At present UAQ counts over 20,000 students, around 650 teachers and researchers, and nearly 500 administrative and technical staff members. Officially established in 1952 (but its origins date back to the 16th century), UAQ has now 7 departments offering a wide range of Bachelor, Master and PhD programmes in biotechnologies, sciences, economics, engineering, education, humanities, medicine, psychology, and sport sciences. Internationalisation has played an increasingly important role at UAQ. The Engineering and the Sciences Faculties have a strong tradition of research in the area of Mathematical Modelling. The Dept of Pure and Applied Math has rich experience in managing International projects (starting in 1996 as coordinator of the FP4 "HCL" TMR , FMRX-CT96-0033). UAQ provides many services for its students, including Career Office, International Relations Office, Quality Assessment Office (of teaching, research and services), Centre for Students with Disabilities, Language Centre, Student Counseling Centre.
Click here for further information on Univaq official web-site.
Bruno Rubino
Department of Information Engineering, Computer Science and Mathematics
University of L'Aquila
via Vetoio (Coppito), 1 – 67100 L'Aquila (Italy)
Phone: +39 0862 434701
Fax: +39 0862 433180
* Students are required to earn 66 ECTS credits, at least, during their first year by successfully attending the following compulsory course units (Semester 1 and 2 amounting to 48 ECTS credits) and picking other 18 ECTS credits (minimum) from the elective ones listed below.
Students will know basic of properties (existence, uniqueness, etc.) and techniques (characteristics, separation of variables, Fourier methods, Green's functions, similarity solutions, etc.) to solve basic PDEs (conservation laws, heat, Laplace, wave equations).
Integral curves and surfaces of vector fields. First order partial differential equations. Linear and quasi linear partial differential equations (PDEs) of first order. Method of characteristics. The initial value problem: existence and uniqueness. Development of shocks.
The Cauchy-Kovalevsky theorem. Linear partial differential operators and their characteristic curves and surfaces. Methods for finding characteristic curves and surfaces. The initial value problem for linear first order equations in two independent variables. Holmgren's uniqueness theorem. Canonical form of first order equations. Classification and canonical forms of second order equations in two independent variables. Second order equations in two or more independent variables. The principle of superposition.
The divergence theorem and the Green's identities. Equations of Mathematical Physics.
LAPLACE'S EQUATION AND HARMONIC FUNCTIONS Elementary harmonic functions. Separation of variables. Inversion with respect to circles and spheres. Boundary value problems associated with Laplace's equation. Representation theorem. Mean value property. Maximum principle. Harnack’s inequality and Liouville’s theorem. Well-posedness of the Dirichlet problem. Solution of the Dirichlet problem for the unit disc. Fourier series and Poisson's integral. Analytic functions of a complex variable and Laplace's equation in two dimensions. The Neumann problem.
GREEN'S FUNCTIONS. Solution to the Dirichlet problem for a ball in three dimensions. Further properties of harmonic functions. The Dirichlet problem in unbounded domains. Method of electrostatic images.
THE WAVE EQUATION. Cauchy problem. Energy method and uniqueness. Domain of dependence and range of influence. Conservation of energy. One-dimensional wave equation. D’Alembert formula. Characteristic parallelogram. Non homogeneous equation and Duhamel’s method. Multi-dimensional wave equation. Well posed problems. Fundamental solution (n=3) and strong Huygens’ principle. Kirchhoff formula. Method of descent. Poisson?s formula (n=2). Wave propagation in regions with boundaries. Uniqueness of solution of the initial-boundary value problem. Separation of variables. Reflection of waves.
THE HEAT EQUATION. Heat conduction in a finite rod. Maximum principle and applications. Solution of the initial-boundary value problem for the one dimensional heat equation. Method of separation of variables. The initial value problem for the one dimensional heat equation. Fundamental solution. Non homogeneous case and Duhamel’s method. Heat conduction in more than one space dimension.
E. C. Zachmanoglou and Dale W. Thoe, lntroduction to Partial Differential Equations with Applications. Dover Publications, Inc.. 1986. ISBN 0-486-65251-3
L.C. Evans, Partial Differential Equations. American Mathematical Society. 2010. Second edition, ISBN-13: 978-0821849743
S. Salsa, Partial Differential Equations in Actions: from Modelling to Theory. Springer-Verlag Italia. 2008. ISBN 978-88-470-0751-2
W. A. Strauss, Partial Differential Equations, Student Solutions Manual: An Introduction. John Wiley & Sons, LTD. 2008. Second edition, ISBN-13: 978-0470260715
W. A. Strauss, Partial Differential Equations: an introduction. John Wiley & Sons, LTD. 2007. Second edition, ISBN-13 978-0470-05456-7
The course provides the basic methodologies for modeling, analysis and controller design for continuous-time linear time-invariant systems.
Frequency domain models of Linear Systems: Laplace Transform, Transfer Function, Block diagrams.
Time domain models of Linear Systems:State space representation. BIBO stability.
Control specifications for transient and steady-state responses. Polynomial and sinusoidal disturbances rejection.
The Routh-Hurwitz Criterion. PID controllers.
Analysis and controller design using the root locus.
Analysis and controller design using the eigenvalues assignment: controllability, observability, the separation principle.
Reference inputs in state space representations.
Controller design using MATLAB.
Advanced topics in control theory.
R.C. Dorf, R.H. Bishop, Modern Control Systems. Prentice Hall. 2008. Eleventh Edition
Ordinary Differential Equations
Linear systems of differential equations: uncoupled linear systems, diagonalization, exponentials of operators, the fundamental theorem for linear systems, planar linear systems, complex eigenvalues, multiple eigenvalues, stability theory, nonhomogeneous linear systems.
Local theory of nonlinear systems: initial value problem, hyperbolic equilibrium point, Stable Manifold Theorem. Hartman-Grobman Theorem. Stability and Liapunov functions. Saddles, nodes, foci and centers. Nonhyperbolic critical points. Center manifold theory.
Global theory of nonlinear systems: limit set, attractor, limit cycle, Poincaré map, stable manifold theorem for periodic orbits, Poincaré-Bendixson theory. Mathematical background: Fundaments of perturbation analysis. The Multiple Scale Method. Basic concepts of bifurcation analysis: Bifurcation points, Linear codimension of a bifurcation, Imperfections, Fundamental path, Center Manifold Theory.
Basic mechanisms of multiple bifurcations: divergence, Hopf, nonresonant or resonant double-Hopf, Divergence-Hopf, Double-zero bifurcation.
