What Classes Should I Take for an Applied Math PhD?

  • Thread starter cfddude123
  • Start date
  • Tags
    Classes
In summary, the speaker is a Math and Statistics undergrad who is planning on taking graduate level classes in preparation for applying to grad school in Applied Math. They are planning on taking Numerical Fluid Dynamics and Measure Theory, but are unsure about what other classes to take. They are considering Graduate ODEs, Graduate PDEs, Graduate Complex Analysis, or Numerical Analysis. They are leaning towards taking at least one differential equations class, but are unsure if they should also take a complex or numerical methods class. They are seeking advice on which classes would be most beneficial for their future in applied math.
  • #1
cfddude123
15
0
Hi PhysicsForum!

Fall 2012 semester will be my last semester as an undergrad in Math and Statistics and I was planning on taking a handful of graduate level classes. I'm planning on applying to grad school in Applied Math and concentrating on differential equations, fluid dynamics, or stochastic processes. I wanted an opinion on the classes I would be choosing.

I am for sure going to take

Numerical Fluid Dynamics:
Addresses numerical techniques for solving linear and nonlinear differential equations in initial value fluid flow problems. Students receive a thorough background in the principles used to evaluate numerical methods, the ability to critically interpret these methods as presented in the literature, and in particular, the practical application of these techniques in modeling multi-dimensional flow on high-performance computers. Temporal and directional splitting, finite differencing/volume methods, and adaptive nesting will be discussed.

and

Measure Theory:
Lebesgue measure on the real line; integration and differentiation of real valued functions of a real variable; and additional topics at discretion of instructor.


But I'm not sure what else to take. I want to take two more classes, but I don't know if I should lean towards theory (i.e. Differential Equations or Complex Analysis) or computing (Numerical Methods), especially since I want to do applied math in grad school. Here are the course descriptions for the classes I'm trying to decide between.

Graduate ODEs:
An introduction to the study of dynamical systems. Considers continuous and discrete dynamical systems at a sophisticated level: differential equations, flows and maps on Euclidean space and other manifolds. Emphasis will be placed on the fundamental theoretical concepts and the interaction between the geometry and topology of manifolds and global flows. Discrete dynamics includes Bernoulli shifts, elementary Anosov diffeomorphisms and surfaces of sections of flows. Bifurcation phenomena in both continuous and discrete dynamics will be studied.

Graduate PDEs:
Basic introduction to the study of partial differential equations; topics include: the Cauchy problem, power-series methods, characteristics, classification, canonical forms, well-posed problems, Riemann's method for hyperbolic equations, the Goursat problem, the wave equation, Sturm-Liouville problems and separation of variables, Fourier series, the heat equation, integral transforms, Laplace's equation, harmonic functions, potential theory, the Dirichlet and Neumann problems, and Green's functions.

Graduate Complex Analysis:
Topics include the Cauchy theory, harmonic functions, entire and meromorphic functions, and the Riemann mapping theorem.

or

Numerical Analysis:
Linear system solvers, optimization techniques, interpolation and approximation of functions, solving systems of nonlinear equations, eigenvalue problems, least squares, and quadrature; numerical handling of ordinary and partial differential equations.

TL;DR: What is more important in preparation for applied math PhD programs, math theory or computing knowledge. Will I get enough computing knowledge from the Numerical Fluid Dynamics class? Which two other classes should I choose.
 
Physics news on Phys.org
  • #2
I don't think you can ever go wrong with a differential equations class. Especially since you mention you would like to study this subject in grad school. Stochastic processes also uses differential equations a lot (or at least something very similar to it). So I would study this.

Whether to study ODE's or PDE's, I don't know. I'm leaning towards PDE's here, but I'm not sure how useful it will be for you later...
 
  • #3
micromass said:
I don't think you can ever go wrong with a differential equations class. Especially since you mention you would like to study this subject in grad school. Stochastic processes also uses differential equations a lot (or at least something very similar to it). So I would study this.

Whether to study ODE's or PDE's, I don't know. I'm leaning towards PDE's here, but I'm not sure how useful it will be for you later...

Well I was planning on taking at least one differential equations class out of the two. I was just wondering if it would be a better idea to take both differential equation classes vs. one differential equation class + complex or numerical methods.
 

What factors should I consider when choosing classes?

When choosing classes, you should consider your major or field of study, your graduation requirements, your interests and strengths, and your future career goals.

How can I determine the difficulty level of a class?

You can determine the difficulty level of a class by looking at the course description, talking to students who have taken the class before, and researching the professor's teaching style and expectations.

Are there any classes that are recommended for all students?

While every student's academic journey is unique, there are some general education or core classes that are recommended for all students, such as writing, math, and science courses.

How many classes should I take per semester?

The number of classes you should take per semester depends on your personal schedule, workload, and academic goals. It is recommended to take around 15-18 credits per semester to stay on track for graduation.

What resources can I use to help me choose the right classes?

You can use resources such as your academic advisor, online course catalogs, student reviews, and career services to help you choose the right classes. You can also attend information sessions or talk to professors in your field of study for guidance.

Similar threads

  • STEM Academic Advising
Replies
5
Views
987
  • STEM Academic Advising
Replies
9
Views
1K
  • STEM Academic Advising
Replies
21
Views
2K
  • STEM Academic Advising
Replies
4
Views
909
  • STEM Academic Advising
Replies
5
Views
1K
Replies
11
Views
1K
  • STEM Academic Advising
Replies
11
Views
522
  • STEM Academic Advising
Replies
13
Views
2K
  • STEM Academic Advising
Replies
2
Views
2K
  • STEM Academic Advising
2
Replies
63
Views
4K
Back
Top