Applied Math vs Computational Science and Engineering (CSE)

[jbrussell93]

I'm a biological engineering major who is starting to lean more towards mathematics. More specifically, I'm interested in mathematical modeling and applying these models to biological systems, geosystems, ecology, etc (mainly scientific problems).

I will be minoring in math in order to supplement my engineering curriculum with applied math courses. My hope has been to get into a graduate program in applied math (at least to a terminal masters), but recently I've discovered numerous Computational Science and Engineering (CSE) programs. They seem to be similar to applied math programs in nature but with additional focus on computer science and applications to engineering problems. This is basically what I've learned from numerous programs websites, but I still can't seem to make a huge distinction in my mind between applied math and CSE programs. It seems as though many applied math programs have this same interdisciplinary feel and often work closely with engineering divisions. On the other hand, some CSE programs also have a focus on problems in science that are often found in applied math departments.

It seems as though my chances of getting into a CSE program would be much greater given my background and the fact that they do not require that Math GRE like most applied math programs do.

I am wondering for which scenarios one program may be better suited than the other. Is one better for entering industry, national lab, or academia after a masters or PhD?

Any and all help is much appreciated!

 

[InternetHuman]

Well, CSE is computer science + applied math (+ some stats) + a discipline where you want to apply computational methods. Compared to an applied math or a pure science master's, there should be more computing and applied math, but less (if at all) science than in a full science and less math than in a full math master's. CSE is often offered just as a small minor to engineering and science majors or computational methods have been integrated to the studies in some other way, but master's programs in CSE have been introduced.

The focus in CSE are computational methods for which CS topics and appiled math are the tools and the domain knowledge (e.g. biology, physics, economy, a branch of engineering...) is for understanding theories and practices to know how to study the subject's phenomena using computers. An ideal candidate is actually someone who has done bachelor level studies in science or engineering, because one has some of the domain knowledge needed to apply computational methods to a science or an engineering branch. But the programs also see people coming from applied math or CS backgrounds. Having a good grasp of and interest in mathematics is essential. I don't know why they don't require the math GRE, unless the GRE is too advanced considering that many enter CSE programs from CS or not so math intensive science/engineering undergraduate programs.

CSE is a good pick, if you're, in addition to your science/engineering interests, into applied math, computers and coding and the "computational science" thing. Career opportunities should be quite vast, because computational methods are used in multiple areas nowadays for research and analysis.

 

[jbrussell93]

Internet Human,
I appreciate your reply, it was very helpful in clarifying!

What would you say is more important prerequisite knowledge for an engineering major interested in CSE? Applied math or CS?

Or in other words: Which is easier to "pick up" in grad school?

 

[InternetHuman]

Internet Human,
I appreciate your reply, it was very helpful in clarifying!

What would you say is more important prerequisite knowledge for an engineering major interested in CSE? Applied math or CS?

Or in other words: Which is easier to "pick up" in grad school?

I personally think CS topics are easier to pick up. Math takes a lot of practice. Although, so does programming. But understanding CS theory, not so much.

 

[jbrussell93]

I personally think CS topics are easier to pick up. Math takes a lot of practice. Although, so does programming. But understanding CS theory, not so much.

Great! What would be the more important applied math classes to consider taking in your opinion?

Here is a list of possibilities:

- matrix theory
Basic properties of matrices, determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and Jordan normal forms. Introduction to writing proofs.

- advanced calc with applications
Linear mappings, Jacobi matrices and determinants, change of variables, vector fields, line and surface integrals, theorems of Green, Gauss and Stokes, sequences and series of functions, uniform convergence, special functions.

- *numerical analysis
Machine arithmetic, approximation and interpolation, numerical differentiation and integration, nonlinear equations, linear systems, differential equations, error analysis. Selected algorithms will be programmed for solution on computers.

- *numerical linear algebra
Solution of linear systems of equations by direct and iterative methods. Calculation of eigenvalues and eigenvectors of matrices. Selected algorithms programmed for solution on computers.

- applied analysis
Solution of the standard partial differential equations (wave, heat, Laplace’s eq.) by separation of variables and transform methods; including eigenfunction expansions, Fourier and Laplace transform. Boundary value problems, Sturm-Liouville theory, orthogonality, Fourier, Bessel, and Legendre series, spherical harmonics.

- mathematical modeling I & II
Solution of problems from industry, physical, social and life sciences, economics, and engineering using mathematical models.

- fluid dynamics and geophysical applications
Mathematical theory of fluid dynamics and applications to meteorology and oceanography.

* require MATLAB experience (which I will have)

I should be able to fit about 3 or 4

 

[InternetHuman]

Numerical analysis is a must.

Otherwise, depends on your interests. If you're interested in biological applications, then do a search about what mathematical theories and practices are useful there. Numerical Linear Algebra (or Matrix theory) and Mathematical modelling I & II at least?