Mathematical Programming

Mathematical Programming

Cod: 21091

Department: DCET

Department: DCET

ECTS: 6

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 156

Total contact time: 26

Total contact time: 26

The objective of this curricular unit is to provide to the students the basic knowledge and skills about the use of open source software (SageMath) in solving computationally problems from elementary mathematics as well as some more advanced optimization problems.

SageMath (open source)

Optimization

Optimization

After concluding this curricular unit the student must be able to:

- Recognize the usefulness of open source software (SageMath) in solving problems in elementary mathematics and optimization;

- Apply the main techniques of non linear optimization.

- Recognize the usefulness of open source software (SageMath) in solving problems in elementary mathematics and optimization;

- Apply the main techniques of non linear optimization.

1. Elementary Mathematics with SageMath: Arithmetic, Equations and systems; Graph and graphs objects, Polynomials, Analysis, Linear algebra;

2. One Variable Optimization with SageMath: Derivative test, Three points search method, Fibonacci search method, Middle term search method;

3. Several Variables Optimization with SageMath: Gradient method, Newton-Raphson method, Hooke-Jeeves search method.

2. One Variable Optimization with SageMath: Derivative test, Three points search method, Fibonacci search method, Middle term search method;

3. Several Variables Optimization with SageMath: Gradient method, Newton-Raphson method, Hooke-Jeeves search method.

J. L. Tábara, Introduccion: Matemáticas Elementales con SageMath (http://www.sagemath.org/es/Introduccion_a_SAGE.pdf).

Bronson, R., Naadimuthu, G., Investigação Operacional, McGraw-Hill de Portugal, 2001.SageMath - Open Source Mathematical Software System (http://www.sagemath.org).

Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a
presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one
final presence-based exam (100%).