Pre-Master's Foundation Programme in Applied Mathematics (PMFP-AM)

University of L'Aquila (UAQ), Italy

Overview: “Pre-Master’s Foundation Programme in Applied Mathematics”

The Pre-Master's Foundation Programme (PMFP) in Applied Mathematics aims at homogenising the competencies portfolios of prospective students of the two Master's Programmes in Mathematical Modelling and Mathematical Engineering at the University of L'Aquila, which include the Erasmus Mundus programme "InterMaths - Interdisciplinary Mathematics", the joint Master's programme "MathMods", and the "InterMaths" Double Degree programme.

Depending on the student's undergraduate study programmes and on the education system in their country of origin, students enrolling in these three programmes may feature very diverse set of skills in disciplines that characterise these Master's programmes. The PMFP in Applied Mathematics is designed to address this issue by covering specific competencies in both theoretical mathematics (Real Analysis and Linear Algebra) and computer programming. As for theoretical mathematics, the main goal of the PMFP is bridging the gap between "calculus" and "real analysis", a typical issue arising quite often for prospective MSc students with a very "applied" background.

The PMFM will include very basic topics of real analysis enabling the students to deal with infinitesimal calculus with a rigorous "real analysis" perspective (including the use of rigorous mathematical proofs). On the other hand, students with a strong "theoretical" background sometimes lack basic programming and computational skills. Hence, the PMFP provides a basic introduction to computer programming and in particular to the computing environment "MATLAB", which is widely used in the numerical analysis courses of the MSc programmes mentioned above.

Modules :: Pre-Master's Foundation Programme in Applied Mathematics (PMFP-AM)


University of L'Aquila


August - April

Delivery Mode

Online and/or Blended

ECTS Credits




Part 1

Differential Equations: Foundations

ECTS Credits: 3    |    Dates: 2 - 27 August 2021    |    Delivery: Online    |    Taught hours: 18    |    Language: English

Unit Coordinator: Bruno Rubino


General introduction to differential equations, Cauchy problems.

Existence and uniqueness of solutions. Peano’s and Cauchy’s theorems. Examples, Peano’s brush.

Introduction to linear differential equations. Examples.

A brief outline of qualitative analysis of Cauchy problems. Comparison of solutions, maximal solutions, global existence of solutions, blow-up of solutions. Examples.

Part 2

Introduction to Programming

ECTS Credits: 3    |    Dates: 27 September - 17 December 2021    |    Delivery: Blended    |    Taught hours: 18    |    Language: English

Unit Coordinator: Luca Forlizzi


Algorithms, programs and programming languages.

Learning environment for the Python programming language and Turtle Graphics. Commands and sequences of commands. Writing and executing a program.

Definite iteration. Procedures: defining and calling Python functions. Procedures with parameters.

Variables and objects. Basic data types in Python. Expressions.

Selection, recursion, and indefinite iteration.

Basic data structures in Python: tuples, strings, lists, dictionaries