Lawrence Perko, Differential equations and dynamical systems, Springer-Verlag, 2001
Linear Algebra. Complex numbers. Differential and integral calculus of functions of real variables.
Basic functional analysis: normed and Banach spaces, Hilbert spaces, Lebesgue integral, linear operators, weak topologies, distribution theory, Sobolev spaces, fixed point theorems, calculus in Banach spaces, spectral theory.
Applications: ordinary differential equations, boundary value problems for partial differential equations, linear system theory, optimization theory.
Ruth F. Curtain, A.J. Pritchard, Functional Analysis in Modern Applied Mathematics, Academic Press, 1977
None
The aim of this course is to provide the student with knowledge of fundamental grammatical structures, vocabulary and comunicative structures of the Italian language. Notions of Italian culture will be given during the course.
On successful completion of this module, the student should be able to:
- recognise familiar words and simple expressions about himself, his family and his background;
- understand simple names and words, such as ads, catalogues, billboards;
- easily interact with an interlocutor, ask questions and give answers on familiar topics or immediate needs;
- describe the place where he lives and people he knows;
- write a short and simple text; fill forms with personal information (name, nationality, address, etc.)
The aim of the course is to develop the following skills:
- AURAL COMPREHENSION: to understand a short speech, with long breaks and a slow pronunciation;
- WRITTEN COMPREHENSION: to understand simple and short texts, understanding names, well-known words and expressions;
- ORAL EXPRESSION: to say easy and isolated phrases about people and places;
- WRITTEN EXPRESSION: to write easy and isolated phrases;
- ORAL INTERACTION: to interact in an easy way and slowly. Answer and ask easy questions, expressing immediate needs;
- WRITTEN INTERACTION: to ask and give personal informations.
During the course the following social-communicative actions will be analyzed and developed:
1. introduce himself;
2. ask and give personal informations;
3. greet and answer to greetings;
4. begin, maintain and finish a conversation;
5. give thanks and answer to thanks;
6. accept or refuse a invitation - invite someone;
7. search, ask and give information in everyday situations;
8. express desires;
9. introduce someone;
10. describe people, objects and places;
11. put events in a timeline;
12. ask and give a permission to do something;
13. give and understand easy instructions;
14. seek clarification and give an explanation.
The following grammar skills will be analyzed and developed:
-Articoli determinativi e indeterminativi;
-Aggettivi qualificativi di alta frequenza;
-Aggettivi e pronomi possessivi e dimostrativi;
-Pronomi personali soggetto;
-Pronomi personali complemento in espressioni fisse;
-Quantificatori;
-Verbi di altissima frequenza;
-Verbi servili;
-Indicativo presente;
-Passato prossimo (solo ricezione);
-Condizionale in formule fisse di frequenza;
-Congiunzioni (e additivo);
-Principali preposizioni semplici in espressioni fisse (a casa; con le mani; di mio fratello);
-Locuzioni avverbiali di alta frequenza (causa, tempo, luogo);
The following semantic fields will be analyzed:
- Family
- House
- Furniture
- Food and drinks
- Nationalities
- Job
- Free time
- Offices, shops, city
The following textbook will be used during the course:
"Nuovo Espresso 1", Alma Edizioni, Firenze 2014, lessons 1-6.
Further learning material will be provided during the lessons.
For further study and exercises:
http://italianoperstranieri.mondadorieducation.it
http://italianoperstranieri.loescher.it
https://www.almaedizioni.it/it/almatv/
Basic programming skills, introductory statistic.
Learn fundamental techniques to examine raw data with the purpose of drawing data-driven decisions. The course deals with the main methods for supervised and non-supervised learning. Particular attention will be given to the statistical foundations of learning. The most established techniques to extract information from data to orient decisions will be treated both in their theoretical motivations and in their practical details. Open source tools will support the course step by step, providing continuous verification of the material.
Introduction to analytics. Data collection, cleaning and preprocessing. Exploratory Data Analysis and Visualization. Statistical inference and regression models. Optimization formulations of data analysis and learning problems. Statistical foundations of learning. Clustering and Principal Component Analysis. Decision trees - Logic methods. Support vector machines - Feature selection and extraction. Methods and tools for supervised learning.
Python Data Science Handbook. Essential Tools for Working with Data
Jake VanderPlas
O'Reilly Media (2016)
An Introduction to Statistical Learning
Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani Springer Texts in Statistics (2015)
An Introduction to R
Version 3.4.1 (2017)
W. N. Venables, D. M. Smith and the R Core Team
Linux/Unix OS and tools;
Basic Fortran (or C);
HPC architecture;
System Scheduler;
Message Passing Interface;
OpenMP;
GPU computing;
Applications: linear algebra, PDEs, ODEs.
Italian language and culture - level A1
The aim of this course is to provide the student with knowledge of pre-intermediate grammatical structures, vocabulary and comunicative structures of the Italian language. Many notions of Italian culture will be given during the course.
On successful completion of this module, the student should be able to:
- recognize words and expression of common usage relating to context concerning himself (for instance basic informations concerning himself and his family, shopping, local geography and job). Catch the essence of short, easy and clear messages and ads.
- read short and easy texts finding specific informations in materials of everyday use such as ads, plans, menus and timetables. Understand short and easy personal correspondence;
-comunicate in simple tasks requiring only an exchange of information concerning usual activities and usual topics. Take part to short conversations, even if usually he doesn't understand what he needs to carry on the conversation;
-use expressions and phrases to describe his family and other people, his living conditions and his current job;
-write simple notes and short messages on topics concerning immediate needs.
Write a very simple personal letter (for instance to thank somebody).
The aim of the course is to develop the following skills:
- AURAL COMPREHENSION: to understand everything necessary aimed at the satisfaction of needs of a concrete type, provided that the speaker speaks slowly and clearly.
- WRITTEN COMPREHENSION: to understand simple and short texts of familiar content and concrete type, formulated in a common vocabulary of everyday life and job;
- ORAL EXPRESSION: to describe and introduce in an easy way people, living conditions, daily tasks, to say what he likes or dislikes etc. using expressions and phrases linked together in order to create a list;
- WRITTEN EXPRESSION: to write expressions and phrases linked by easy connective as "e", "ma" and "perché";
- ORAL INTERACTION: to interact with ease in structured situations and short conversations with the collaboration of the interlocutor. To take part in easy routine conversations; to ask and answer to simple questions; to share ideas and information about familiar topics in everyday situations;
- WRITTEN INTERACTION: to write short and simple notes about immediate needs using conventional formulae.
