Help Me Decide: Math 481 vs CS 457 for Physics Majors

[iacephysics]

Hi guys, I am trying to decide between these two courses. Which one is more useful for a physics major?

MATH 481 Intro to Differential Geometry (Vector and Tensor Analysis)

The basic tools of differential geometry will be introduced at the undergraduate level, by focusing on examples. This is a good first course for those interested in, or curious about, modern differential geometry, and in applying differential geometric methods to other areas.

Manifolds: configuration spaces, differentiable manifolds, tangent spaces, tangent bundles, orientability.
Calculus on manifolds: Vector fields, flows, tensor fields.
Differential forms and exterior calculus.
Integration theory: Generalized Stokes theorem, de Rham cohomology.
Riemannian geometry: Riemannian metrics, geodesics.

Text: The Geometry of Physics, An Introduction, T. Frankel, Cambridge U.P. 1997


Or

CS 457 Numerical Methods II

Orthogonalization methods for linear least squares problems. QR factorization and singular value decomposition

Iterative methods for systems of linear algebraic equations. Stationary iterative methods. Krylov subspace methods

Eigenvalue problems. Power, inverse power, and QR iterations. Krylov subspace methods

Nonlinear equations and optimization in n dimensions. Newton and Quasi-Newton methods. Nonlinear least squares

Initial and boundary value problems for ordinary differential equations. Accuracy and stability. Multistep methods for initial value problems. Shooting, finite difference, collocation, and Galerkin methods for boundary value problems

Partial differential equations. Finite difference methods for heat, wave, and Poisson equations. Consistency, stability, and convergence

Fast Fourier transform. Trigonometric interpolation. Discrete Fourier transform. FFT algorithm

 

[malawi_glenn]

If you like theoretical Physics more, go for the first one :-)

If you like experimental Physucs more, go for the second one :-)

So it depends on what KIND of physics major you are deling with.

 

[Mene]

I would suggest that both courses have their own unique benefits for a physics major. Math 481, being an introductory course in differential geometry, would provide a strong foundation in advanced mathematical concepts that are crucial in modern physics. The course covers topics such as manifolds, tensor analysis, and Riemannian geometry, which are all important tools in fields such as general relativity and quantum field theory.

On the other hand, CS 457 focuses on numerical methods, which are essential for solving complex mathematical problems that arise in physics. This course covers topics such as linear and nonlinear equations, optimization, and partial differential equations, all of which are commonly encountered in physics research. The use of computational methods is becoming increasingly important in solving problems that are too complex for analytical solutions, making this course highly relevant for a physics major.

Ultimately, the decision between these two courses may depend on your specific interests and career goals. If you are more interested in theoretical physics and want to pursue research in areas such as general relativity or quantum field theory, then Math 481 may be the better choice. However, if you are interested in applying your physics knowledge to practical problems and want to develop strong computational skills, then CS 457 may be the more useful course for you. It is also worth considering if your university offers any other courses in either differential geometry or numerical methods, as taking both may provide a well-rounded education in advanced mathematical concepts and their applications in physics.