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7.1. Basic Mathematics (Mandatory)

7.1.1. Justification ↑ Back to top

The Basic Mathematics course is mandatory and provides the conceptual tools necessary for logical reasoning and problem solving. The course ranges from propositional logic and set theory to the study of real numbers, complex numbers, polynomials, and matrices. These concepts are fundamental for developing the abstraction and mathematical formalization skills required in the later stages of the Computer Science program.

7.1.2. Generales Goals ↑ Back to top

1. Develop logical reasoning and critical thinking skills through the use of formal languages.
2. Understand and apply the properties of number systems (real and complex) in problem solving.
3. Manipulate polynomial and matrix structures to solve systems of equations and interpret results.
4. Introduce basic concepts of statistics and probability for data analysis.

7.1.3. Contribution to Outcomes ↑ Back to top

ABET-1) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics. (Familiarity)

7.1.4. Content ↑ Back to top

7.1.4.1. Logic and Sets (16 hours) [Skills ABET-1] ↑ Back to top

Bibliography: (Lipschutz, 1991; Rojo, 1995)

Topics

1. Propositional logic: Connectives, truth tables, and validity.
2. Logical-mathematical quantifiers.
3. Set theory: Operations, relations, and functions.
4. Families of sets and Cartesian product.

Learning Outcomes

1. Formalize natural language statements into propositional language [Familiarity].
2. Operate with sets using algebraic laws and Venn diagrams [Usage].
3. Prove basic properties of sets and logical relations [Assessment].

7.1.4.2. Number Systems (16 hours) [Skills ABET-1] ↑ Back to top

Bibliography: (Gentile, 1985; Álvaro Pinzón, 1973)

Topics

1. The real number system: Field and order axioms.
2. Mathematical induction and Newton's binomial theorem.
3. Complex numbers: Binomial, polar, and exponential forms.
4. Roots of complex numbers and De Moivre's theorem.

Learning Outcomes

1. Identify the algebraic structure of real and complex numbers [Familiarity].
2. Apply the principle of mathematical induction in proofs of summations [Usage].
3. Solve equations in the complex number field using various representations [Assessment].

7.1.4.3. Polynomials and Matrices (16 hours) [Skills ABET-1] ↑ Back to top

Bibliography: (Gentile, 1984; Rojo, 1995)

Topics

1. Polynomials: Division algorithm and roots of polynomials.
2. Matrices: Types, operations, and determinants.
3. Inverse matrix and rank of a matrix.
4. Systems of linear equations: Gauss-Jordan method.

Learning Outcomes

1. Recognize the structure of polynomial rings and matrix algebra [Familiarity].
2. Use elementary row operations to calculate the inverse of a matrix [Usage].
3. Model and solve systems of linear equations applied to contextual problems [Assessment].

7.1.4.4. Statistics and Probability (16 hours) [Skills ABET-1] ↑ Back to top

Bibliography: (Peterson, 2005)

Topics

1. Descriptive statistics: Measures of central tendency.
2. Dispersion measures and graphical representation.
3. Probability concepts: Sample space and events.
4. Conditional probability and independence.

Learning Outcomes

1. Describe data sets using basic statistical indicators [Familiarity].
2. Calculate probabilities of simple and compound events in random experiments [Usage].
3. Interpret statistical results for decision making in scientific environments [Assessment].

7.1.5. Bibliography ↑ Back to top

Lipschutz, S. (1991). Teoría de conjuntos y temas afines. McGraw-Hill.

Rojo, A. (1995). Álgebra I. El Ateneo.

Gentile, E. (1985). Aritmética Elemental. Colección de Monografías Científicas Ser.

Álvaro Pinzón (1973). Conjuntos y estructuras. Blaisdell Publishing Company.

Gentile, E. (1984). Notas de álgebra. Editorial Universitaria de Buenos Aires.

Peterson, J. (2005). Matemática básica. Prentice-Hall.