Applied mathematics is a branch of mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional

Professional

A professional is a person who is paid to undertake a specialised set of tasks and to complete them for a fee. The traditional professions were doctors, lawyers, clergymen, and commissioned military officers. Today, the term is applied to estate agents, surveyors , environmental scientists,...

 specialty in which mathematicians work on practical problems; as a profession focused on practical problems, applied mathematics focuses on the formulation and study of mathematical models.