Can you expand on that with some nice examples that really are beyond arithmetic, basic calculus, linear algebra and integral transforms?
One thing that has been touched upon is 'mathematical chemistry', which does use some graph theory, combinatorics and topology. There is also quantum chemistry, but I think as dealing with more than a few interacting particles explicitly is impossible one resorts to numerical methods - I am not sure that many people in this field really need deep results from topological algebra, operator theory and spaces.
Chemical engineering - as suggested in this