The application of mathematics and statistics to economics is normally called "econometrics," a term whose first known use was by Paweł Ciompa in 1910, although Ragnar Frisch is usually credited with the term in its modern usage. Essentially, econometrics is an example of applied mathematics.
Students taking classes in econometrics will normally cover the following topics:
Great places to find books on econometrics would be Amazon.com and Google books. The University of Illinois has a terrific econometrics tutorial, and don't forget to check out MIT's OpenCourseware for econometrics.