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I'm planning on going to grad school for soft condensed matter/biological physics. I'm generally interested in learning as much math as possible, but being a senior, I don't have much time.. I was hoping to hear some opinions/advises about which of the following courses would be most benefitial to me. I've pretty much decided that I want to do experiment, but I think some modeling skills would be good to have, even for an experiementalist. Also, it is possible that biological physics would become pretty theoretically advanced during my career span, so I would want to be able to understand what theoreticians say..

Thanks in advance for any input!

1. Abstract Algebra (a year long course)

Groups and their structure, including the Sylow

theorems; elementary ring theory; polynomial rings; basic field theory; Galois

theory; Module theory, including application to canonical form theorems of linear algebra.

2. Real Analysis (year long)

Rigorous analysis in Euclidean space and on metric spaces. Metric space topology, properties of Euclidean spaces, limits and continuity, differentiation and integration, sequences and series, the inverse and implicit function theorems. Lebesgue integration with applications

3. Differential equations of mathematical physics (2 quarters)

Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green's functions, distribution theory, integral equations, transforms, potential theory, diffusion equation, wave equation, maximum principles, and variational methods.

4. Numerical solution of partial differential equations (1 or 2 quarters)

Numerical solution of partial differential equations by finite difference methods and spectral methods. Construction of algorithms, consistency, convergence, and stability of numerical methods. Matrix iterative analysis.

It would be nice if you can even rank them in the order of usefulness :)

Thanks in advance for any input!

1. Abstract Algebra (a year long course)

Groups and their structure, including the Sylow

theorems; elementary ring theory; polynomial rings; basic field theory; Galois

theory; Module theory, including application to canonical form theorems of linear algebra.

2. Real Analysis (year long)

Rigorous analysis in Euclidean space and on metric spaces. Metric space topology, properties of Euclidean spaces, limits and continuity, differentiation and integration, sequences and series, the inverse and implicit function theorems. Lebesgue integration with applications

3. Differential equations of mathematical physics (2 quarters)

Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green's functions, distribution theory, integral equations, transforms, potential theory, diffusion equation, wave equation, maximum principles, and variational methods.

4. Numerical solution of partial differential equations (1 or 2 quarters)

Numerical solution of partial differential equations by finite difference methods and spectral methods. Construction of algorithms, consistency, convergence, and stability of numerical methods. Matrix iterative analysis.

It would be nice if you can even rank them in the order of usefulness :)

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