
 Mathematicians 
  Applied mathematicians, on the other hand, use theories and techniques, such as mathematical modeling and computational methods, to formulate and solve practical problems in business, government, and engineering and in the physical, life, and social sciences. 
  Applied mathematicians start with a practical problem, envision the separate elements of the process under consideration, and then reduce the elements to mathematical variables. 
  In early 2005, the average annual salary for mathematicians employed by the Federal Government in supervisory, nonsupervisory, and managerial positions was $88,194; that for mathematical statisticians was $91,446; and for cryptanalysts the average was $70,774. 
 www.bls.gov /oco/ocos043.htm (1727 words) 
