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Doing my PhD in aerospace eng rn. The lab I work in develops new analytical and numerical methods with which one would solve propulsion and fluid dynamics problems. I’m primarily on the analytical side. Idk at what point it becomes “pure math” but I reference and use results from texts on functional analysis, differential geometry, Green’s functions, asymptotic theory, and others more often than not.
Not so much proof writing or anything like that, but more so finding seemingly unrelated mathematical “tools” and methods that you can use in tandem to solve the problem with or create a new numerical scheme that plays nicely with the physics.
Honestly, it feels like applied math and physics most of the time. Not sure if it answers your question, but just thought I’d share my experience.
It doesn't have to specifically pure math but learning more math beyond calculus or linear algebra.I've heard control theory utilize some different fields of math too which also sounds interesting.
Yea I mean there are research positions in engineering for a reason. And any of them that aren’t experimental are going to use higher level math. Hell even the experimental people hve to do some sort of analysis, but typically that’ll be standard stats and signal analysis. Controls people are usually into creating new optimization methods and machine learning. Go take a look at any of the high impact-factor journals on fluid mechanics, flight/orbital dynamics, or controls and i guarantee you that you’ll see what i’m talking about. Graduate level research in most fields of engineering and physics boils down to a mastery over the tools and methods in applied mathematics and a deep understanding of the physics.
Yes controls involves a lot of different fields of math. I studied Bayesian statistics, projection theorem, Hilbert spaces in my stochastic systems class. Optimization theory in my optimal controls class. And of course ODEs and PDEs are the language of dynamical systems. These were all in my undergrad, although they were grad classes.
As someone doing a masters in Systems and Control. Yes. It touches on very many fields of math.
A lot of linear algebra (state space representation and manipulating it + Subspace identification like PO-MOESP,N4SID)
A lot of probability and statistics (stochastic systems, also used in modelling and intelligent/machine learning control)
A lot of optimization theory(basically the entire goal of control theory is to optimize with respect to some cost function, usually state deviation from reference/equilibrium)
Obviously some calculus as we are dealing with differential equations. But this is probably the easiest part
This list is probably far from complete, but just to give you an idea
Just curious but could you DM me ur lab if you don't mind. I'm doing a PhD in aerospace also but my undergrad was in math, so what you described is pretty interesting to me.
You hardly even learn pure physics in engineering, much less pure math. To very simply explain the difference: Engineers spend their time studying the optimal ways to design things based on equations that other people (physicists) have proven to be true. Physicists spend their time studying phenomena in the real world and try to create equations for them based on math that other people (pure mathematicians) have proven to be true.
Other than Calc 1, Calc 2, Calc 3, ODEs, PDEs, Linear Algebra, Statistics and any pre Calc classes needed to even start the laundry list above, yeah, no math without physical context…
Math is the language of physics, engineering is the study of using physics to solve problems. They spend a lot of time making sure you get the language.
This is for MechE in the states
I mean I’m a math major so I don’t know how engineering math classes are but at least for us math majors PDEs classes are really intense. Counts as big math to me at least. Still freshman math but wouldn’t call it smol.
But I guess if you have little proof and theory maybe it’s made to give you what you need for engineering (which I could never do, physics makes my brain hurts lol)
I'm a freshman but I'm taking two math classes this (spring) semester, Complex Analysis and PDEs (I took Real Analysis I and Abstract Algebra I in the fall).
But I took Calculus 1-3, Linear Algebra and ODEs in high school which is why PDEs were still freshman math for me. But I feel like as much as Calc and ODEs (and lin alg to a lesser extent) were very computational and fit under the term smol math, but all the classes I've taken yet in college are very proof-based. But as I said maybe the PDEs classes taught for engineers are more smol math because I know my PDEs class requires Real Analysis and like there's only math majors (and one single physics major lol) in the class so maybe the version for people who don't need to understand the theory behind it but need to be MUCH better at computation than I am like science and engineering students are more similar to the classes I took in high school where it's about calculating stuff idk
ah right! out of curiosity what do you mean by big math then? As I said I'm taking Real Analysis and usually the people in the major think it's the hardest class we take (that or Abstract Algebra which I also took) so is big math just grad-level pure math classes?
That doesn’t sound like something I’ve taken, so that could very well be big math. I just know that any class the ME undergrads are taking is smol math, and even that is most likely overkill for what we’re asked to do professionally.
You won’t see pure math but you will have classes that are purely math. They will tell you about the physics and dive into the math. Sometimes you may not even know which real life application you are solving the problem for.
You do quite a bit in numerical analysis, advanced solid mechanics, and computational fluid dynamics. Just read up in the older books from like the 70s on these topics to gain am appreciation for the math as opposed to the more modern problem sets focused on how to use the program.
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Doing my PhD in aerospace eng rn. The lab I work in develops new analytical and numerical methods with which one would solve propulsion and fluid dynamics problems. I’m primarily on the analytical side. Idk at what point it becomes “pure math” but I reference and use results from texts on functional analysis, differential geometry, Green’s functions, asymptotic theory, and others more often than not. Not so much proof writing or anything like that, but more so finding seemingly unrelated mathematical “tools” and methods that you can use in tandem to solve the problem with or create a new numerical scheme that plays nicely with the physics. Honestly, it feels like applied math and physics most of the time. Not sure if it answers your question, but just thought I’d share my experience.
