# Pre-Master's Foundation Programme in Applied Mathematics

## 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 perspective 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 bachelor study programmes and on the education system in their country of origin, students enrolling 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 perspective 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.

### Teaching delivery mode

In order to pass the exam of each course, students will have to pass at least two tests, to be fixed at least two weeks apart from each other. Courses ending by the 30th of September 2023 will be held remotely. For the remaining courses, the lecturer may opt for a blended mode.

### Admission

- Mathematical Engineering

- Mathematical Modelling

in the 2023 cohort, who have obtained their Bachelor degree abroad will, as a rule, attend this Pre-Master’s Foundation Programme. The Mathematical Engineering Council (CAD di Ingegneria Matematica) will appoint a committee to evaluate the academic documents submitted by each student who has expressed interest into enrolling the two MSc programmes by the 30th of June 2023, with the goal of detecting specific skills previously obtained by the student which overlap (partially or totally) the aims and objectives of the Pre-Master’s Foundation Programme. In the latter case, the aforementioned committee may admit the student to the PMFP with a personal plan, with less ECTS than those provided by the standard study plan.

If deemed necessary, the committee may decide to complement the evaluation of the academic documents with an interview.

## Pre-Master's Foundation Programme in Applied Mathematics (PMFP-AM) :: 2023 Structure

### Campus

### Dates

Part 2: March-April 2024 (TBD)

### Delivery Mode

### ECTS Credits

### Language

### Part 1

**|** ECTS Credits:
3 **|** **|** Delivery:
Online **|** Taught hours:
18 **|** Language:
English

Unit Coordinator: Carmela Scalone

Content:

Linear spaces, linear dependence, bases of a linear space, dimension of a linear space, linear subspaces.

Matrices, basic operations with matrices, change of coordinates, determinants, rank. A brief account on linear systems and Gauss elimination.

Diagonalisation of squared matrices, eigenvalues, eigenvectors. Inner products, bilinear forms and quadratic forms.

### Part 2

ECTS Credits:
3 **|** Dates:
February 28 - March 16, 2023 **|** Delivery:
Blended **|** Taught hours:
18 **|** Language:
English

Unit Coordinator: Antonio Cicone

Content:

The MATLAB environment, Basic computer programming, Variables and constants, operators and simple calculations, Formulas and functions. MATLAB toolboxes.

Matrix and linear algebra review, Vectors and matrices in MATLAB, Matrix operations and functions in MATLAB.

Algorithms and structures, MATLAB scripts and functions (m-files), Simple sequential algorithms, Control structures (if...then, loops).

Reading and writing data, file handling, Personalized functions, MATLAB graphic functions. Interactive hands-on-sessions.

# Schedule of lectures

##### Online classes will be conducted on MS Teams, where class materials will be made available for students, too.

##### Once you've signed in on MS Teams, you will find a list of all the forthcoming classes under the "Posts" tab or alternatively, in your own calendar, as shown in the screenshots below. Class materials (lectures notes, video recordings etc.) are available for downloading under the "Files" tab, instead.

##### Join online classes from the "Posts" tab

##### Join online classes from your own calendar

##### Do not start your own meeting!

##### Download Class Materials

### Pre-Master's Foundation Programme in Applied Mathematics (PMFP-AM) :: 2022 Structure

### Campus

### Dates

Part 2: March-April 2024 (TBD)

### Delivery Mode

### ECTS Credits

### Language

### Part 1

**|** ECTS Credits:
3 **|** **|** Delivery:
Online **|** Taught hours:
18 **|** Language:
English

Unit Coordinator: Carmela Scalone

Content:

Linear spaces, linear dependence, bases of a linear space, dimension of a linear space, linear subspaces.

Matrices, basic operations with matrices, change of coordinates, determinants, rank. A brief account on linear systems and Gauss elimination.

Diagonalisation of squared matrices, eigenvalues, eigenvectors. Inner products, bilinear forms and quadratic forms.

### Part 2

ECTS Credits:
3 **|** Dates:
February 28 - March 16, 2023 **|** Delivery:
Blended **|** Taught hours:
18 **|** Language:
English

Unit Coordinator: Antonio Cicone

Content:

The MATLAB environment, Basic computer programming, Variables and constants, operators and simple calculations, Formulas and functions. MATLAB toolboxes.

Matrix and linear algebra review, Vectors and matrices in MATLAB, Matrix operations and functions in MATLAB.

Algorithms and structures, MATLAB scripts and functions (m-files), Simple sequential algorithms, Control structures (if...then, loops).

Reading and writing data, file handling, Personalized functions, MATLAB graphic functions. Interactive hands-on-sessions.