Computational Mathematics and Educational Software

Credits

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/08 Numerical Analysis.

Examination method

Oral exam and possible additional short paper/project.

Learning
objectives

The course aims to explore some concepts relating to the basic tools for the computational solution of mathematical problems (problem solving) and to compare them with analytical/geometric methods. The laboratory work aims at acquiring skills in the use of widely used educational software (e.g. Matlab, Mathematica, Geogebra).

Syllabus

Revisiting and exploring in greater depth some basic topics of numerical analysis from a teaching perspective, with an approach that compares them with analytical/geometric methodologies.

From the mathematical formalisation to the numerical solution of a problem;
problem solving: direct problems and inverse problems;
exact solution vs approximate solution: assessing the quality of a numerical solution.

Presentation of some case studies drawn from applications (for example: representation, filtering and reconstruction of an image, valuation of an optimal financial portfolio, the diet problem, formulation and solution of an equilibrium problem) using numerical methods (direct and iterative) for solving linear systems, numerical interpolation methods, numerical solvers for ordinary differential equations, solution of linear and nonlinear systems. Dynamic mathematics software for numerical and symbolic computation (GeoGebra, Matlab, Octave, Mathematica, wxMaxima, …). Design of lessons and exercise sessions in educational software environments.

Expected learning
outcomes

At the end of the course, students must demonstrate that they

know and understand the ideas underlying the solution of a mathematical problem by computer, as well as the main software tools used in teaching;
are able to apply the knowledge acquired to design teaching activities involving the solution of mathematical problems by computer;
are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
are able to identify the most appropriate methods to analyse and solve a problem related to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Command of the subject matter, clarity of presentation, rigour in the use of language, confidence in using the notions acquired, proficiency in the use of specific educational software.

Computational Mathematics and Educational Software