and is there as an intellectual hurdle rather than as a useful tool. That should change, but won't, until people other than those with PhDs set the curriculum at the Bachelors level.
EdStainless
Materials
I wish that they had taught calculus basics in 6th grade when they introduced physics.
I am in metallurgy and have never used calculus for anything other than heat transfer problems since school. But when I have a problem that I know is non-linear or indeterminate, that even though I solve it using algebra (linear algebra is the best) I know what the limits are and how to estimate the values.
Personally I have never met a real good engineer that couldn't estimate well. If you can't get an order of magnitude value without calculation aids then how do find errors?
= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube
I am in metallurgy and have never used calculus for anything other than heat transfer problems since school. But when I have a problem that I know is non-linear or indeterminate, that even though I solve it using algebra (linear algebra is the best) I know what the limits are and how to estimate the values.
Personally I have never met a real good engineer that couldn't estimate well. If you can't get an order of magnitude value without calculation aids then how do find errors?
= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube
"The difference between an engineer and a technician or designer is that an engineer understands the physics behind a systems behavior, and a technician/designer has enough experience observing that behavior that they can usually predict it. There is a big difference there, and what some software companies are doing to reduce the perceived theoretical knowledge required to actually be an engineer vs. a technician or designer is doing a dis-service to the engineering development community by giving inexperienced managers the idea they can replace experienced engineers with CAD operators. Are fewer engineers now required for lower level tasks due to the efficiency multiplier from 3D CAD and FEA? Yea but, a part of an engineers training as a design engineer is those lower level design (CAD modeling and drawing/MBD generation) tasks as well as learning advanced FEA methods. On many occasions I have come in to fix/save projects where a designer/technician has gone beyond their true understanding and used FEA incorrectly (like, most meshing needs manual intervention to get accurate answers, especially for the stress concentration areas where failure either occurs or not) or accepted answers that were obviously wrong for other reasons because sanity check hand calcs were not done. Most larger corporations have degreed engineers and not technicians/designers as design engineers, as they know the long term cost of under-qualified engineering staff. Beware the art-to-part and push button meshing promises of some CAD salespeople, it is still an accountants pipe dream and not an engineering design/development reality."
Quote from "scottlee" who commented below the article.
je suis charlie
Quote from "scottlee" who commented below the article.
je suis charlie
moltenmetal
Chemical
Calculus fundamentals are important to understanding many engineering principles, even though they may not be much used on a daily basis- especially when integrated form solutions in a textbook or numerical solutions via a math software tool or even an Excel spreadsheet are easy to come by. The key skill is understanding how to set up the underlying differential model.
Analytical integration of PDEs has very little to do with understanding engineering principles. It's not completely irrelevant, but it is just a tool used to obtain a solution to a math problem- a method used to derive some of the integrated form equations we use in engineering on a daily basis. It's not necessary to understand every step of that derivation to understand the underlying principles, nor to make proper use of the integrated form solution. There are many such tools available to mathematicians for centuries that we don't bother teaching to engineers.
I too agree that they should teach calculus when they teach elementary physics. It need not be over-complicated in the way it frequently is by math teachers.
Analytical integration of PDEs has very little to do with understanding engineering principles. It's not completely irrelevant, but it is just a tool used to obtain a solution to a math problem- a method used to derive some of the integrated form equations we use in engineering on a daily basis. It's not necessary to understand every step of that derivation to understand the underlying principles, nor to make proper use of the integrated form solution. There are many such tools available to mathematicians for centuries that we don't bother teaching to engineers.
I too agree that they should teach calculus when they teach elementary physics. It need not be over-complicated in the way it frequently is by math teachers.
"I too agree that they should teach calculus when they teach elementary physics. "
I think in most of the US, they do. AP Calc and AP Physics are available at the same time. Even still, you'd need to take AP Calc before AP Physics, because half of the required calculus doesn't get taught until the second half of the course, while physics gets into derivatives and integrals simultaneously. I don't recall my or my kids having issues, one way or another.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529
I think in most of the US, they do. AP Calc and AP Physics are available at the same time. Even still, you'd need to take AP Calc before AP Physics, because half of the required calculus doesn't get taught until the second half of the course, while physics gets into derivatives and integrals simultaneously. I don't recall my or my kids having issues, one way or another.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529
-
1
- #13
Mathematics, and specifically Newtonian (and subsequent) calculus are the lingua franc of engineering. To not know and understand calculus would be equivalent to not knowing English and trying to work in the US or (non-Quebec) Canada. Sure, you might get by in some isolated corners, but you will be perpetually hamstrung.
I completely concur in teaching calculus principles early in students' studies in elementary school. While I enjoyed science and physics in primary and secondary school, I didn't get it until after learning calculus. And that's because I was being taught a subject without knowing the language of said subject. Unfortunately, such a goal is so unlikely to occur, because most primary school teachers have a fear and disdain for even the most elementary arithmetic (speaking from experience as a father of a daughter in elementary school).
Of course, this is said by an engineer who actually writes integrals and PDEs on his whiteboard...
I completely concur in teaching calculus principles early in students' studies in elementary school. While I enjoyed science and physics in primary and secondary school, I didn't get it until after learning calculus. And that's because I was being taught a subject without knowing the language of said subject. Unfortunately, such a goal is so unlikely to occur, because most primary school teachers have a fear and disdain for even the most elementary arithmetic (speaking from experience as a father of a daughter in elementary school).
