Excerpts from lecture notes:

Mathematical economics is an approach to economic analysis, in which the economists make use of mathematical symbols in the statement of the problem and also draw upon known mathematical theorems to aid in reasoning.

The purpose of this course is to introduce the most fundamental aspects of the mathematical methods such as those matrix algebra, mathematical analysis, and optimization theory.

Mathematical Versus Nonmathematical Economics

Since mathematical economics is merely an approach to the economic analysis, it should not and does not differ from the nonmathematical approach to economic analysis in any fundamental way. The difference between the two approaches is that in the former, the assumptions and conclusions are stated in mathematical symbols rather than words and in equations rather than sentences.

Advantages of the Mathematical Approaches

(1) the analysis is more rigorous;
(2) it allows us to treat the general n-variable case; and
(3) the "language" used is more concise and precise.