The following social-communicative actions will be analyzed and developed:
1. introduce himself;
2. ask and give personal informations;
3. greet and answer to greetings;
4. begin, maintain and finish a conversation;
5. give thanks and answer to thanks;
6. accept or refuse a invitation - invite someone;
7. search, ask and give information in everyday situations;
8. express desires;
9. introduce someone;
10. describe people, objects and places;
11. describe a place and put an element in a place;
12. speak about himself and ask questions about past events;
13. put events in a timeline;
14. express and ask questions about time and dates;
15. put events in a sequence;
16. express moods, feelings and emotions;
17. express the wish to do something;
18. ask and give the permission to do something;
19. order or ban somebody to do something;
20. give and understand simple instructions;
21.give an explanation;
22. express judgments and personal opinions;
23. make simple assumptions.
The following grammar skills will be analyzed and developed:
-opposizione articolo determinativo e indeterminativo;
-aggettivi qualificativi di alta frequenza;
-aggettivi numerali, cardinali e ordinali;
-aggettivi e pronomi possessivi e dimostrativi;
-pronomi personali soggetto;
-pronomi personali complemento;
-uso appropriato del che;
-quantificatori;
-verbi di alta frequenza;
-verbi servili;
-indicativo presente;
-passato prossimo;
-futuro semplice;
-imperfetto (ricezione);
-condizionale in formule fisse di richiesta;
-congiunzioni (e additivo, ma avversativo, o disgiuntivo);
-principali preposizioni semplici in espressioni fisse (a casa; con le mani; di mio fratello);
-locuzioni avverbiali di alta frequenza (causa, tempo, luogo);
-frasi impersonali;
-verbi riflessivi;
-verbi zerovalenti;
-subordinate causali e temporali.
The following semantic fields will be analyzed:
-family
-house
-forniture
-food and drinks
-nationalities
-job
-free time
-offices, shops, city
-natural events
-university
-body and health
The following textbook will be used during the course:
"Nuovo Espresso 1", Alma Edizioni, Firenze 2014, lessons 7-10.
Further learning material will be provided during the lessons.
Basics of Algebra
The course aims to provide the arithmetical and algebraic background and the basic techniques for symmetric cryptography, public-key cryptography and error correction coding.
At the end of the course the student should be able to understand the fundamental concepts of modular arithmetic and finite fields and to be able to apply them to the study of basic cryptographic techniques and basic error correcting codes described during the course.
On successful completion of this course, the student should
1) have knowledge of the basic techniques of cryptography and error correction codes introduced;
2) understand the fundamental concepts of arithmetic and algebra and their interactions and be aware of their applications in cryptography and coding theory;
3) have knowledge of how to apply the notions of arithmetic and algebra to the study of cryptographic techniques and error correction codes;
4) understand and analyze the mathematical and application problems underlying the cryptographic schemes studied;
5) demonstrate skill in reasoning and arithmetic calculation and ability to understand the proofs of the theoretical and cryptographic results studied;
6) demonstrate ability to read and understand other scientific texts on related subjects.
Topics of the module include:
Overview of Cryptography and attack scenarios.
Elementary arithmetics: Integers, divisibility, prime numbers, Euclidean division and g.c.d., Bezout's Identity, Eucledian Algorithm, Extended Eucledian Algorithm, Congruence classes, Chinese remainder theorem, cyclic and abelian
groups, Lagrange theorem, Fermat's Little Theorem, Euler theorem, the structure of invertible classes mod N, Fields with p elements, Primitive Roots, polynomials, Euclidean division and g.c.d., Congruence classes of polynomials, Finite fields, primitive elements and polynomials.
Introduction to Probability. Probability and Ciphers, Introduction to Shannon Theory, Perfect secrecy, Shannon Theorem, one time pad, Substitution Ciphers.
Symmetric Cryptography, Feistel Networks, Substitution Permutation Networks, Advanced Encryption Standard - Rijandel.
Group generated by a round functions and Imprimitive attack.
Differential cryptanalysis, example of differential cryptanalysis on a small variant of PRESENT.
Public-key Cryptography, Discrete logarithms problem (DLP), Computational Diffie-Hellmann Problem (DHP), between DLP and DHP, Diffie-Helman Key exchange.
RSA Algorithm, Trial Division, Fermat's test, Miller Rabin Test, AKS primality test, Factoring and factoring-related problems (SQRROOT and RSA Problem), Security of RSA, Coppersmith Theorem, Hastad Attack, Wiener Attack.
Hash function, Digital signatures, RSA signatures, Hashing and signing, DSA.
Error correcting codes, Binary block codes, distance and correction of errors, singleton bound, Hamming bound, Gilbert-Varshamov bound, linear codes, Syndrome decoding, dual codes, Hamming codes, Simplex codes,cyclic codes, Reed-Solomon codes.
1) Trappe and Washington, "Introduction to Cryptography with Coding Theory", second edition, Pearson Pretince Hall, 2006;
2) Smart, "Cryptography made simple", Information Security and Cryptography, Springer, 2016;
3) Heys, "A Tutorial on Linear and Differential Cryptanalysis",
https://www.engr.mun.ca/~howard/PAPERS/ldc_tutorial.pdf
Knowledge of all topics treated the Mathematical Analysis courses in the first and second year: real functions of real variables, limits, differentiation, integration; sequences and series of funcions; ordinary differential equations
Knowledge of basic topics of complex analysis: elementary functions of complex variable, differentiation, integration and main theorems on analytic functions . Ability to use such knowledge in solving problems and exercises
- Complex numbers. Sequences. Elementary functions of complex numbers. Limits, continuity. Differentiation. Analytic functions. Harmonic functions.
- Contour integrals. Cauchy's Theorem. Cauchy's integral formula. Maximum modulus theorem. Liouville's theorem. Morera's theorem.
- Series representation of analytic functions. Taylor's theorem. Laurent's series and classification of singularities.
- Calculus of residues. The residue theorem. Application in evaluation of integrals on the real line and Principal Value. The logarithmic residue, Rouche's theorem.
- Fourier transform for L^1 functions. Applications. Fourier transform for L^2 functions. Plancherel theorem.
- Laplace transform and applications.
- J.E. Marsden, M.J. Hoffman, Basic complex analysis , Freeman New York.
- W. Rudin, Real and complex analysis , Mc Graw Hill.
The student must know the basics of algebra and mathematical analysis. He must also have a basic knowledge of the mechanics of the material point and of the rigid body.
