Introducción a Matemáticas para Finanzas y Negocios

This module explores linear functions and their applications in finance and business. Students will learn about the geometric representation of linear equations and their application to simple interest calculations. The module covers key concepts such as slope and elasticity, and examines simultaneous equation models in their structural and reduced forms. Students will analyze equilibrium characteristics (existence, uniqueness, and stability) through supply and demand models, providing a foundation for understanding market dynamics.

This module focuses on matrices and vectors as mathematical tools for solving business and economic problems. Students will learn matrix operations including addition, multiplication, and inversion for solving equation systems. The module applies these concepts to determining macroeconomic equilibrium and fiscal multipliers. It also introduces the No-arbitrage Principle and its geometric vector representation, teaching students how to value financial assets through replication portfolios, a fundamental concept in modern finance.

This module examines non-linear functions and their applications in business decision-making. Students will study polynomial characteristics, their geometric interpretation, and root determination methods. Applications include project decision-making through Present Value and Internal Rate of Return calculations. The module also covers exponential and logarithmic equations, properties of exponential functions, and concepts of concavity and convexity, with applications to continuous interest calculation and decision-making under uncertainty using Jensen's inequality.

This module delves into financial mathematics with a focus on money market instruments and fixed income securities. Students will learn about different instrument types, yield rates, discount rates, compounding frequencies, and day count conventions. The module applies these concepts to calculate the price of treasury bills and compare yields using effective rates. It also covers the derivation of formulas for perpetuities, bonds, and annuities, with applications to mortgage valuation and corporate bond pricing.

This module introduces infinitesimal calculus concepts for business optimization problems. Students will learn function differentiation rules and how to determine first and second-order conditions for identifying maxima and minima. Applications include determining a company's optimal production amount. The module also covers constrained optimization using Lagrange multipliers and first-order conditions, with applications to constructing minimum variance stock portfolios, providing powerful tools for financial decision-making and resource allocation.