Mechanical engineer to physicist/mathematician

[hihiip201]

Hi:



As graduation approaches, I would like to evaluate my strength, weakness and interest in engineering as well as other fields.


Well , to begin with, I would like to address that I will be getting my B.S in mechanical engineering, specializing in mechatronics.


But as I have taken more and more mechanical engineering courses, I found the following:


1. classes in engineering are usually very experimental based, any theories are usually very complex and involve math and physics that are not expected of undergraduate level students.

2. classes such as systems, fluid mechanics, are usually very mathematical based, one could easily learn the terminologies after knowing thoroughly the math behind the course.

for instant, in control systems, it's essentially an application version of differential equations and linear analysis, maybe non-linear too but that falls into numerical analysis.

fluid mechanics is essentially vector calculus and F=Ma, ( bernoulli's principle can be derived straightly from navier stoke's equation which is really just differential form of conservation of momentum).


my personal strength, weakness and interset:


1. I would begin by saying that, even in "science" classes in engineering I have made serious mistakes that haunt me still (I made some very serious mistakes in one of the lab in heat transfer), I tried to fit experimental data into theory (a no no for any science practice) . But I still believe that I'm more interested in the theory over practical applications, despite that I did make mistakes in a science class.


2. I am usually more interested in the physical explanation behind things other than its application. For instance, in my manufacturing classes, I spent significant amount of researching why climb cutting gives better surface finish over conventional cutting, when everyone else are probably busy making their parts for the project already...


3. I excel all my mathematics and science based class, as I said even though I made a big mistakes in my heat transfer class I did excellent on the exams and I'm confident that I learned the material throughout, I have yet to have anything less than a 4.0 in all my mathematics classes.


4. often I feel like in engineering, engineers are the "organizers" who uses various physics, chemistry principles for practical purposes. They only concern about the physics as much as they immediately need, they are not concern for exploration of the theories.




At first I was hoping that, as a mechanical engineer I would be able to design groundbreaking mechanisms that can change the way certain things work, for different applications, but after having been exposed to engineering, I find that most of the time engineers spend their time trying to make things work rather than exploring what other things could work(new mechanisms, scientific principles). And Now I am getting the impression that the latter are usually only achieved by physicist or mathematicians.





I wouldn't mind going to graduate school while working at the same time, but I really just want to figure out what major really suits me, I want to make new discoveries, or design new mechanisms. If you have read this far, I'm sure you are here to help, any suggestion and advice would be helpful.



thanks!

 

[fourier jr]

1. classes in engineering are usually very experimental based, any theories are usually very complex and involve math and physics that are not expected of undergraduate level students.

2. classes such as systems, fluid mechanics, are usually very mathematical based, one could easily learn the terminologies after knowing thoroughly the math behind the course.

for instant, in control systems, it's essentially an application version of differential equations and linear analysis, maybe non-linear too but that falls into numerical analysis.

fluid mechanics is essentially vector calculus and F=Ma, ( bernoulli's principle can be derived straightly from navier stoke's equation which is really just differential form of conservation of momentum).

something from the Feynman lectures that seems applicable here:

Mathematicians, or people who have very mathematical minds, are often led astray when "studying" physics because they lose sight of the physics. They say: "Look, these differential equations - the Maxwell equations - are all there is to electrodynamics; it is admitted by the physicists that there is nothing which is not contained in the equations. The equations are complicated, but after all they are only mathematical equations and if I understand them mathematically inside out, I will understand the physics inside out." Only it doesn't work that way. Mathematicians who study physics with that point of view - and there have been many of them - usually make little contribution to physics and, in fact, little to mathematics. They fail because the actual physical situations in the real world are so complicated that it is necessary to have a much broader understanding of the equations.

What it really means to understand an equation - that is, in more than a strictly mathematical sense - was described by Dirac. He said: "I understand what an equation means if I have a way of figuring out the characteristics of its solution without actually solving it." So if we have a way of knowing wht should happen in given circumstances without actually solving the equations, then we "understand" the equations, as applied to these circumstances. A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist.

that said, I say why not? Banach started out in engineering.

 

[hihiip201]

something from the Feynman lectures that seems applicable here:that said, I say why not? Banach started out in engineering.

well I kind of feel like i wasted 4 years of my life.

ok maybe just 2.

 

[fourier jr]

well I kind of feel like i wasted 4 years of my life.

ok maybe just 2.

in what way? because you decided at some point you would do engineering rather than math & now you've changed your mind? If you decide that math is your thing, your experience in mech would give you a perspective that maybe other people in math wouldn't have. you would have a better idea through your labs, etc what might be important/interesting/difficult from an engineering POV, which would likely influence what you do with your math. someone who's only ever done math up to now might not.

 

[hihiip201]

in what way? because you decided at some point you would do engineering rather than math & now you've changed your mind? If you decide that math is your thing, your experience in mech would give you a perspective that maybe other people in math wouldn't have. you would have a better idea through your labs, etc what might be important/interesting/difficult from an engineering POV, which would likely influence what you do with your math. someone who's only ever done math up to now might not.

you are right,
I just have the impression that sometimes engineers don't really care much about the physics, or at least they only care about physics up to a certain point, which is understandable, a necessary ignorance.


But at the same time I have doubt in myself, I fear that I am only giving up on engineering because I'm no good at it, maybe if I can't handle engineering, there's no reason why I should think I can deal with Physics.


so many uncertainties...

 

[ZapperZ]

It is a bit unclear on what exactly it is that you are asking. Are you asking if you have the capability to continue into Math/Physics graduate school with your background? Or are you asking if you can still do math/physics if you stick to engineering? It is also unclear on what exactly you intend to do in Math/Physics. Most people have a jaundice view of physics being "string/elementary particle/nuclear/etc." without realizing how wide the field is (physics is not just the LHC, it is also your iPhone).

You should also realize that there are many fields of study that straddled both physics and engineering. I've mentioned one such field in this thread:

https://www.physicsforums.com/showthread.php?t=410271

It is imperative that you don't just consider whether you want to, but also consider whether you are sufficiently equipped to do it. Do you have to take remedial courses in math or physics to not only be successful in those graduate programs, but also to pass the qualifying exams? At some point, things have to be grounded in reality rather than just idle speculation. While certainly anything is possible, often reality bites!

Zz.

 

[Dustinsfl]

Here is a different view point.

I received my undergraduate degree in Mathematics. I went to graduate school for crypto but realized I preferred Applied Math. So I transferred to a school that offers applied math and complex systems. I ended up taking Mechanical Engineering courses since I had enough of Real Analysis (I was on my 3 or 4 course of this stuff in applied math at that!) I do enjoy Complex and Fourier Analysis though. So I have had 6 years of Math education. This semester was my first semester as a graduate student in Mechanical Engineering.

I have noticed that many applied math graduate programs require a lot of pure math. So if you think that just jumping into applied math will be all finding new real world problems, you may be wrong. When I was in applied math, I took Mathematical Bio & Eco, Complex Analysis, Fourier Series & Integral Transforms, Analysis, and Engineering Analysis. When I was in crypto, I took Algebra, Linear Algebra, and Topology. Now in ME, I take Continuum Mechanics, Orbital Mechanics, and Classical Mechanics. I am doing more applied math in ME than I ever was before. Next semester it will be Mathematical Physics and Nonlinear PDEs maybe another course.

 

[ilmareofthemai]

Maybe look into Material Science. They don't work on just physics principles, but what they build/test/make/research is very closely related to them, kind of like between a physicist and an engineer from what I understand.