Space of configurations: the finite dimensional case. Space of configurations: the infinite dimensional case. The configuration space for the Euler-Bernoulli beam. Elements of model theory. The problem of the determination of the motion for finite dimensional systems. The principle of minimum action, Lagrangians: the finite dimensional case. Deduction of Euler-Lagrange conditions for the finite dimensional case. Numerical methods for solving ordinary differential equations. The principle of minimum action for infinite dimensional systems. Space of three-dimensional Continuous configurations. Euler theory of the deformable beam. Stable equilibrium as a minimum of energy. The concept of constraint for finite dimensional systems: the Dini theorem. Discretization of infinite-dimensional models. Timoshenko beam. Wave propagation: applications.
Gurtin, Morton E. An introduction to continuum mechanics. Vol. 158. Academic press, 1982.
Sanjay Govindjee. A First Course on Variational Methods in Structural Mechanics and Engineering. University of California, Berkeley.
Ability to recognize and model network optimization problems as Integer Linear Programming problems. Knowledge of fundamental algorithmic techniques for solving large scale Integer Linear Programming problems. Knowledge of commercial and open source Integer Linear Programming solvers.
1. Formulations of Integer and Binary Programs: The Assignment Problem; The Stable Set Problem; Set Covering, Packing and Partitioning; Minimum Spanning Tree; Traveling Salesperson Problem (TSP); Formulations of logical conditions.
2. Mixed Integer Formulations: Modeling Fixed Costs; Uncapacitated Facility Location; Uncapacitated Lot Sizing; Discrete Alternatives; Disjunctive Formulations.
3. Optimality, Relaxation and Bounds. Geometry of R^n: Linear and affine spaces; Polyhedra: dimension, representations, valid inequalities, faces, vertices and facets; Alternative (extended) formulations; Good and Ideal formulations.
4. LP based branch-and-bound algorithm: Preprocessing, Branching strategies, Node and variable selection strategies, Primal heuristics.
5. Cutting Planes algorithms. Valid inequalities. Automatic Reformulation: Gomory's Fractional Cutting Plane Algorithm. Strong valid inequalities: Cover inequalities, lifted cover inequalities; Clique inequalities; Subtour inequalities. Branch-and-cut algorithm.
6. Software tools for Mixed Integer Programming.
7. Lagrangian Duality: Lagrangian relaxation; Lagrangian heuristics.
8. Network Problems: formulations and algorithms. Constrained Spanning Tree Problems; Constrained Shortest Path Problem; Multicommodity Flows; Symmetric and Asymmetric Traveling Salesman Problem; Vehicle Routing Problem Steiner Tree Problem; Network Design. Local Search Tabu search and Simulated Annealing MIP based heuristics.
9. Heuristics for network problems: local search, tabu search, simulated annealing, MIP based heuristics.
L.A. Wolsey, Integer Programming. Wiley. 1998.
Basic Numerical Analysis and Linear Algebra.
The Aim of this course is to provide the student with knowledge of Numerical Linear Algebra and Numerical Optimisation and ability to analyze theoretical properties and design mathematical software based on the proposed schemes.
On successful completion of this module, the student should
- have profound knowledge and understanding of the most relevant numerical methods for Numerical Linear Algebra and Numerical Optimisation and the design of accurate and efficient mathematical software;
- demonstrate skills in choosing the most suitable method in relation to the problem to be solved and ability to provide theoretical analysis and mathematical software based on the proposed schemes;
- demonstrate capacity to read and understand other texts on the related topics.
- J. Stoer, R. Bulirsch, Introduction to numerical analysis , Springer. 2002.
- J. Nocedal, S. J. Wright, Numerical optimization , Springer. 1999.
- A. Quarteroni, R. Sacco, F. Saleri, P. Gervasio, Numerical Mathematics, Springer (2014).
Probability theory and Real Analysis
Students should:
1. Develop the skills to model simple real problems and propose a solution;
2. Solve theoretical problems, using the appropriate mathematical tools;
3. Read the related texts and gain access to more advanced courses;
4. Get a first flavour of the relevant research problems.
1. Discrete time processes: Markov chains in finite and countable space, limiting distribution;
2. Continuous time processes: density and distribution of into-event time for Poisson process, applications and extensions: e.g. birth-and-death processes, queues, epidemics;
3. Renewal processes: ordinary renewal process, renewal theorem, equilibrium
renewal process, application to queues;
4. Wiener processes and basic stochastic calculus: basic definitions and properties, It\^o's formula, Stochastic Differential Equations.
1. Markov Chains, J.R. Norris, Cambridge University Press;
2. Introduction to Stochastic Processes, G. Lawler, Chapman & Hall;
3. Basic Stochastic Processes, A Course Through Exercises, Z. Brzezniak and T. Zastawniak, Springer;
4. Probability and Random Processes, G. Grimmett and D. Stirzaker, 3rd Edition, Oxford University Press;
5. A first look at Rigorous Probability Theory, J. Rosenthal, World Scientific.
*Students are required to earn 60 ECTS credits, at least, during their second year by successfully attending the following compulsory course units (Semester 1 and 2 amounting to 48 ECTS credits) and picking other 12 ECTS credits (minimum) from the elective ones listed below.
Basic notions of functional analysis, functions of complex values, standard properties of classical solutions of semilinear first order equations, heat equation, wave equation, Laplace and Poisson's equations.
Knowledge of mathematical methods that are widely used by researchers in the area of Applied Mathematics, as Sobolev Spaces, distributions. Application of this knowledge to a variety of topics, including the basic equations of mathematical physics and some current research topics about linear and nonlinear partial differential equations.
Distributions. Locally integrable functions. The space of test function D(U). Distributions. Distributions associated to Locally integrable functions. Singular distributions. Examples. Operations on distributions: sum, products times functions, change of variables, restrictions, tensor product. Differentiation and his properties; comparison with classical derivatives. Differentiation of jump functions. Partition of unity. Support of a distribution; compactly supported distributions.
Convolution. Convolution in Lp spaces. Regularity of the convolution. Regularizing sequences and smoothing by means of convolutions. Convolution between distributions and regularization of distributions. Denseness of D(U) in D'(U).
Sobolev spaces. Definition of weak derivatives and his motivation. Sobolev spaces Wk,p(U) and their properties. Interior and global approximation by smooth functions. Extensions. Traces. Embeddings theorems: Gagliardo-Nirenberg-Sobolev inequality and Embedding theorem for p < n. Embedding theorem for p = n. Hölder spaces. Morrey inequality. Embedding theorem for p > n. Sobolev inequalities in the general case. Compact embeddings: Rellich-Kondrachov theorem, Poincaré inequalities. Characterization of the dual space H-1.
