Recommended non-math courses for applied Mathematics?

[battousai]

Hello everyone. I am going to be majoring in applied math. Outside the math courses, I would like to know the recommended courses to take that will be of interest to an applied mathematician. From fields like computer science, physics, engineering, and the like..

 

[battousai]

anyone?

 

[Bourbaki1123]

Well, the two biggest areas I know about are computer science and physics. Then there's statistics, which can also fit in with computer science if you're into AI/machine learning, and it can fit in with physics (Quantum mechanics, statistical mechanics, Brownian motion etc.) What interests you?

 

[battousai]

Well, I'm an incoming freshman, so I don't know what interests me yet. I'm just trying to figure out the courses that I will be eventually taking. The institution that I'm going to isn't exactly flexible in terms of classes and units so I'm planning out my courses in advance.

 

[hadsed]

I would say take some algorithms and machine learning, for CS. Those can get to be pretty mathematical. Perhaps neural networks as well. I think anything having to do with A.I. can be interesting to an applied mathematician.

As for physics, if I were you I'd want to maybe do some statistical mechanics class. It really depends on what you're interested in. I know you said you weren't sure, but just try and think about what you're curious about. What sounds better to you, learning how a computer works at the fundamental level or the microchips? Maybe even deeper, do you want to know how the particles interact (QM)? Maybe you're interested in something completely different, like biophysics or optics. There's some cool stuff that can get pretty mathematical with non-linear optics and quantum optics. You just have to read around a bit and see what you like. That goes for doing CS or physics. It might be in your best interest to pick one or the other, that way you can have a more complete understanding of whatever your interests may be.

EDIT: Wow, Bourbaki said everything I said. Woops!

 

[Dembadon]

Here's a list of courses outside of the mathematics department at my university that one is permitted to take as electives for an applied mathematics degree:

CS 365 Mathematics of Computer Science
CS 465 Theory of Computation
CS 467 Analysis of Algorithms

CE 487 Computer-Aided Analysis of structures

EE 351 Electric and Magnetic Fields
EE 371 Control Systems
EE 484 Digital Signal Processing

Geol 414 Hydrologic Fluid Dynamics
Geol 415 Geological Thermodynamics
Geol 490/690 Elementary Seismology

ME 367 Elementary Fluid Mech
ME 303 Applied Numerical Methods

Phys 473 Electricity and Magnetism

CHEM 353 Physical Chemistry I
CHEM 354 Physical Chemistry II

EC 440 Mathematical Economics
EC 441 Econometrics

Your institution probably won't have the same names, but the topics might give you some direction and/or ideas.

 

[battousai]

I guess I have a variety of interests right now. I would love to learn about the mathematical aspect of computing: algorithms, combinatorics, graphs/trees, and such, and their applications. I would like to work in the industry after graduating. Maybe with a company like IBM or the like. Do these places have a space for applied mathematicians?

But I am also interested in studying dynamical systems, or network theory. I've read a bit about it, and it fascinates me. Mostly the work of Steven Strogatz. Maybe apply some maths to fields like sociology or neuroscience..

Physics is very intriguing too. I guess with an applied maths degree I would be working with the mathematical aspect of it, but I would like to learn more before making any conclusions.

 

[battousai]

bump

What do you guys think of this specialization? Would it be suitable for graduate school studies? Medical school? Working outside academia?

http://www.math.ucla.edu/ugrad/majors/major.aplsci.medlife.shtml

For a guide of what the codes correspond to:

http://www.registrar.ucla.edu/schedule/catsel.aspx

 

[lsaldana]

You mentioned Strogatz which brings up Nonlinear Dynamics. I know a lot of applied math majors at my school who are taking or took an upper-level physics course on Nonlinear Dynamics and Chaos. I work with a couple of applied math majors in my (physics) lab where they work with robot locomotion etc. You might also want to check your math department for a class on Dynamics or Bifurcations which covers similar topics.

