Twenty-one reasons why you should take

"Mathematical Principles in Science" (Math 5101, 5202)

In Math 5101 ("Linear Mathematics in Finite Dimensions") you will learn, among others

1. The mathematics of the states of a linear system (vector space theory)
2. The mathematics of reference frames and their transformations (bases and the representation theorem)
3. The mathematics of linear systems (the four fundamental subspaces of a matrix)
4. The mathematics of covectors and metrics (linear functionals and dual vector space theory)
5. The mathematics of least squares approximations (subspaces and inner products)
6. The mathematics of stable and unstable systems (phase portrait of coupled system of differential equations)
7. The mathematics of vibrating systems (eigenvalue and eigenvector theory)
8. The mathematics of spectra (normal matrices and the spectral theorem)
9. The mathematics of normal modes and of linear systems with quadratic and linear constraints
10. (Rayleigh quotient and its geometry)
11. The mathematics of rectangular matrices (singular value decomposition theory)
In Math 5102 ("Linear Mathematics in Infinite Dimensions") you will learn, among others
12. The mathematics of bounded linear systems (Sturm-Liouville theory)
13. The mathematics of infinite dimensional inner product spaces (Hilbert space theory)
14. The mathematics of a ticking clock and a phase-locked laser (Fourier theory)
15. The mathematics of signal processing (wavelet and orthonormal wave packet analysis)
16. The mathematics of the unit impulse response of a linear system (Green's function theory)
17. The mathematics of representing symmetries of the Euclidean plane by cylinder waves and plane waves (special function theory)
18. The mathematics of the rotationally and translationally symmetric waves in the Euclidean plane

19. (Hankel and Bessel function theory)
20. The mathematics of high frequency waves (the method of steepest descent and stationary phase)
21. The mathematics of translating cylindrical waves (the cylindrical addition theorem)
22. The mathematics of wave propagation inside and outside a cylindrical pipe

23. (interior and exterior boundary value problems)
24. The mathematics of potentials and waves on a spherical background (algebraic method for solving linear partial differential equations)