Second order parabolic equations. Definition of parabolici operator. Weak solutions for linear parabolici equations. existence of weak solutions: Galerkin approximation, construction of approximating solutions, energy estimates, existence and uniqueness of solutions. Existence of solutions of viscous scalar conservation laws.
First order nonlinear hyperbolic equations. Scalar conservation laws: derivation, examples. Weak solutions, Rankine-Hugoniot conditions, entropy conditions. L1 stability, uniqueness and comparison for weak entropy solutions. Convergence of the vanishing viscosity and existence of the weak, entropy solution. Riemann problem. Definition of hyperbolic system. Quasilinear hyperbolic systems, symmetric and symmetrizable systems. Existence of solutions: approximations, a priori estimate, local existence of classical solutions.
V.S. Vladimirov, Equations of Mathematical Physics. Marcel Dekker, Inc..
C.M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics. Springer.
L.C. Evans, Partial Differential Equations. AMS.
M.E. Taylor, Partial Differential Equations, Nonlinear equations. Springer.
H. Brezis, Sobolev Spaces and Partial Differential Equations. Springer.
Basic notions of functional analysis, functions of complex values, standard properties of the heat equation, wave equation, Laplace and Poisson's equations.
This course is designed to give an overview of fluid dynamics from a mathematical viewpoint and to introduce students to the mathematical modeling of fluid dynamic type. At the end of the course students will be able to perform a qualitative and quantitative analysis of solutions for particular fluid dynamics problems and to use concepts and mathematical techniques learned from this course for analysis of other partial differential equations.
Derivation of the governing equations: Euler and Navier-Stokes.
Eulerian and Lagrangian description of fluid motion; examples of fluid flows.
Vorticity equation in 2D and 3D.
Dimensional analysis: Reynolds number, Mach Number, Frohde number.
From compressible to incompressible models.
Fluid dynamic modeling in various fields: biofluids, atmosphere and ocean, astrophysics.
Existence of solutions for viscid and inviscid fluids.
Linux/Unix OS and tools;
Basic Fortran (or C);
HPC architecture and libraries;
Application (ex ODEs, PDEs, elastodynamics).
A good knowledge of the basic arguments of a course of Functional Analysis, in particular, a good knowledge of the theory of Lebesgue's integral and the L^p spaces.
The first module of the course, in particular a good knowledge of the theory of distributions and Sobolev spaces.
Aim of the course is the knowledge of advanced techniques of mathematical analysis and in particular the basic techniques of the modern theory of the partial differential equations.
Abstract Measure theory.
AC and BV functions.
Fourier transforms.
Second order elliptic equations.
Variational methods.
Basics of Algebra
The course aims to provide the arithmetical and algebraic background and the basic techniques for symmetric cryptography, public-key cryptography and error correction coding.
At the end of the course the student should be able to understand the fundamental concepts of modular arithmetic and finite fields and to be able to apply them to the study of basic cryptographic techniques and basic error correcting codes described during the course.
On successful completion of this course, the student should
1) have knowledge of the basic techniques of cryptography and error correction codes introduced;
2) understand the fundamental concepts of arithmetic and algebra and their interactions and be aware of their applications in cryptography and coding theory;
3) have knowledge of how to apply the notions of arithmetic and algebra to the study of cryptographic techniques and error correction codes;
4) understand and analyze the mathematical and application problems underlying the cryptographic schemes studied;
5) demonstrate skill in reasoning and arithmetic calculation and ability to understand the proofs of the theoretical and cryptographic results studied;
6) demonstrate ability to read and understand other scientific texts on related subjects.
Topics of the module include:
Overview of Cryptography and attack scenarios.
Elementary arithmetics: Integers, divisibility, prime numbers, Euclidean division and g.c.d., Bezout's Identity, Eucledian Algorithm, Extended Eucledian Algorithm, Congruence classes, Chinese remainder theorem, cyclic and abelian
groups, Lagrange theorem, Fermat's Little Theorem, Euler theorem, the structure of invertible classes mod N, Fields with p elements, Primitive Roots, polynomials, Euclidean division and g.c.d., Congruence classes of polynomials, Finite fields, primitive elements and polynomials.
Introduction to Probability. Probability and Ciphers, Introduction to Shannon Theory, Perfect secrecy, Shannon Theorem, one time pad, Substitution Ciphers.
Symmetric Cryptography, Feistel Networks, Substitution Permutation Networks, Advanced Encryption Standard - Rijandel.
Group generated by a round functions and Imprimitive attack.
Differential cryptanalysis, example of differential cryptanalysis on a small variant of PRESENT.
Public-key Cryptography, Discrete logarithms problem (DLP), Computational Diffie-Hellmann Problem (DHP), between DLP and DHP, Diffie-Helman Key exchange.
RSA Algorithm, Trial Division, Fermat's test, Miller Rabin Test, AKS primality test, Factoring and factoring-related problems (SQRROOT and RSA Problem), Security of RSA, Coppersmith Theorem, Hastad Attack, Wiener Attack.
Hash function, Digital signatures, RSA signatures, Hashing and signing, DSA.
Error correcting codes, Binary block codes, distance and correction of errors, singleton bound, Hamming bound, Gilbert-Varshamov bound, linear codes, Syndrome decoding, dual codes, Hamming codes, Simplex codes,cyclic codes, Reed-Solomon codes.
1) Trappe and Washington, "Introduction to Cryptography with Coding Theory", second edition, Pearson Pretince Hall, 2006;
2) Smart, "Cryptography made simple", Information Security and Cryptography, Springer, 2016;
3) Heys, "A Tutorial on Linear and Differential Cryptanalysis",
https://www.engr.mun.ca/~howard/PAPERS/ldc_tutorial.pdf
The goal of this course is to provide the motivations, definitions and techniques for the translation of topological problems into algebraic ones, hopefully easier to deal with. On successful completion of this module, the student should understand the fundamental concepts of algebraic geometry and should be aware of potential applications of algebraic topological invariants in other fields as theoretical physics , including the computational fluid mechanics and electrodynamics.
General topology: topological spaces and continuous maps, induced, quotient and product topology, metric spaces, Hausdorff spaces, compact spaces, connected spaces, paths and path connected spaces
Manifolds and surfaces: the pancake problems, n-dimensional manifolds, surfaces and classification of surfaces.
Homotopy: Retracts and contractible spaces, paths and multiplication, the fundamental group, the fundamental group of the circle.
