Applied mathematics in economics

The discipline aims to develop students’ capacity to understand and apply mathematical tools in the study of economic phenomena. It emphasizes the mathematical modeling of functions and economic operations, ensuring that learners acquire the necessary foundation to approach specialized subjects in higher years of study. Through this course, students will strengthen their ability to use mathematical reasoning for the analysis and interpretation of economic processes, while becoming familiar with the specialized language of the field. The course also fosters skills in collecting, processing, and interpreting economic data, thus supporting the development of analytical and problem-solving competencies essential for both academic progression and professional practice.

1. Linear algebra. Matrices. Systems of linear equations. Gauss's total elimination method. Calculation of the inverse with the Gauss elimination method.

2. Vector spaces. Vector subspaces. Generator systems. Linear dependence and linear independence. The base. Dimension. Change of coordinates when changing the base.

3. Mathematical analysis complements. Strings and series of numbers. Strings of real numbers. Series with positive terms, convergence criteria. Geometric series.

4. Differential calculation. Derivative and difference of a real function of a real variable. Higher order derivatives. Functions of several real variables. Partial and differential derivatives for functions of several real variables.

5. Local extrema for functions of two or more real variables.

6. Euler integrals.

7. Elements of probability theory. Introductory notes. Events. Operations with events. Probability. Field of probability. Properties of probability. Independent events. Conditional probability.

8. Total probability formula. Bayes formula.

9. Random variables. Discrete random variables, continuous random variables. Numerical characteristics of the random variable. Average, Variation.

10. Discrete two-dimensional random vectors.

11. Elements of selection theory. Population, selection data. Repeated selection, non-repeated selection. Empirical selection distribution. Selection distribution function. Selection functions (statistics). Selection characteristics.

12. Linear regression.

13. Financial operations. The mathematical definition of interest. Simple interest. The elements of simple interest. Compound interest. Elements of compound interest. Equivalent operations in the simple and compound interest regime.

14. Installment payments. Annually staggered payments (annuities). Immediate temporary posticipated annuities. Immediate temporary annuities. Deferred temporary annuities. Temporary deferred annuities.

Professional Competencies

C1: Students will be able to collect, organize, and analyze information about the interaction between an enterprise/organization and its external environment to support informed decision-making.

C3: Students will be able to plan, coordinate, and manage the activities of a subdivision within a company or organizational structure, ensuring operational objectives are met.

Transversal Competencies

CT2: Students will be able to identify the roles and responsibilities of team members in a multi-specialized team and apply effective communication and collaboration techniques to achieve team objectives.