Much of the study of economics requires an understanding of mathematical and statistical methods, so what exactly is mathematical economics? Mathematical economics is best defined as a sub-field of economics that examines the mathematical aspects of economics and economic theories. Or put into other words, mathematics such as calculus, matrix algebra, and differential equations are applied to illustrate economic theories and analyze economic hypotheses.

Proponents of mathematical economics claim that the primary advantage of this particular approach is that it permits the formation of theoretical economic relationships through generalizations with simplicity. Mind you, the "simplicity" of this approach to the study of economics is certainly subjective. These proponents are likely to be skilled in complex mathematics. An understanding of mathematical economics is particularly important for students considering the pursuit of a graduate degree in economics as advanced economics studies make great use of formal mathematical reasoning and models.

### Mathematical Economics vs. Econometrics

As most economics student will attest to, modern economic research certainly doesn't shy away from mathematical modeling, but its application of the math differs within the various subfields. Fields like econometrics seek to analyze real-world economic scenarios and activity through statistical methods. Mathematical economics, on the other hand, could be considered econometrics' theoretical counterpart. Mathematical economics allows economists to formulate testable hypotheses on a wide array of complicated subjects and topics. It also permits economists to explain observable phenomena in quantifiable terms and provide the basis for further interpretation or the provision of possible solutions. But these mathematical methods that economists use are not limited to mathematical economics. In fact, many are often utilized in the studies of other sciences as well.

### The Math in Mathematical Economics

These mathematical methods generally reach far beyond typical high school algebra and geometry and are not limited to one mathematical discipline. The importance of these advanced mathematical methods is captured perfectly in the mathematics section of books to study before going to graduate school in economics:

"Having a good understanding of mathematics is crucial to success in economics. Most undergraduate students, particularly those coming from North America, are often shocked by how mathematical graduate programs in economics are. The math goes beyond basic algebra and calculus, as it tends to be more proofs, such as "Let (x_n) be a Cauchy sequence. Show that if (X_n) has a convergent subsequence then the sequence is itself convergent."

Economics uses tools from essentially every branch of mathematics. For instance, a great deal of pure mathematics, such as real analysis, appears in microeconomic theory. Numerical method approaches from applied mathematics are also used a great deal in most subfields of economics. Partial differential equations, which are normally associated with physics, show up in all kinds of economics applications, most notably finance and asset pricing. For better or for worse, economics has become an incredibly technical topic of study.