Covering spaces: the fundamental group of a covering space, the fundamental group of a orbit space, lifting theory and existence theorems, the Borsuk-Ulam theorem, the Seifert-Van Kampen theorem, the fundamental group of a surface.
Introduction to singular homology: standard and simplicial simplexes.
Czes Kosniowski, A first course in algebraic topology. Cambridge University Press. 1980.
Aim of the course is to present some mathematical models currently used in the analysis of collective phenomena, such as vehicular and pedestrian traffic, and flocking phenomena. Emphasis will be given to the mathematical treatment of specific problems coming from real world applications.
Macroscopic traffic models. LWR model, its derivation. Fundamental diagrams. The Riemann problem, examples. Second order models for traffic flow: Payne-Whitham model, description, drawbacks; Aw-Rascle model, shocks description, domains of invariance, instabilities near vacuum.
Theory: systems of conservation laws, strict hyperbolicity, Rankine-Hugoniot conditions; Lax admissibility condition. The Riemann problem for systems: the linear case; GNL and LD fields; rarefactions and contact discontinuities. BV functions, examples and properties. A compactness theorem.
Wave front tracking algorithm: approximate rarefactions, possible types of interactions. Bounds on number of waves and on total variation. Compactness of approximate solutions. The initial-boundary value problem on the half line: boundary Riemann problem, interactions with the boundary, control of the total variation by means of a Lyapunov-type functional. The Toll gate problem.
Networks, basic definitions, conservation of the flux. Examples. Distributions along the roads, maximization of the flux. Riemann problem on a junction composed by 2 incoming roads and 2 outgoing roads. The case of 2 incoming roads and 1 outgoing road: the "right of way" rule. Junction between one incoming and one outgoing road, different fluxes.
Pedestrian flow: normal and panic situation. Macroscopic models for evacuation, conservation of "mass", eikonal equation. The Hughes model for pedestrian flow. The eikonal equation: non uniqueness, viscosity solutions, relation with vanishing viscosity approximation. The Hughes model in one space dimension. Curve of turning points, Rankine-Hugoniot conditions. The case of constant initial density and of symmetric initial data; conservation of the left and right mass; an example with mass exchange across the turning point. Macroscopic models for pedestrian flow that include: knowledge of a preferred path, discomfort from walking along walls, tendency of avoiding high densities of pedestrian in a neighborhood (nonlocal term of convolution type), angle of vision, obstacle in the domain. Linearized stability around a smooth solution.
Introduction to the theory of flocking. Examples: Krause model for opinion dynamics, Cucker-Smale model, model for attraction-repulsion phenomena. The Cucker-Smale flocking model: basic properties, estimates on the kinetic energy. A "flocking theorem": proof by bootstrapping method (Ha and Tadmor). Some drawbacks of the model. Introduction to the kinetic limit for flocking: the N-particle distribution function, Liouville equation, marginal distribution, continuity equation. The formal mean-field limit: a Vlasov-type equation.
M.D. Rosini, Macroscopic models for vehicular flows and crowd dynamics: theory and applications. Springer. 2013. http://link.springer.com/book/10.1007/978-3-319-00155-5/page/1
M. Garavello, B. Piccoli, Traffic flow on networks. Conservation laws models. AIMS Series on Applied Mathematics. 2006. http://www.aimsciences.org/books/am/AMVol1.html
Basic calculus and analysis (differential and integral calculus with functions of many variables).
Ordinary differential equations.
Basics in finite dimensional dynamical systems.
Elementary methods for the solution of linear partial differential equations (separation of the variables).
1) To learn the basics in the mathematical modelling of population dynamics.
2) To provide a mathematical description of ODE models in population dynamics and the intepretation of the qualitative behaviour of the solutions.
3) To get the basic notions in mathematical models in epidemiology and reaction kinetics.
4) To learn the mathematical modelling of population models in heterogeneous environment, described by partial differential equations.
5) To deal with advanced models in biology such as chemotaxis models and structured dynamics equations.
6) To get a sound background in reaction diffusion phenomena, Turing instability, and pattern formation.
Continuous Population Models for Single Species. Continuous Growth Models. Delay models. Linear Analysis of Delay Population Models: Periodic Solutions.
Continuous models for Interacting Populations. PredatorPrey Models: Lotka-Volterra Systems. Realistic Predator–Prey Models. Competition Models: Principle of Competitive Exclusion. Mutualism or Symbiosis.
Reaction kinetics. Enzyme Kinetics: Basic Enzyme Reaction. Transient Time Estimates and Nondimensionalisation. Michaelis-Menten Quasi-Steady State Analysis.
Dynamics of Infectious Diseases: Epidemic Models and AIDS. Simple Epidemic Models (SIR, SI) and Practical Applications. Modelling Venereal Diseases. AIDS: Modelling the Transmission Dynamics of the Human Immunodeficiency Virus (HIV).
Time-space dependent models: PDEs in biology. Diffusion equations. Diffusion and Random walk. The gaussian distribution. Smoothing and decay properties of the diffusion operator. Nonlinear diffusion.
Reaction–diffusion models for one single species. Diffusive Malthus equation and critical patch size. Travelling waves. Fisher–Kolmogoroff equation.
Reaction–diffusion systems. Multi species waves in Predator-Prey Systems. Turing instability and spatial patterns.
Chemotaxis modelling. Diffusion vs. Chemotaxis: stability vs. instability. Diffusion vs. Chemotaxis: stability and blow–up. Chemotaxis with nonlinear diffusion. Models with maximal density.
Nonlocal interaction models in biology. Mathematical models of swarms. Approximation with interacting particle systems. Asymptotic behaviour.
Structured population dynamics. An example in ecology: competition for resources. Continuous traits. Evolutionary stable strategy in a continuous model.
James D. Murray, Mathematical Biology I: an introduction. Springer.
James D. Murray, Mathematical Biology II: Spatial models and biomedical applications . Springer.
Benoit Perthame, Transport equations in biology. Birkaeuser.
Probability theory and Real Analysis
Students should:
1. Develop the skills to model simple real problems and propose a solution;
2. Solve theoretical problems, using the appropriate mathematical tools;
3. Read the related texts and gain access to more advanced courses;
4. Get a first flavour of the relevant research problems.
1. Discrete time processes: Markov chains in finite and countable space, limiting distribution;
2. Continuous time processes: density and distribution of into-event time for Poisson process, applications and extensions: e.g. birth-and-death processes, queues, epidemics;
3. Renewal processes: ordinary renewal process, renewal theorem, equilibrium
renewal process, application to queues;
4. Wiener processes and basic stochastic calculus: basic definitions and properties, It\^o's formula, Stochastic Differential Equations.
