Background.
Basic multivariable calculus and basic numerical analysis/scientific computing with error analysis, norms, numerical solution of algebraic linear systems with direct and iterative solvers, basics on numerical solution of nonlinear algebraic systems and ordinary differential equations.

Program.
A brief introduction to linear diffusion, advection and advection-diffusion problems and their discretization. Using the scructures (even if no apparent structure is present) to solve the discretized problems. Some hints for the multi-iterative solution of nonlinear systems. The course will include lab.

Download the notes of this lecture course

These are the slides of lecture n. 1

Reference:
A.Bortoletti, C.Di Fiore, On a set of matrix algebras related to discrete Hartley-type transforms, Linear Algebra and its Applications 366 (2003) 65-85

The following reference can be helpful for lecture n. 2

References:
Vandebril, Van Barel, Mastronardi, A note on the representation and definition of semiseparable matrices, 2003

Dario Fasino, Numerical Linear Algebra with Applications, 2005

D. Fasino, A brief introduction to quasiseparable matrices. Lecture course notes.

Some references:

Mark E. J Newman, Networks - An introduction
A Bonato, A course on the web graph
Meyer, Langville, Google search engine and beyond

Free Preprints:
M. Newman, the structure and function of complex networks
S. Fortunato, comuntity detection in graphs

The slides of the lecures and the problems proposed can be found here.

Abstract of the lecture course.

1-st lecture: Slides
2-nd lecture: Slides
3-rd lecture: Slides
4-th lecture: Slides

The chapter in Gantmakher's "The Theory of Matrices" titled "Matrix Equations"
is a good preliminary reading for this mini-course.

Some problems regarding the course

Course notes (1 of 2)
Course notes (2 of 2)

Please refer to this pdf for further informations about the lecture course

Main References:

- Nikolskij, Course of Mathematical Analisys, 1975: Chapters 15 and 16 (perhaps also 14)
- Massimo A. Picardello, Note di Analisi di Fourier e trattamento dei segnali (in italian), Chapters 8, 9, 10, 11 and, mainly, 13 (This notes can be found here)
- Aldroubi and Grochenig, Nonuniform sampling and reconstruction in shift-invariant spaces, (download)

Foreword.
Applications do not necessarily mean practical computations. In these notes, in particular, we can see some very useful applications of linear algebra to ancient problems of construction by compasses and ruler and then to the problem of solvability of algebraic equations by radicals. In this lecture course we go straightforwardly to some famous results of algebra in the hope that a concise and rigorous exposition may help to make difficult topics more friendly and less difficult. The notes produce the whole picture of the course and contain all basic steps and fundamental theorems. However, the proofs are not in the notes and will be presented during the school. Please be aware that next to none of the steps evolved in these notes is trivial. So the proofs are essential part of the course. I hope we can enjoy them together as the ideas and even details of the proofs are deep, ingenious and beautiful.

Background knowledge.
Groups, cyclic groups, subgroups, normal sub-groups, quotient (factor) groups, symmetric groups, alternating groups, abelian groups, conjugate elements, isomorphisms, homomorphisms. Fields, subfields, extension fields. Algebraic equations, fundamental theorem of algebra. Symmetric polynomials, elementary symmetric polynomials.

Download the notes of this lecture course

1. Unstructured mesh generation technologies
Lecture: 2 hours. Practicum: 2 hours.
Download the presentation of the first lecture

2. Discretization of BVP's on unstructured meshes
Lecture: 2 hours. Practicum: 2 hours.

3. Computational techniques for solving sparse linear systems
Lecture: 2 hours. Practicum: 2 hours.

Lecture course notes.