Jobs in Physics/Mathematics that Actually do Calculus

[Harshna]

Hi,

I am finding it a bit difficult to find a job where pure maths is actually done and looking for some ideas or examples from people who have done this please. I am in my last semester of a Graduate Diploma of Science (Applied Data Science) and am considering what to study for my Masters/pHD next. I would ideally like to be working in something that involves physics that is in demand and will actually end up giving me a job in Australia after study. I know that Mathematics/Physics is applied to many jobs, but actually performing calculations and not just having a computer give the results of calculations (as in people just need a background in physics/maths to know how it works, but don't actually really use it a lot) is where I am not finding much except for research in Physics, for which the demand is very low and there are barely any jobs for.

I have been considering things in demand such as computational mathematics/physics, machine learning, data mining, operations research, forecasting, engineering, etc. Ideally I would like mathematics applied to science and this is why physics interests me (I have done physics before in high school), but not too sure about whether I will get a job soon after studying physics or at all. Also does anyone know if there are many in demand opportunities for pure mathematics applied to science, instead of just finance, insurance, economics, etc.?

Also would like to add that I have done some programming in my Grad Dip and am working in Data Science, but programming is not my strongest field and ideally I would like to do as less of it as possible (especially long complicated coding like javascript, python, etc (SQL, R, etc which uses smaller coding is fine)).

Thank you in advanced for help

 

[Locrian]

What do you mean by "actually do calculus"?

Let's be clear about something: This is the twenty first century. Computers calculate.

Humans find the problems, assess the problems, build the models or programs meant to solve the problems, run the programs, validate and assess the output, interpret the results, deliver the results.

The PhD's I work with are mostly involved with the "build models or programs" piece. They have extensive mathematical backgrounds. None of them "do calculus" day to day. Instead, their job is to figure out the best way to get computers to "do" math for us. If that sounds like what you mean, you could be in luck.

If your goal is to calculate, you're already obsolete.

 

[fresh_42]

Have a look on the discussion here:
https://www.physicsforums.com/threa...es-use-calculus-in-their-field-of-work.910790

 

[Harshna]

What do you mean by "actually do calculus"?

Let's be clear about something: This is the twenty first century. Computers calculate.

Humans find the problems, assess the problems, build the models or programs meant to solve the problems, run the programs, validate and assess the output, interpret the results, deliver the results.

The PhD's I work with are mostly involved with the "build models or programs" piece. They have extensive mathematical backgrounds. None of them "do calculus" day to day. Instead, their job is to figure out the best way to get computers to "do" math for us. If that sounds like what you mean, you could be in luck.

If your goal is to calculate, you're already obsolete.

Hi Locrian,

Thank you for this insight, that's very helpful

 

[Harshna]

Have a look on the discussion here:
https://www.physicsforums.com/threa...es-use-calculus-in-their-field-of-work.910790

Thank you for this - Actuarian was one of the jobs I was also looking at, so a nice insight

 

[Harshna]

Just something else to add on to my first thread - if anyone knows about job prospects for computational physics - like if I do this will I likely end up with a job? Also any recommendations of Australian Universities to study computational physics (possibly Masters) would be great. Thank you

 

[Dr. Courtney]

Hi. In our consulting and other research in blast and ballistics, we use Calculus just about every day. High speed video has become a common tool of our trade, so we use something like Tracker to determine position vs. time for points of interest in a video and then compute velocities and acceleration by differentiation. There are some subtleties for smoothing out experimental noise and error checking, including things like making sure the area under the curve agrees with physical laws.

Similar analysis applies to ballistic radar data. The "raw" data from the instrument is projectile velocity vs. distance and projectile velocity vs. time. Analysis is similar to video data: smooth, differentiate, error check. Lather, rinse, repeat.

Rocket test codes and modelling programs are similar, but with some added complexities veering more deeply into numerical solutions of differential equations.

We also commonly use Fourier transform codes that actually perform (numerically) the integrals that define Fourier transforms rather than their FFT approximations.

 

[Harshna]

Hi. In our consulting and other research in blast and ballistics, we use Calculus just about every day. High speed video has become a common tool of our trade, so we use something like Tracker to determine position vs. time for points of interest in a video and then compute velocities and acceleration by differentiation. There are some subtleties for smoothing out experimental noise and error checking, including things like making sure the area under the curve agrees with physical laws.

