Mathematical Economics I (3rd year course)

ECO 3145: Mathematical Economics I is an intermediate undergraduate course on the mathematical foundations of economic analysis. The course develops the tools needed to read, construct, and solve formal economic models.

The central reference for the course is my textbook, Mathematics for Economics and Business. The course follows the book closely and combines formal definitions, propositions, proofs, examples, exercises, and economic applications. The goal is not only to teach mathematical techniques, but to show how mathematics becomes a language for economics.

The course covers matrix algebra, linear systems, functions, optimization with and without constraints, implicit functions, comparative statics, Taylor series, the envelope theorem, integration, difference equations, and differential equations. Applications are drawn from consumer theory, producer theory, welfare analysis, equilibrium analysis, and dynamic economic systems.

Main themes include:

• Matrix algebra and linear systems

• Functions of one and several variables

• Limits, differentiation, and comparative statics

• Unconstrained optimization

• Constrained optimization with equality and inequality constraints

• Economic applications of optimization

• Integration

• First-order difference equations

• First-order differential equations

• Mathematical modelling in economics

Textbook

Mathematics for Economics and Business

Aggey Simons

This textbook was written to support the course and to give students a coherent path through the mathematical tools used in modern economics. It emphasizes both rigor and intuition: definitions and proofs are developed together with economic examples, diagrams, exercises, and applications.

The manuscript is one of my major teaching projects. It grew out of many years of teaching mathematical economics and reflects my view that students should not only memorize techniques, but understand why these techniques matter for economic reasoning.