Most 'practical' high level math/sci/eng courses?

[TecHNooB]

For anyone who has done grad school, list the classes you feel were/are the most useful for 'general' application. I kind of have an idea of which courses I'd like to take, but I wanna see what comes up

 

[Farmer]

Numerical methods/applied linear algebra at any level, discrete math/algorithms at any level, any kind of CS class where the assignments are project based on a real language (C, Java), because unless your pure theory it'd be hard not to need to program.

Otherwise, you really need to tell us your particular field. For instance, abstract algebra and group theory would be extremely "practical" for theoretical physicists, but totally useless to an aerospace engineer.

 

[Gibsons]

Statistics. Useful for almost any field. Not sure if it counts as "high level" though.

 

[esun]

Probability and/or stochastic processes. Probability is ridiculously useful across a huge number of fields AND in everyday life. Can't beat it.

 

[CP5670]

I recall that you're an electrical engineer, and it depends on what sub-field you are into and how much you want to do research in it, as opposed to being a practitioner. The stuff Farmer mentioned is always useful, along with basic probability.

 

[TecHNooB]

is tensor calculus useful? i kinda want to learn that for some reason might want to take a rigorous course on relativity too.

 

[A5]

is tensor calculus useful? i kinda want to learn that for some reason might want to take a rigorous course on relativity too.

The only place I've seen tensors used is in Optics (non-linear optics at that), and frankly once the prof finishes the derivation you just deal with them the same way you did Algebra 2 in high school (or some Linear Algebra if you get really advanced) .

If you're going to be focusing on anything involving semiconductors or materials, a quantum mechanics class wouldn't hurt, either.

 

[ncalipari]

Statistics.

Both Kolmogorov's and Bayes versions.



Then probability (but much less than statistics).


Then Differential Equations and analysys.

 

[Farmer]

The only place I've seen tensors used is in Optics (non-linear optics at that), and frankly once the prof finishes the derivation you just deal with them the same way you did Algebra 2 in high school (or some Linear Algebra if you get really advanced) .

If you're going to be focusing on anything involving semiconductors or materials, a quantum mechanics class wouldn't hurt, either.

Outside of GR, tensors are widely used in applied electromagnetics, plasma.

 

[slugg]

I'd say algorithms. Gotta be able to solve the general case, right?

 

[Ajay]

I'd say algorithms. Gotta be able to solve the general case, right?

+1 :thumbsup:

 

[Ajay]

Otherwise, you really need to tell us your particular field. For instance, abstract algebra and group theory would be extremely "practical" for theoretical physicists, but totally useless to an aerospace engineer.

There are practical solutions in E&M that use abstract algebra and group theory. Don't ask me what they are, it been too long; I just remember solving real problems with them.

 

[Farmer]

There are practical solutions in E&M that use abstract algebra and group theory. Don't ask me what they are, it been too long; I just remember solving real problems with them.

As there are in organic chemistry, I think. I was just pointing out an example.

 

[GoSharks]

Outside of GR, tensors are widely used in applied electromagnetics, plasma.

+mechanics

Probability/Stats is prob the most useful in a general, doesn't matter what you are studying, sense.

 

[CP5670]

There are practical solutions in E&M that use abstract algebra and group theory. Don't ask me what they are, it been too long; I just remember solving real problems with them.

Algebra is also used a fair bit in coding theory and error correction.

 

[Bootleg Betty]

Not sure. But

- Linear algebra is useful for physics, graphics, machine learning, data analysis.
- General algebra is basis of pretty much any modern cryptography.
- Statistics is basis for humanities, machine learning, data analysis, manufacturing processes, economy and stuff.
- Optimization theory is useful for economy, machine learning and engineering in general.
- Discrete mathematics (with graph theory) is basis for computer science, algorithms, computer networks and stuff.
- Differential equations are for physics.
- Fourier (and Laplace) analysis is used in electric engineering and in digital signal processing.

So I'd say statistics.

However, in most "high-end" fields, you get most of it combined. Physics in general is pretty much linear algebra, calculus and differential equations at once, and that's before statistics comes in.

Or like in machine learning, where you derive something from bayes decision rules (statistics and probability), make derivates and see where it converges (calculus), use optimization to find approximate parameters for the model (optimization featuring doing second derivates of whole matrices at once) while working in Hilbert space of possibly infinite dimension defined by strange yet working inner product (general algebra + madness).

So that.

 

[mrkun]

Probability and/or stochastic processes. Probability is ridiculously useful across a huge number of fields AND in everyday life. Can't beat it.

QFT