Why does the engineering math need to be so rigerous?

[Nikitin]

Why does it have to be so rigorous when it comes to proving things that are so obvious they (seemingly to me) don't need to be proven?

I just started on my engineering degree, and I am extremely surprised at how proof-based the math is in my country. Why can't it be more intuition based? For instance, explaining something so utterly obvious as limits in terms of epsilons and deltas seems like a waste of time. Same thing with using 40 pages to explain proofs of the fundamental theorems of calculus + rieman sums, when a more intuitive explanation could be offered in 5 pages. An example of such an explanation is that the derived of a function over a period of time will change the function in a similar way as acceleration changes velocity.

So why is the situation like this? Who is responsible for thinking that overworked engineering students will get a deeper understanding of math if they try to memorize complex proofs, instead of getting a short and easy intuitive explanation + do loads of problems?

I mean, I talked to engineers and they have told me they never used this proof stuff. They just calculate. So if proofs neither help with understanding math nor does it have practical applications, why focus on learning it?

However, if anyone here can give good arguments for learning proofs, I will be happy to spend less time socializing and more time learning this stuff to the bone...

 

[Nikitin]

Btw it's not like that I hate proofs: I find proving non-obvious things in problems by using proof by induction, or just plain calculus, interesting and fulfilling.

It's when I try to follow a complex 8 page proof of something obvious because my math professor is obsessed with proofs, I start wanting to destroy things...

 

[nsaspook]

Would you like some cheese with that ... Buck-up and get with the program. Every discipline does the same thing with a recruit. Just like a DI reinforces every tiny detail on a Marines gun to make it automatic to him when something is wrong with the weapon.

Try explaining to management why you need company money on a "intuition based" project that has a major human safety factor. You will find that it's usually the "obvious" and mundane that cause the most problems because people assume it's good because it's easy while putting a huge effort in proving complex issues. Just ask the FTL neutrino guys ...

 

[MachX]

I think it has to do with preparing you to be an actual engineer as a career. You need to know the origins in order to be efficient in a job and to be 100% accurate. I started a degree in Mechanical Engineering Technology with a weak math background, and WOW It was a slap in the face. I toughed it out and learned what I needed to learn to catch up and pass statics, kinematics, etc.. but I realized a few years in, that Engineering and machining to me was more of a passionate hobby, and I did not want to do highly detailed math as a job for 40 hours/week. I found that I was more of a concept driven person so I switched majors for a B.S. in another profession, even though I still use what I learned all the time in my projects.

I think proof work develops the method of proving that will be required of an Engineer throughout projects. However if you don't love all math to death then just think of it as temporary.

 

[gmax137]

Why can't it be more intuition based...

you should realize, this is like asking your French professor, "just speak English, it's so much easier to understand..."

The mathematicians learned a long time ago, intuition is not proof, and it is often wrong.

 

[Antiphon]

I think the OP has a valid point. His english may not be good enough to make the point. Use "intuitive" in place of "intuition" and he makes more sense.

Engineers don't need to do a lot of epsilon delta profs. It's a waste of time because there is a bunch of more useful stuff to learn and not enough time to learn it.

Do two simple E-D proofs and move on. He's right.

 

[Nikitin]

well, when we were using integrals to find the surface areas of rotated graphs, I discovered that the integral sum-proofs were useful after-all. I was wrong :p

 

[Topher925]

My honest opinion of why some engineering curriculums force students to do rigorous proofs is because many math professors have some sort of god complex. Proofs will not help you become a better engineer. A wide and diverse education in mathematics will. I am always in awe with math programs which force students to prove inane theorems but refuse to teach subjects such as numerical methods.

 

[Jupiter6]

Check out this thread:

https://www.physicsforums.com/showthread.php?t=231180