34739 - Numerical Calculus and Teaching Software

Learning outcomes

At the end of the course, students know foundamental numerical algorithms and is able to use software for education and numerical applications.

Course contents

The course aims to provide students with fundamental concepts and tools in computational mathematics, numerical analysis, and mathematical modelling, with a particular focus on their application to the design of teaching activities for secondary school.

Special attention will be devoted to the development of computational thinking, the algorithmic formulation of mathematical problems, the use of the computer laboratory as an environment for mathematical exploration, and the design of learning activities supported by digital technologies.

The course will cover the following topics (Modules 1 and 2):

• Computational thinking and algorithm design: problem solving, the concept of algorithms, flowcharts, pseudocode, and introductory coding.
• Elements of numerical analysis: numerical methods for unconstrained and constrained optimization, fundamentals of linear programming, the graphical method for two-variable linear programming problems, and numerical methods for ordinary differential equations.
• Introduction to mathematical modelling: formulation and analysis of simple mathematical models, with applications to scientific and educational problems, with particular emphasis on contexts relevant to secondary school mathematics.
• Computational mathematics laboratory: use of computational environments and digital tools for algorithm implementation, numerical exploration, mathematical simulation, and the design of laboratory activities for mathematics teaching.

Readings/Bibliography

• A. Quarteroni, F. Saleri, Calcolo Scientifico esercizi e problemi risolti con Matlab/Octave. Springer (2008);
• V. Comincioli, Analisi Numerica: metodi, modelli, applicazioni. Apogeo, on-line ed.(2005)

Teaching methods

Classroom lectures for the theory, and computer Laboratory for codes implementation and analysis of proposed examples.

In consideration of the type of activity and teaching methods adopted, the frequency of this training activity requires the prior participation of all students in Modules 1 and 2 of safety training in the places of study, in e-learning mode.

Assessment methods

The assessment consists of an individual project and an oral examination.

The project consists of the design and development of a laboratory activity based on the computational mathematics tools and teaching methodologies presented during the course. The project topic must be agreed upon with the instructor. The project is intended to assess the student's ability to design and develop a teaching activity that integrates computational mathematics and digital technologies into mathematics education.

The project must be submitted at least one week before the date of the oral examination. Submission of the project is a mandatory prerequisite for admission to the oral examination. Students who fail to submit the project by the prescribed deadline will not be admitted to the examination.

The oral examination will cover the theoretical and methodological topics addressed during the course and will also include a discussion of the submitted project. The assessment will focus on the student's knowledge and understanding of the course topics, the ability to apply the acquired methods critically, the quality of the proposed laboratory activity, and the ability to communicate mathematical concepts using appropriate scientific terminology.

The final grade will take into account both the evaluation of the project and the performance in the oral examination.

Teaching tools

Slides provided by the teacher. The teaching material will be available on the University of Bologna e-learning platform (https://virtuale.unibo.it).

Office hours

See the website of Germana Landi

See the website of Alessandro Lanza