Similar analysis applies to ballistic radar data. The "raw" data from the instrument is projectile velocity vs. distance and projectile velocity vs. time. Analysis is similar to video data: smooth, differentiate, error check. Lather, rinse, repeat.

Rocket test codes and modelling programs are similar, but with some added complexities veering more deeply into numerical solutions of differential equations.

We also commonly use Fourier transform codes that actually perform (numerically) the integrals that define Fourier transforms rather than their FFT approximations.

Hi Dr. Courtney,

Thank you for this - just wondering for these jobs do you guys use computers to do the calculus i.e. like analysis on the computer that you guys interpret? What your company does sounds quite interesting.

 

[Dr. Courtney]

Hi Dr. Courtney,

Thank you for this - just wondering for these jobs do you guys use computers to do the calculus i.e. like analysis on the computer that you guys interpret? What your company does sounds quite interesting.

There's always a combination of computer analysis and human thinking, application, and interpretation. But, we're definitely not crunching the numbers by hand.

Suppose we use some video analysis program to produce raw x vs. t and y vs. t data that we need to then convert to velocity, acceleration, force, etc. Data is never perfect. Frame rates, pixel resolution, and other factors usually necessitate a manual path. We use a spreadsheet for a lot of it, but there are often careful choices for how to smooth the data, which technique to use to compute the derivatives numerically, and lots of double checks that things are making sense - got to know what all those derivatives and integrals mean physically to execute all the double checks.

One key aspect of calculus we use a lot recently is that a lot of rules of calculus do not apply at a point where a function cannot be differentiated. In a video, that happens (for practical purposes) when a collision occurs in a time span shorter than the time between frames. The velocity of the objects (for practical purposes) changes instantaneously between the frames, so we need to manually recognize the frame where that occurred and make sure any derivatives computed occur before that frame, or after that frame, but not ACROSS that frame.

High speed video (and lots of other high speed measurement) attempts to approximate delta t going to zero for practical purposes in a measurement. But the fact that delta t is never really zero combines with resolution and accuracy of the independent variable to keep it interesting. You can't just apply formulas for difference ratios and expect things to make sense.

 

[Harshna]

There's always a combination of computer analysis and human thinking, application, and interpretation. But, we're definitely not crunching the numbers by hand.

Suppose we use some video analysis program to produce raw x vs. t and y vs. t data that we need to then convert to velocity, acceleration, force, etc. Data is never perfect. Frame rates, pixel resolution, and other factors usually necessitate a manual path. We use a spreadsheet for a lot of it, but there are often careful choices for how to smooth the data, which technique to use to compute the derivatives numerically, and lots of double checks that things are making sense - got to know what all those derivatives and integrals mean physically to execute all the double checks.

One key aspect of calculus we use a lot recently is that a lot of rules of calculus do not apply at a point where a function cannot be differentiated. In a video, that happens (for practical purposes) when a collision occurs in a time span shorter than the time between frames. The velocity of the objects (for practical purposes) changes instantaneously between the frames, so we need to manually recognize the frame where that occurred and make sure any derivatives computed occur before that frame, or after that frame, but not ACROSS that frame.

High speed video (and lots of other high speed measurement) attempts to approximate delta t going to zero for practical purposes in a measurement. But the fact that delta t is never really zero combines with resolution and accuracy of the independent variable to keep it interesting. You can't just apply formulas for difference ratios and expect things to make sense.

Hi Dr. Courtney,

Thank you for this - I am getting more ideas as to how maths is used in jobs out there, which is what I was after!

 

[Devils]

You really have to work in some research-related area.For example in engineering, you may be an expert in grad/div/curl and calculus, but if you are designing a building all that is done for you by software.

I worked in a research organisation decades ago. We woked on algorithms and softtware for computational geometry. We stored representations of geometric objects (land boundaries) in relational databases. We wrote and solve the software.

To work in these areas you need some luck and often a higher degree. I think there morw interesting jobs are accessible if you have an engineering degree eg embedded systems with input from sensors