What is Meant by Mathematical Methods in Economics?

Question: What is Meant by Mathematical Methods in Economics?

Answer: Perhaps the best explanation of Mathematical Economics can be found at Wikipedia. They explain that "Mathematical economics is the sub-field of economics that explores the mathematical aspects of economic systems. Modern mainstream economic research typically makes extensive use of mathematical modelling... Mathematical economics can be regarded as the "theoretical" counterpart of Econometrics, which attempts to analyse the real world of economic activity using statistical techniques. The mathematical tools economists use are often applied in other sciences as well."

The mathematics mentioned in the Wikipedia article can go far beyond typical highschool alegbra and geometry. This idea is expressed 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 every branch of mathematics. A great deal of pure mathematics, such as real analysis, appears in microeconomic theory. Numerical methods approaches from applied mathematics are used a great deal in most subfields of economics. Partial differential equations, normally associated with physics, show up in all kinds of economics applications, most notably finance and asset pricing. For better of for worse, economics has become an incredibly technical topic of study.

If you'd like to learn more about mathematical economics, I highly recommend finding some of the texts I mention in Books to Study Before Going to Graduate School in Economics.