Of course, this is said by an engineer who actually writes integrals and PDEs on his whiteboard...
georgeverghese
Chemical
In chemical engineering, you wont get very far in understanding engineering thermodynamics, mass transfer or reaction kinetics without a good grip on differential calculus. Knowing the premises and assumptions used in the derivation of some formulas is also relevant.
Having said that, I've yet to understand how some of these Laplace transforms are used to solve partial differential equations in mass tranfer - work in progress.
Having said that, I've yet to understand how some of these Laplace transforms are used to solve partial differential equations in mass tranfer - work in progress.
There are lots of jobs that depend on understanding Fourier, Laplace, etc., transforms and you can't get there without the calculus. The various studies have found that most engineering graduates aren't working as engineers; likely, they're the ones that didn't do so well in math. As I alluded to earlier, if these guys were up to snuff on math and engineering they're be wanting to compete with us for our jobs, so supply/demand would say that our salaries would nosedive, barring all else.
Fortunately for us, engineering isn't just about math, or even science, it's also about what Dilbert has, the "knack." Not every engineer has the "knack" to the level that Dilbert does, but we all have some fraction of Dilbert's knack; otherwise, we'd suck as engineers, and would be a know-it-all packing bags at Piggly Wiggly.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529
Fortunately for us, engineering isn't just about math, or even science, it's also about what Dilbert has, the "knack." Not every engineer has the "knack" to the level that Dilbert does, but we all have some fraction of Dilbert's knack; otherwise, we'd suck as engineers, and would be a know-it-all packing bags at Piggly Wiggly.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529
-
1
- #16
When I got my bachelors in 2014 at an American university, I was required to take calc 1 - 3 and then a specialty math course that was taught by math professors but was developed by the ChemE department. In this class I learned the basics of PDEs, basics of liner algebra, and how to solve liner and non-liner ODEs (analytical and MATLAB). This course was great because the context for the math was different physical problems (spring systems, a couple reactor kinetics examples). I think engineers would benefit from having the math we need to learn, and I think calculus and PDEs are necessary because the software tools we use make use of this level of mathematics, couched in the physical world.
I didn't know many engineers in school that enjoyed math for itself and I didn't learn to appreciate pure mathematics until I found the Youtube channel Numberphile.
I didn't know many engineers in school that enjoyed math for itself and I didn't learn to appreciate pure mathematics until I found the Youtube channel Numberphile.
SandCounter
Mechanical
If you want to stand on other people's shoulders, you don't need the math. There are plenty of standards, laws, regulations, and design software packages that will allow you to mix and match known solutions like Lego bricks to your heart's content. As described in the article, what Cullimore has achieved here is the fruit of iterative prototyping in a low risk environment, i.e. computer simulation. If you bang on a keyboard long enough, you will eventually get a word, or even a sentence. . . a story perhaps. Used like this knowledge is traded for time.
Math unleashed in engineering, all things considered, lets you get it right the first time. And if you want to do something truly original, dare I say overcome the impossible, learn math and create your own bricks.
I used to count sand. Now I don't count at all.
Math unleashed in engineering, all things considered, lets you get it right the first time. And if you want to do something truly original, dare I say overcome the impossible, learn math and create your own bricks.
I used to count sand. Now I don't count at all.
@SandCounter
I think engineering defies the notion you posit in your first sentence because without understanding the fundamentals of your discipline, which I am saying mathematics is, how can you even start to climb onto said shoulders? Whenever I work on first draft P&IDs, knowing how Bernoulli's equation is derived (and the idea of changes in momentum) informs my decisions of piping placement. In my mind, I wouldn't be able to do this type without understanding the math of fluid dynamics.
As TGS4 put it, math is the lingua franc of the ideas we use in the engineering disciplines so I equate mathematical literacy with the ladder you'd use to climb onto the shoulders of others.
I think engineering defies the notion you posit in your first sentence because without understanding the fundamentals of your discipline, which I am saying mathematics is, how can you even start to climb onto said shoulders? Whenever I work on first draft P&IDs, knowing how Bernoulli's equation is derived (and the idea of changes in momentum) informs my decisions of piping placement. In my mind, I wouldn't be able to do this type without understanding the math of fluid dynamics.
As TGS4 put it, math is the lingua franc of the ideas we use in the engineering disciplines so I equate mathematical literacy with the ladder you'd use to climb onto the shoulders of others.
You stand on others' shoulders when you use any simulation or calculation tool, like FEA, or a circuit simulator. The math is all being done for you behind the scenes; you merely need to select the correct components and connect them correctly. Anyone can download SPICE or OpenFOAM, and start cranking answers; without the math, however, you cannot begin to check whether your results are correct and whether you made errors in component selection or connection. Or, whether your model is even remotely representative of the problem you are trying to solve.
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529
TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529
Diff E, linear algebra, and calculus are necessary to understand some basic engineering courses, however, advanced calc may no longer be relevant as many of those methods of solving or integrating diff e's were displaced by the modern numerical methods made possible by computer advances. Computer programming and numerical analysis should be substituted for adv calc to ensure the engineer knows the limitations of computers and possible sources for errors. At a minimum, the engineer should not assume that the program output is correct and valid simply because the program did not indicate an error and the output contains pretty colored graphs . However, the pretty graphs will keep the VP's happy, at least until the product failures start coming in.
"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick
"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick
- Status
Similar threads
- Question
- Locked
- Question
- Locked
- Question
