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Mathematical economics is understood as the application of mathematical tools to represent theories , develop models, and analyze economic problems . Reference is made to complex mathematical tools such as integral and differential calculus, differential equations, matrix algebra, mathematical programming and computational methods, and applications of statistical mathematics. The use of mathematical tools in economics allows rigorous formulations of theories and models, generalizable to complex systems, and which lead to concrete solutions that would not be possible to achieve otherwise.
Mathematical economics and econometrics
At first glance, one might think that mathematical economics is somewhat similar to econometrics, since the general definition of this branch of economics is similar, and refers to the use of mathematical and statistical models to analyze economic systems. But mathematical economics and econometrics approach the problems of economics from different angles. Econometrics analyzes concrete economic scenarios using statistical methods while mathematical economics could be considered as the theoretical counterpart of econometrics. It is based on mathematical economics that economists formulate hypotheses and theories, and develop models of complex economic systems. Mathematical economics also allows them to explain phenomena of interest,
Mathematics and economics
A thorough understanding of the complex mathematical tools on which mathematical economics is based is essential to fully approach this discipline. And the mathematical tools that are used are very diverse. For example, mathematical analysis is used in microeconomics; differential calculus and differential equations, convex sets, and graph theory are widely applied in economic theory; linear mathematical models have a wide variety of applications as do mathematical optimization methods, and so on.
Sources
Mankiw, N. Gregory. Principles of economics . Second edition. mcgrawhill
Martha Puig. Introduction to microeconomics. University of Barcelona, Spain, 2006.
Omar Alejandro Martinez Torres. Economic analysis . Astra editions, Mexico, 1984.
