Mathematical economics is the application of mathematical methods to represent theories and analyze problems that apply to economics. The applied methods which are used include integral calculus, difference and differential equations, matrix algebra, mathematical programming and computational methods. Mathematics allows economists to form meaningful, testable proposition about wide-ranging and complex subjects. Most of the economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify assumptions and implications.
Many theories in classical economics can be presented in simple geometric terms or elementary mathematical notation. Mathematical economics makes use of calculus and matrix algebra in economic analysis in order to make powerful claims that would be more difficult without such mathematical tools. It has become increasingly dependent upon mathematical methods and the mathematical tools it employs.