mathematical rigore for an engineer!

Question

I recently bought a used copy of "Mathematical Analysis" by Apostol for \$1.0 and "Probability and Measure Theory" by Robert Ash for \$3.0 (well another \$3.99 for shipping)! When I read the first few chapters of these books it made me believe that there were many concepts that I was taught as an engineer that lack mathematical rigor and many proofs with handwaving arguments. It bugs me a bit but at the same time it is understandable to some degree. I was so excited to continue reading the books and getting nice and clear understanding of some of the concepts but I came across this post today Can I use my powers for good? and got cold feet :(

I don't want to be a mathematician but I don't want to end-up feeling "so what!?"

I guess I'm just looking for some advice from the other side of aisle, mathematicians of course :) Should I continue what I felt "really exciting" and dive into rigorous math, or stay focused on what I've been doing for the past 15 years (practicing engineering and enjoy elementary but challenging math problems and pyzzles as a hobby) and forget about all this?

Thanks!

Answer 1

I assume you are just doing this reading in your free time. In my opinion, any leisure activity that doesn't harm you and brings enjoyment is something you should pursue until it doesn't interest you anymore. I think nothing negative will come from learning things that interest you- if that happens to be mathematics, then more power to you!

Answer 2

Three benefits of learning analysis:

1. You will understand things we take for granted (limits, continuity, etc) at a solid and foundation level.
2. You will never again forget to check conditions before applying a theorem.
3. You will learn some very "out there" concepts like different infinities, Devil's Staircase, etc.

I would definitely go for it if you have the time and mental fortitude. The latter is a requirement.

Answer 3

As a mathematician working as an engineer, it has surprised me just how much mathematics I have been able to apply. Unsurprisingly, numerical methods have been a big requirement. But other aspects that you just don't expect to use in practice (though they are vital in understanding the theory) occasionally crop up. I've had cause to do differentiations and integrations, found that applying complex numbers to a purely mechanical problem simplified it considerably, did considerable investigation into linear operators in an effort to figure out how best to salvage rounded inertia values. And many others.

The point is, investigate what you find interesting as long as you find it interesting. If you never use it, well you have still explored something enjoyable. If you do find use for it, that is just a bonus!