Math graduate programs which work closely with the applied math department?

It may depend on what applied area(s) you are interested in.

Some math departments include the applied areas, rather than having applied math as a separate department. But some applied areas may be in other departments, such as statistics, (theoretical) computer science, and operations research / industrial engineering.

Probably best to look on the web sites of each math department to see whether its areas of research (which may require looking in each faculty member’s web page) include those which you are interested in, and check if the college has other departments which may include the areas you are interested in.

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