1. Markov Chains, J.R. Norris, Cambridge University Press;
2. Introduction to Stochastic Processes, G. Lawler, Chapman & Hall;
3. Basic Stochastic Processes, A Course Through Exercises, Z. Brzezniak and T. Zastawniak, Springer;
4. Probability and Random Processes, G. Grimmett and D. Stirzaker, 3rd Edition, Oxford University Press;
5. A first look at Rigorous Probability Theory, J. Rosenthal, World Scientific.
Mathematical Analysis, Fourier transform.
This course provides an introduction to the classical kinetic theory of gases and the principles of kinetic modeling.
A special focus is given to the derivation of hydrodynamic equations from kinetic models by means of non-perturbative techniques and to the analysis of numerical schemes for the simulation of fluid flows.
On successful completion of this module the student has the knowledge on the basic principles and the simulation strategies of kinetic models.
Boltzmann equation and the principles of kinetic description.
Kinetic models: BGK,Maxwell molecules, Vlasov equation and Fokker-Planck equation.
The closure problem and methods of reduced description: Chapman-Enskog expansion, Grad's Moment method.
Non-perturbative techniques in kinetic theory: the method of the slow invariant manifold.
Overview on Lattice Boltzmann models.
Monte Carlo simulations of lattice gas models.
The course is an introduction to Time Series Analysis and Forecasting. The level is the first-year graduate in Mathematics with a prerequisite knowledge of basic inferential statistical methods.
The aim of the course is to present important concepts of time series analysis (stationarity of stochastic processes, ARIMA models, forecasting etc.). At the end of the course, the student should be able to select an appropriate ARIMA model for a given time series.
Stochastic processes (some basic concepts)
Stationary stochastic processes
Autocovariance and autocorrelation functions
Ergodicity of a stationary stochastic process
Estimation of moment functions of a stationary process
ARIMA models
Estimatiom of ARIMA models
Building ARIMA models
Forecasting from ARIMA models
[1]Time Series Analysis Univariate and Multivariate Methods, 2nd Edition, W. W. Wei, 2006, Addison Wesley.
[2] Time Series Analysis, J. Hamilton, 1994, Princeton University Press.
[3] Time Series Analysis and Its Applications with R Examples, Shumway, R. and Stoffer, D., 2006, Springer.
[4]Introduction to Time Series and Forecasting. Second Edition, P. Brockwell and R. Davis, 2002, Springer.
I assume familiarity with vector and topological spaces, and with the standard model of the real numbers. I assume that you know the basic facts about metric spaces, normed and seminormerd spaces, Banach and Hilbert spaces.
On successful completion of this course, the student should:
- Know the fundamental fixed point theorems for set-valued maps and the basic existence results for equilibrium problems and variational inequalities.
- Explain some interconnections among these various results.
- Apply this analysis to game and economic theory
Sperner’s lemma
The Knaster-Kuratowski-Mazurkiewicz lemma
Brouwer's fixed point theorem
Variational inequalities and equilibrium problems
Generalized monotonicity and convexity
Brézis-Nirenberg-Stampacchia theorem and Fan's minimax principle
Continuity of correspondences
Browder, Kakutani and Fan-Glicksberg fixed point theorems
Gale-Nikaido-Debreu theorem
Nash equilibrium of games and abstract economies
Walrasian equilibrium of an economy
An application to traffic network
Basic notions of functional analysis, functions of complex values, standard properties of classical solutions of semilinear first order equations, heat equation, wave equation, Laplace and Poisson's equations.
Knowledge of mathematical methods that are widely used by researchers in the area of Applied Mathematics, as Sobolev Spaces, distributions. Application of this knowledge to a variety of topics, including the basic equations of mathematical physics and some current research topics about linear and nonlinear partial differential equations.
Distributions. Locally integrable functions. The space of test function D(U). Distributions. Distributions associated to Locally integrable functions. Singular distributions. Examples. Operations on distributions: sum, products times functions, change of variables, restrictions, tensor product. Differentiation and his properties; comparison with classical derivatives. Differentiation of jump functions. Partition of unity. Support of a distribution; compactly supported distributions.
Convolution. Convolution in Lp spaces. Regularity of the convolution. Regularizing sequences and smoothing by means of convolutions. Convolution between distributions and regularization of distributions. Denseness of D(U) in D'(U).
Sobolev spaces. Definition of weak derivatives and his motivation. Sobolev spaces Wk,p(U) and their properties. Interior and global approximation by smooth functions. Extensions. Traces. Embeddings theorems: Gagliardo-Nirenberg-Sobolev inequality and Embedding theorem for p < n. Embedding theorem for p = n. Hölder spaces. Morrey inequality. Embedding theorem for p > n. Sobolev inequalities in the general case. Compact embeddings: Rellich-Kondrachov theorem, Poincaré inequalities. Characterization of the dual space H-1.
Second order parabolic equations. Definition of parabolici operator. Weak solutions for linear parabolici equations. existence of weak solutions: Galerkin approximation, construction of approximating solutions, energy estimates, existence and uniqueness of solutions. Existence of solutions of viscous scalar conservation laws.
First order nonlinear hyperbolic equations. Scalar conservation laws: derivation, examples. Weak solutions, Rankine-Hugoniot conditions, entropy conditions. L1 stability, uniqueness and comparison for weak entropy solutions. Convergence of the vanishing viscosity and existence of the weak, entropy solution. Riemann problem. Definition of hyperbolic system. Quasilinear hyperbolic systems, symmetric and symmetrizable systems. Existence of solutions: approximations, a priori estimate, local existence of classical solutions.
V.S. Vladimirov, Equations of Mathematical Physics. Marcel Dekker, Inc..
C.M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics. Springer.
L.C. Evans, Partial Differential Equations. AMS.
M.E. Taylor, Partial Differential Equations, Nonlinear equations. Springer.
H. Brezis, Sobolev Spaces and Partial Differential Equations. Springer.
Basic notions of functional analysis, functions of complex values, standard properties of the heat equation, wave equation, Laplace and Poisson's equations.
This course is designed to give an overview of fluid dynamics from a mathematical viewpoint and to introduce students to the mathematical modeling of fluid dynamic type. At the end of the course students will be able to perform a qualitative and quantitative analysis of solutions for particular fluid dynamics problems and to use concepts and mathematical techniques learned from this course for analysis of other partial differential equations.
Derivation of the governing equations: Euler and Navier-Stokes.
Eulerian and Lagrangian description of fluid motion; examples of fluid flows.
