Why might researchers distinguish their interests between applied math and computational math? I often see PhD students and faculty members describe their research interests on their web pages as something like:


  I am broadly interested in applied and computational mathematics.


What is the difference between applied math and computational math? 

Do applied mathematicians not necessarily work on computations and computational mathematicians not necessarily work on applied math?
"Applied" math is in opposition to "pure" mathematics: that is, applied mathematics is used for a specific ("real-world") problem, such as fluid mechanics, statistical physics, or even the biosciences. This need not be computational: in many cases, it involves the study of differential equations and other analytical tools (expansions and other techniques). 

In contrast, "computational" mathematics implies mathematics that cannot be solved by "pen and paper" techniques but instead require the use of a computer—either desktop or cluster—to solve.