Its useful. Its interesting, and yes it has applications in physics theory and pde theory, as well as geometry and geometric analysis. I'm sure there's more. It won't make you 'emperor tier' at anything, its just another field of math, and one fairly useful to an analyst.
>emperor tier in the math community >something that won't get grants because it's too abstract with no applications
Your Prof is an idiot if he actually told you to do this what your career. He should be telling you to get the fuck out of Pure Maths as soon as possible and get something that gives you some practical skills so you can leave Academia if you can't make it.
Which sadly, with the quality of teaching, projects and supervision. It will happen sooner rather than later for most people.
Not at all. I was spared being overqualified and good at a field which I couldn't make a living at.
Great. Try making a career out of doing a thesis in those areas. You have no practical skills and you are relying on a postdoc then an academic career.
If you are smart enough to do this shit, maybe you should be smart enough not to put all of your eggs in the one basket and give yourself some options so you don't end up stocking shelves or hanging around when you are unwanted at 30.
>>7809411 Almost every system is modeled with non-linear PDEs, but studying functional analysis isn't the same as learning how to apply PDEs to problem solving which is a completely different skillset and knowledge base.
Even the actual general solutions to some classes of non-linear PDEs aren't completely useless to anyone because real systems are usually coupled to hell with other non-linears (in far worse ways than simple equations like the navier stokes).
I don't know about grants, I actually can't imagine that any mathematical field would be scare on grants since theory reseach so cheap, but I definitely won't be hiring any mathematicains to work in our research group (and they're fine with that because their research is different). If you can stay in academia though it's probably a good choice.
Take a look how many postdocs or PhD scholarships are being offered, then look at school's faculty, their grants and their publications and ask yourself how can you convince someone to choose you over some Engineering PhD who has 5 years or research experience in CFD.
Einstein Equations and Yang-Mills is Theoretical Physics, so you are now fighting with Physics majors. So unless you are incredible, you aren't taking anything from them.
>compromise my studies because i might make a higher salary
Try making a salary at all. If you have a purely theoretical major with no practical skills in the way of internships or relevant research for industry or academia and you aren't some stellar student who came in with a scholarship and collected them ever since, you will be struggling to find work.
Yeah you sure as hell aren't getting hired into engineering research over a CFD guy with only a math background. Not even academic engineering groups. Physics is even more competative to get into.
If you go for a math field like this you should know that from that point on you are officially 100% vying for an academic career in math. You need to be extremely commited, get more pulications out than profs. typically expect from typical elements of their grad-student slave force. Start applying to post-docs long before you graduate your PhD. Along the way try to make friends with ambitious profs; whoever you think will be dean in 5-10 years in all the departments you work, they generally have pull over who gets hired because they exchange favours/funds with every group in the department.
If don't think you can beat your way into a faculty position one day, you should go the actuary route instead and pick up some programming certs both for employability and a backup.
>>7809485 if i can derive the same Methodology i see no reason why i couldn't meet their criteria.
you are comparing two different specializations that you have no knowledge over. the fact you think CFD is even remotely difficult to get into with knowledge of fluid mechanics is proof. you are applying numerical methods and discreet math to it. three areas that are already studied in math.
your argument can be used against you going straight into the work force without any experience. why should someone hire you if they could get someone else? might as well get a trade diploma if you want to be even more "realistic" about it.
>>7809504 I don't really know how to explain this to you. It's just completely different. It might as well be biology. The results of mathematical side do not really concern the applied side at all at all.
>you are comparing two different specializations that you have no knowledge over. I've worked with CFD groups before and have publications in the field, my main field is optimization so I regularly colloborate with them. I've audited functional classes from our math grad. department and keep up with non-linear PDEs math research as a hobby. I know update both fields unlike your snot nosed undergrad self.
> three areas that are already studied in math. They are areas also studied in engineering, in addition to a lot more programming, simulation experience and an engineering background; important since CFD concerns systems other than pure fluid continuum systems.
You might believe that you can compete for places these groups, but no one else does, the group itself certainly won't take your application seriously when unless they have zero engineering students applying that year.
>your argument can be used against you going straight into the work force without any experience. why should someone hire you if they could get someone else? They generally don't hire at all unless no one with experience applies. There's only so many people in this world , but any job can get oversaturated. >might as well get a trade diploma if you want to be even more "realistic" about it. Math doesn't supersede engineering research, it's the other way around, engineering researchers pick up the math they need on the job. Going the pure math route you're losing out on broader qualifications. It takes far longer to pick up on 4-5 years of requisite engineering classes than 2-3 years of requisite math classes.
>>7809231 >emperor tier in the math community not really, but it's clearly usefull and beautiful. It's a mix of classical results (back to Lagrange) and modern results (from convex analysis and nonlinear PDEs mainly). Main connections are with physics/PDE, but mathematical economy uses it and also probabilists and statisticians (gaussian isoperimetry, log-sobolev inequalities too).
Just FYI there's an new excellent book about it : Functional analysis, calculus of variations and optimal control by F. Clarke (2013 i think).
>gaussian isoperimetry Okay so this sounds like lots of fun, the way you phrased it makes it sound like a sub-field of some sort. But all I can find though is a 'gaussian isoperimetric inequality', which is one specific, uh, 'mathematical instance'.
I'm in pretty far over my head here, but that's how I learn. Care to help clear up my confusion a little on gaussian isoperietry and its relation to nonlinear function analysis?
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