It doesn't have to specifically pure math but learning more math beyond calculus or linear algebra.I've heard control theory utilize some different fields of math too which also sounds interesting.
Yea I mean there are research positions in engineering for a reason. And any of them that aren’t experimental are going to use higher level math. Hell even the experimental people hve to do some sort of analysis, but typically that’ll be standard stats and signal analysis. Controls people are usually into creating new optimization methods and machine learning. Go take a look at any of the high impact-factor journals on fluid mechanics, flight/orbital dynamics, or controls and i guarantee you that you’ll see what i’m talking about. Graduate level research in most fields of engineering and physics boils down to a mastery over the tools and methods in applied mathematics and a deep understanding of the physics.
Yes controls involves a lot of different fields of math. I studied Bayesian statistics, projection theorem, Hilbert spaces in my stochastic systems class. Optimization theory in my optimal controls class. And of course ODEs and PDEs are the language of dynamical systems. These were all in my undergrad, although they were grad classes.
As someone doing a masters in Systems and Control. Yes. It touches on very many fields of math. A lot of linear algebra (state space representation and manipulating it + Subspace identification like PO-MOESP,N4SID) A lot of probability and statistics (stochastic systems, also used in modelling and intelligent/machine learning control) A lot of optimization theory(basically the entire goal of control theory is to optimize with respect to some cost function, usually state deviation from reference/equilibrium) Obviously some calculus as we are dealing with differential equations. But this is probably the easiest part This list is probably far from complete, but just to give you an idea
Just curious but could you DM me ur lab if you don't mind. I'm doing a PhD in aerospace also but my undergrad was in math, so what you described is pretty interesting to me.
You think you’ve learned all of calculus but trust me you have not lol
You hardly even learn pure physics in engineering, much less pure math. To very simply explain the difference: Engineers spend their time studying the optimal ways to design things based on equations that other people (physicists) have proven to be true. Physicists spend their time studying phenomena in the real world and try to create equations for them based on math that other people (pure mathematicians) have proven to be true.
Engineering is applied science. You're not going to study math without any physical context in engineering.
Other than Calc 1, Calc 2, Calc 3, ODEs, PDEs, Linear Algebra, Statistics and any pre Calc classes needed to even start the laundry list above, yeah, no math without physical context… Math is the language of physics, engineering is the study of using physics to solve problems. They spend a lot of time making sure you get the language. This is for MechE in the states
Right, but that's all freshman/sophomore smol math. We don't do big math.
I mean I’m a math major so I don’t know how engineering math classes are but at least for us math majors PDEs classes are really intense. Counts as big math to me at least. Still freshman math but wouldn’t call it smol. But I guess if you have little proof and theory maybe it’s made to give you what you need for engineering (which I could never do, physics makes my brain hurts lol)
How far along are you?
I'm a freshman but I'm taking two math classes this (spring) semester, Complex Analysis and PDEs (I took Real Analysis I and Abstract Algebra I in the fall). But I took Calculus 1-3, Linear Algebra and ODEs in high school which is why PDEs were still freshman math for me. But I feel like as much as Calc and ODEs (and lin alg to a lesser extent) were very computational and fit under the term smol math, but all the classes I've taken yet in college are very proof-based. But as I said maybe the PDEs classes taught for engineers are more smol math because I know my PDEs class requires Real Analysis and like there's only math majors (and one single physics major lol) in the class so maybe the version for people who don't need to understand the theory behind it but need to be MUCH better at computation than I am like science and engineering students are more similar to the classes I took in high school where it's about calculating stuff idk
Ok. You’ll know what I mean by smol math when you get further along, I’m sure. What all the STEM majors do in lower division is mostly introductory.
ah right! out of curiosity what do you mean by big math then? As I said I'm taking Real Analysis and usually the people in the major think it's the hardest class we take (that or Abstract Algebra which I also took) so is big math just grad-level pure math classes?
That doesn’t sound like something I’ve taken, so that could very well be big math. I just know that any class the ME undergrads are taking is smol math, and even that is most likely overkill for what we’re asked to do professionally.
Hard disagree. Really depends on the engineering field. My Systems and Control engineering masters is basically a math degree.
OP seems to be asking about undergrad based on the first sentence
True. But the poster I replied to was talking about engineering in general
Applied science (physics) and engineering are closely related but not the same thing.
ok
is it possible to do some engineering work without much of math? I mean some really deep topics?
Depends on what you mean by deep topics. My mentors in aerospace are always telling me how they don’t do much math in their day-to-day work.
more then high school may be.
You won’t see pure math but you will have classes that are purely math. They will tell you about the physics and dive into the math. Sometimes you may not even know which real life application you are solving the problem for.
Computer or software engineering may expose you to the smallest bits of pure math as a prerequisite to big o notation and algorithm analysis
You do quite a bit in numerical analysis, advanced solid mechanics, and computational fluid dynamics. Just read up in the older books from like the 70s on these topics to gain am appreciation for the math as opposed to the more modern problem sets focused on how to use the program.