For anyone interested in applying traditionally pure fields, Applied Topology has been slowly gaining steam lately (as reflected in the article: "topological" is now a hot word).
Robert Ghrist of UPenn has been at the forefront of bringing topology into applied fields; and has written a good text on the subject.
Robert Ghrist of UPenn has been at the forefront of bringing topology into applied fields; and has written a good text on the subject.