Math High impact on society, reality tested, and heavy use of logic and symbolic math

[ygolo]

I am looking to make a career shift.

I am looking for a career track with the following characteristics:

1) Heavy use (and need to learn) advanced mathematical concepts (especially symbolic in nature). I want to be working with equations and logic in a symbolic manner on a daily basis.

2) A career in which the theories are readily tested/testable. I may or may not want to do the testing, depending on how tedious it is. If it is tedious to test, I would rather not. If the testing is easy or fun, I like having the immediate feedback.

3) A career where the work will be of great significance to humanity. --The potential for ground breaking discoveries or inventions that move society forward.

Any suggestions?Also, what credentials would I need to obtain to enter these fields?

So far, I have:
A B.S. in Computer Engineering
A B.S. in Applied Discrete Mathematics
An M.S. in Electrical Engineering
8+ years in Integrated Circuits industry

 

[ygolo]

After further discussion with others, I've decided to add a fourth criteria:

4) A field in which people are mainly there due to their passion, curiosity, etc.

 

[calvinuk]

If anyone here knew of a job like that, they'd be doing it, and they wouldn't tell you.

 

[Astronuc]

I am looking to make a career shift.

I am looking for a career track with the following characteristics:

1) Heavy use (and need to learn) advanced mathematical concepts (especially symbolic in nature). I want to be working with equations and logic in a symbolic manner on a daily basis.

2) A career in which the theories are readily tested/testable. I may or may not want to do the testing, depending on how tedious it is. If it is tedious to test, I would rather not. If the testing is easy or fun, I like having the immediate feedback.

3) A career where the work will be of great significance to humanity. --The potential for ground breaking discoveries or inventions that move society forward.

4) A field in which people are mainly there due to their passion, curiosity, etc.

Any suggestions?


Also, what credentials would I need to obtain to enter these fields?

So far, I have:
A B.S. in Computer Engineering
A B.S. in Applied Discrete Mathematics
An M.S. in Electrical Engineering
8+ years in Integrated Circuits industry

Probably computational physics. Companies like Wolfram or Comsol, which develop simulation/engineering software.

People who get involved in startup companies have the passion, curiosity, etc.

 

[Locrian]

Probably computational physics. Companies like Wolfram or Comsol, which develop simulation/engineering software.

Only if he equates computer simulations with "working with equations and logic." That might seem a reasonable connection to us, but a lot of people out there would imagine "working with equaitons and logic" to require us to actually push the equations around, not use a computer to solve second order diffeq.

I'm actually going to guess that what he wants doesn't really exist anymore, though I could be underestimating how well he understands the subject.

 

[Astronuc]

I think jobs that are strictly devoted to symbolic math or equations are few and far between.

In my job, we do simulations which are basically finite element analyses of the thermo-mechancial behavior of solid objects. We use proprietary software developed in-house as well as commercial software like ANSYS, ABAQUS, Fluent, . . .

Part of the development process is to sit down with pencil/pen and paper and derive the consitutive equations, and then cast them into computer code. Then there are an array of thermophysical and mechanical properties models. The theory manual is extensive.

Every now and then we get new data with which to modify an existing model or add a new model. That involves fitting experimental data, or manipulating differential or differentio-integral equations, and casting them into code (FORTRAN).

Our simulations are validated against experiments, and in some cases are used to make predictions, which are ultimately tested by performance or in some cases measurements.

Part of the time we develop methods, but a lot of the time, we apply the methods.

And my colleagues and I are pretty passionate about what we do, and we like to think that it benefits humanity in someway.

 

[ygolo]

Only if he equates computer simulations with "working with equations and logic." That might seem a reasonable connection to us, but a lot of people out there would imagine "working with equaitons and logic" to require us to actually push the equations around, not use a computer to solve second order diffeq.

I'm actually going to guess that what he wants doesn't really exist anymore, though I could be underestimating how well he understands the subject.

I meant more the requirement to use and learn more advanced mathematics from a conceptual point of view. That's the part of math I like--the conceptual understanding. I could care less if a computer does the grinding rather than me. I would prefer there to be much higher conceptualization to grinding ratio in general.

Frankly, every form of engineering has extensive use of simulations and trial and error, and I am quite familiar and experienced doing these. Spice, Modelsim, and Matlab/Simulink in particular.

This stuff bores me to tears.

I think jobs that are strictly devoted to symbolic math or equations are few and far between.

In my job, we do simulations which are basically finite element analyses of the thermo-mechancial behavior of solid objects. We use proprietary software developed in-house as well as commercial software like ANSYS, ABAQUS, Fluent, . . .

Part of the development process is to sit down with pencil/pen and paper and derive the consitutive equations, and then cast them into computer code. Then there are an array of thermophysical and mechanical properties models. The theory manual is extensive.

Every now and then we get new data with which to modify an existing model or add a new model. That involves fitting experimental data, or manipulating differential or differentio-integral equations, and casting them into code (FORTRAN).

Our simulations are validated against experiments, and in some cases are used to make predictions, which are ultimately tested by performance or in some cases measurements.

Part of the time we develop methods, but a lot of the time, we apply the methods.

And my colleagues and I are pretty passionate about what we do, and we like to think that it benefits humanity in someway.

The bold-ed part appeals to me (though FORTRAN? really?). I wouldn't mind working on getting the simulations to run and scale really well on cluster machines--that part of coding is a lot of fun for me--making the algorithm match the machine.

I should have mentioned also that this is meant for me to create long-range goals.

Just because I have a computer engineering back-ground doesn't mean I have to stick with computers.

To put it another way:
Having to go back to school to learn something different, may actually be a plus.

For instance this thread makes little sense to me, but learning enough to understand it is very motivating for me.

The thing is, I don't know if GUTs are readily testable--but if they are they seem like they have long-term potential for a great impact on society.