Introduction to Mathematics for Finance and Business

This course will allow you to use mathematical equations to describe and analyze certain problems that appear in the areas of business and finance. For example, it analyzes how the performance of an asset or distributing a product is modeled, how an optimization process is done in a portfolio or how aversion to risk can be described to an investor. Additionally, it will help you understand how certain algorithms are solved to analyze large amounts of data, make forecasts and describe trends. The course uses programming and simulation tools to convey the main concepts.

The course starts from the concept of function, that is the basis of mathematical modeling and allows identifying the relationship between a group of variables of interest. Different types of functions are analyzed , such as linear, polynomial and exponential functions, providing specific examples to the areas of finance and business. The concepts are supported with the help of packages such as R / Python or Matlab. In this way, interactive and visual learning is motivated, which in addition to transmitting mathematical concepts, establishes the bases to develop computational skills.

Topic 1: Linear Functions

1.1 Geometric presentation of a linear equation. Linear interpolation. Slope concept.

1.2 First order difference equation. Introduction to simulation.

Topic 2: Linear Algebra

2.1 Solution of simultaneous equations. Concept of a vector and a matrix.. Geometric representation.

2.2 Matrix operations. Characterization of the number of solutions in a system. Linear Transformation Concept.

Topic 3: Nonlinear functions

3.1 Polynomials and root determination. Concepts of Concavity and Convexity.

3.2 Exponential and Logarithmic Equations .

Topic 4: Infinitesimal calculus.

4.1 Concept of limit and derivation rules. Interpretation of the derivative as a measure of sensitivity.

4.2 Approach to nonlinear functions through Taylor series. Non-linear optimization and First Order Conditions.

Topic 5 : Financial Mathematics.

5 .1 Yield and Discount Rates, Geometric Series, Present Value Formulas,

5 .2 Calculation of Perpetuities, Annuities and IRR of a bond.