- Code: DT0633
- Unit Coordinator: Carmela Scalone
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of L'Aquila
- Language: English
- Aims:
Learning objectives.
The aim of the course is to provide knowledge and skills in the field of numerical modelling in the epidemiological field, creating an effective bridge between the understanding of the continuous model, its qualitative properties and their counterparts in the discrete.
Learning outcomes.
At the end of the course, the student should
- have a deep knowledge and understanding of the most relevant computational techniques for the treatment of models in the epidemiological field, together with aspects related to their implementation in accurate and efficient mathematical software;
- demonstrate the ability to evaluate the most appropriate discretization in relation to the problem to be solved and ability in theoretical analysis and mathematical software design;
- demonstrate ability to read and understand other texts on related topics. - Content:
- Compartmental models in Epidemiology.
- Stochastic models.
- Epidemiological models based on pds.
- An introduction to network models for the spread of epidemics.For each theme, the presentation will be twofold: presenting the continuous model, its qualitative properties and, jointly, presenting the most appropriate numerical approach to the approximation of solutions and the discrete conservation of the properties of the model. In addition, advanced techniques of numerical linear algebra and optimization for large linear systems arising from semi-discretization of PDEs in epidemiology will be presented.
- Pre-requisites:
Basic knowledge of Numerical Analysis, differential equations, linear algebra.
- Reading list:
- F. Brauer et al., Mathematical Epidemiology, Springer-Verlag (2008).
- J. D. Lambert, Numerical methods for ordinary differential systems: the initial value problem, John Wiley (1991).
- A. Quarteroni, Numerical Models for Differential Problems, Springer (2017).
- E. Isaacson, H.Keller, Analysis of numerical methods, Dover Publications (1994).
- D.J. Higham and P. E. Kloeden, An Introduction to the Numerical Simulation of Stochastic Differential Equations, SIAM, 2021.
--Walter Gander, Martin J. Gander, Felix Kwok. Scientific Computing
An introduction using Maple and MATLAB. Springer.
- Unit Coordinator: Raffaele D'Ambrosio
- Programme: InterMaths
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of L'Aquila
- Language: English
- Delivery: In-class
- Aims:
Learning objectives.
The aim of the course is to provide knowledge and skills in the field of numerical modelling of Health Care systems, creating an effective bridge between the understanding of the continuous model, its qualitative properties and their counterparts in the discrete.
Learning outcomes.
At the end of the course, the student should
• have a deep knowledge and understanding of the most relevant computational techniques for the treatment of models in the Health Care field, together with aspects related to their implementation in accurate and efficient mathematical software;
• demonstrate the ability to evaluate the most appropriate discretization in relation to the problem to be solved and ability in theoretical analysis and mathematical software design;
• demonstrate ability to read and understand other texts on related topics. - Content:
Introduction to mathematical models for Health Care based on ordinary, stochastic and partial differential equations;
For each theme, the presentation will be twofold: presenting the continuous model, its qualitative properties and, jointly, presenting the most appropriate numerical approach to the approximation of solutions and the discrete conservation of the properties of the model.
Methods that preserve the positivity of solutions have particular relevance in this field.
In addition, advanced techniques of numerical linear algebra and optimization for large linear systems arising from semi-discretization of PDEs will be presented. - Pre-requisites:
Basic knowledge of Numerical Analysis, differential equations, linear algebra.
- Reading list:
- F. Brauer et al., Mathematical Epidemiology, Springer-Verlag (2008).
- J. D. Lambert, Numerical methods for ordinary differential systems: the initial value problem, John Wiley (1991).
- A. Quarteroni, Numerical Models for Differential Problems, Springer (2017).
- E. Isaacson, H.Keller, Analysis of numerical methods, Dover Publications (1994).
- W. Hundsdorfer, J. G. Verwer - Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations
- D.J. Higham and P. E. Kloeden, An Introduction to the Numerical Simulation of Stochastic Differential Equations, SIAM, 2021.
- Walter Gander, Martin J. Gander, Felix Kwok. Scientific Computing An introduction using Maple and MATLAB. Springer.
- ECTS Credits: 5
- Semester: 1
- Year: 2
- Campus: Gdansk University of Technology
- Code: DT0641
- Unit Coordinator: Markus Faustmann, Claudia Blaas-Schenner
- Programme: InterMaths
- ECTS Credits: 8
- Semester: 2
- Year: 1
- Campus: Vienna University of Technology
- Language: English
- Aims:
Scientific Programming
- formulate (certain) mathematical problems in algorithmic form,
- explain the difference between imperative and object-oriented programming,
- implement mathematical algorithms in Matlab, C, and C++,
- present and explain own solutions, and
- constructively discuss and analyze own solutions as well as those of other students.Parallel Programming
- understand and apply the main concepts of parallel programming
- master the basic skills to write parallel programs using MPI and OpenMP
- parallelize serial programs using basic features of MPI and OpenMP
- be familiar with the components of an high-performance computing cluster
- know the principles to take advantage of shared and distributed memory systems as well as accelerators and how to exploit the capabilities of modern high-performance computing systems - Content:
Scientific Programming:
- Introduction to Matlab, C, and C++.
- Representation of integer and floating point numbers.
- Conditioning of given problems.
- Computational cost of algorithms.
- Variables and standard data types.
- Pointers.
- Loops and if-else.
- Functions and recursion.
- Call by value vs. call by reference.
- Objects and classes (resp. structures),
- Operator overloading, Inheritance.
- Templates.
- Visualization in MATLAB.
- Programming exercises.Parallel Programming:
- Basic features of parallel programming with MPI (Message Passing Interface) and OpenMP (Open Multi-Processing) using C
- A look at CUDA to offload parts of the computation to GPUs
- Students will do the hands-on labs directly on the Vienna Scientific Cluster, the high-performance computing facility of Austrian universities, and hence will learn about and get some experience in high-performance computing. - Pre-requisites:
Basic skills in programming in C (e.g., as learnt during the lecture "Scientific Programming for Interdisciplinary Mathematics") as well as Linux command line and usage of an editor (vi or nano).
- Reading list:
- Scientific programming in mathematics:
lecture notes
- Programming with MATLAB:
Otto and Denier, An Introduction to Programming and Numerical Methods in MATLAB
Brian Hahn, Essential MATLAB for Engineers and Scientists
Stormy Attaway, Matlab: A Practical Introduction to Programming and Problem Solving
- Basics of Parallel Computing:
Rauber, Rünger: Parallel programming. Second Edition, Springer 2013.
Schmidt, Gonzalez-Dominguez, Hundt, Schlarb: Parallel Programming. Concepts and Practice. Morgan Kaufmann 2018.