 

[battousai]

Well, this is the link to the physics course offerings at my school:

http://www.registrar.ucla.edu/schedule/catalog.aspx?sa=PHYSICS&funsel=3

but I don't see a Nonlinear Dynamics class. I do see it under "Classical Mechanics" though.

 

[SpaceDomain]

DIGITAL SIGNAL PROCESSING!

That is the most practical I think.

I have talked to math majors that tell me they study everything used in DSP but they do not know how it is used practically.

Also, you will learn programming skills practicing DSP.

 

[lsaldana]

Well, this is the link to the physics course offerings at my school:

http://www.registrar.ucla.edu/schedule/catalog.aspx?sa=PHYSICS&funsel=3

but I don't see a Nonlinear Dynamics class. I do see it under "Classical Mechanics" though.

The analytic mechanics classes seem useful for any applied mathematician. If you want to see more varied and abstract math applications, then I'd suggest quantum mechanics or general relativity.

 

[SpaceDomain]

Quantum Mechanics and General Relativity may be fun to study, but the most practical thing to learn would be DSP.

Every engineer and computer scientist should know the basics of DSP. I don't think as many people need to understand quantum mechanics.

 

[deRham]

know the recommended courses to take that will be of interest to an applied mathematician.

What do you want to do? Obviously you should concentrate on that.

Almost anything in physics is probably of some interest. In CS, see Bourbaki's post, and statistics / advanced probability are great things to know.

Other than that, there are various computational aspects of the sciences. Anything training you in simulations is probably a nice thing - you can find that in operations research classes, finance, all sorts of things.

Knowing programming is not strictly applied mathematics, but really helps for applied mathematics endeavors.

I'd say more than specific knowledge, you should develop an interest for using certain kinds of thinking, because the nature of applied mathematics is that it can be very broad.

Familiarity with simulations, knowledge of advanced statistics, probability, differential equations, and knowledge of programming, together with a basic undergraduate math foundation should prepare you to specialize in almost anything. Oh and you should be comfortable with Fourier transforms for sure.

 

[SpaceDomain]

Familiarity with simulations, knowledge of advanced statistics, probability, differential equations, and knowledge of programming, together with a basic undergraduate math foundation should prepare you to specialize in almost anything. Oh and you should be comfortable with Fourier transforms for sure.

Sorry if I am over-posting, but I would like to point out that all of this is used in DSP, except maybe differential equations. But you will use discrete differential equations (difference equations).

 

[battousai]

bump

What do you guys think of this specialization? Would it be suitable for graduate school studies? Medical school? Working outside academia?

http://www.math.ucla.edu/ugrad/majors/major.aplsci.medlife.shtml

For a guide of what the codes correspond to:

http://www.registrar.ucla.edu/schedule/catsel.aspx

looking for an answer to this

 

[deRham]

One addition would be Stochastic mathematics.

And yes, I agree signal processing covers a lot of applied math that can be widely used, and also gives experience working with relevant simulations.

 

[battousai]

What is stochastic mathematics?

 

[battousai]

bump

when picking courses at the undergraduate level, with graduate school in mind, is it better to work on a breadth of courses or focus on depth?

 

[clope023]

What is stochastic mathematics?

Statistics of random processes

http://en.wikipedia.org/wiki/Stochastic_process

 

[hadsed]

bump

when picking courses at the undergraduate level, with graduate school in mind, is it better to work on a breadth of courses or focus on depth?

I would expect it wouldn't matter much that I'm talking from a physics perspective. I think it'd be difficult to know exactly what you'll want to do in graduate school while you're an undergrad. Plus, narrowing yourself sooner than you have to I think isn't a very good thing. I would say breadth is the name of the game if you're an undergrad, it only makes sense. Of course, maybe you could hold off on some purer maths and instead sign up for some numerical or applied math classes, but that's different I think. Better to be familiar with everything when you're making such a big decision (when the day comes).