Vorticity equation in 2D and 3D.
Dimensional analysis: Reynolds number, Mach Number, Frohde number.
From compressible to incompressible models.
Fluid dynamic modeling in various fields: biofluids, atmosphere and ocean, astrophysics.
Existence of solutions for viscid and inviscid fluids.
Linux/Unix OS and tools;
Basic Fortran (or C);
HPC architecture and libraries;
Application (ex ODEs, PDEs, elastodynamics).
Mathematical Analysis, Fourier transform.
This course provides an introduction to the classical kinetic theory of gases and the principles of kinetic modeling.
A special focus is given to the derivation of hydrodynamic equations from kinetic models by means of non-perturbative techniques and to the analysis of numerical schemes for the simulation of fluid flows.
On successful completion of this module the student has the knowledge on the basic principles and the simulation strategies of kinetic models.
Boltzmann equation and the principles of kinetic description.
Kinetic models: BGK,Maxwell molecules, Vlasov equation and Fokker-Planck equation.
The closure problem and methods of reduced description: Chapman-Enskog expansion, Grad's Moment method.
Non-perturbative techniques in kinetic theory: the method of the slow invariant manifold.
Overview on Lattice Boltzmann models.
Monte Carlo simulations of lattice gas models.
Browse the tabs below to get useful information about L'Aquila
L'Aquila is an Italian city of about 70,000 inhabitants and nearly 30,000 university students. It is the capital of the Abruzzo region and it is conveniently located 100 km (62 miles) to the east of Rome. The city is on a hill at 720 m (2365 ft) above sea level and is surrounded by mountains, most notably to the north by the Gran Sasso range, which includes the highest peaks (up to 2900 m) of the Apennines, with a number of small lakes, trails and mountain climbing routes as well as deep caves. Within the province of L’Aquila there are also two national parks (Parco Nazionale Gran Sasso Monti della Laga and Parco Nazionale della Majella).
The city itself is full of history, traditions, beautiful buildings (like the Spanish Fortress) and churches (like the Basilica of Collemaggio). There are also a lot of good restaurants, pubs and places where students get together every night. The city is also home to L'Aquila Rugby: this team won the Italian championship five times!
For further practical and historical information on L'Aquila, click here.
The cost per person ranges from 200 to 300 euros per month depending on several factors (e.g. shared or private rooms, utility bills included or not). Students will receive detailed information by email about accommodation in good time before leaving their own country (usually in July).
Please refer to the official webpage for up-to-date references and conditions (available in Italian only): link
For reservations and for other nearby options, just visit Booking, Trivago, Tripadvisor, Airbnb and other popular accommodation search engines.
- www.univaq.it/section.php?id=911
as for the Trenitalia, check the article for possible regional trains to and from L'Aquila.
There are three bus companies operating in L'Aquila that you will find particulary usefull in your everyday life
Besides these busses, there are also
The public transport in L'Aquila is covered by the AMA bus company. Depending on how busy the trip can get thet run orange/blue/green/black busses "l'autobus" or blue vans called "pulmino".
The final destination of the bus is always written on the front side of the bus and together with the bus number can be seen from far. You need to get used to the way the timetable is written, as you can either search for number, or the bus stop (not for the time or "from-to destination trip"). To search for the time online, please check the name of your bus stop and then search for this destination in Linee e Orari to find the bus number you need to take. The other way is to search for the number and then check where it goes. Moreover, there is nowadays nice and clear time table on every bus stop. You can find the map of lines here.
You are obliged to enter a bus with a ticket and validate it in the yellow machine inside the bus. The complete list of ticket selling places can be found here. The closest one to university Coppito is Self copy SaS di Epifano - just across of the road from University. Please mind, that not every place sells all types of tickets.
Here are the most useful types of tickets with prices:
The controllers occasionaly get on the bus and wear the dark blue company clothes. They don't speak english and the fine for not having a validated ticket can get up to 160 Euros.
* the same system as for Arpa holds here as well: in order to be allowed to buy the montly ticket you need to register and buy a card at Terminal Bus Station or Sangritana Viaggi e vacanze Fontana Luminosa. You need to fill in a form and bring ID or passport and 2 passport size fotos. The card is valid until you lose it and costs around 15 Euros.
Regional public bus transport is run by the Arpa company - blue or white with blue stipes busses.
It is the bus company you will use daily for reaching the University. For more information about this daily routine see this article about transfer between L'Aquila and Pizzoli, or how to get to Rome from L'Aquila.
Timetables for other Arpa rides can be found here.
Arpa is the intercity Abruzzo regional bus company that offers transport within the region and also runs to Rome. It is the best option for Rome trips (11 Euros one way). Their offices can be found in several places, moreover, it is possible to buy a ticket at every SISAL place - for example at the Bar in Motel Amiternum.
As for Pizzoli - you can get the tickets in every bar in Pizzoli. For Pizzoli - L'Aquila trip the ticket Tariffa 2 is needed. You are obliged to validate it in the machine inside the bus.
You'll find all Gaspari timetables on their webpage. There are 2 lines that might be on your interest:
Gaspari tickets can be bought both, on the bus and online. Their page hasn't been translated into english yet but this article describing how to buy tickets on gaspari webpage in english might be useful. We recommend to buy your ticket online, so you assure yourself with the seat on the bus in case it gets busy (which has recently been happening). When entering the bus, pasangers with online tickets go first.
As for car transport possibilities in&around L'Aquila you can consider following options
If you wish to bring your own car to L'Aquila there is no problem. There has so far been at least one person bringing their car from each generation. Parking next to our student residences in Pizzoli is possible just next to your flat. When arriving to L'Aquila by car please mind that in Italy we pay for highway everytime we enter.
L'Aquila can be reached either via motorway or road:
There is only one taxi company in L'Aquila, Radio Taxi. They can be reached by phone +39086225165 or in front of Motel Amiternum.
Erasmus Mundus students are meant to get the special price of 15 Euros for the trip Pizzoli-L'Aquila and vise versa. The usual trip Motel Amiternum-city center is aroun 4 Euros.
Radio Taxi are available every day until 12am; on Thursdays and Saturdays until 3am. Aside from these times it is possible to make a pick up agreement in advance, however, if you have a early flight (therefore early gaspari bus) we reccomend to stay at friends place in L'Aquila for this special occasion.
Students often use auto rental services for weekend or daily trips. There are several car rental company, just search for 'car rental in L'Aquila' in your browser or ask older students.
In 2014 there were students renting a car from Europcar, na Via della Croce Rossa. For approximately 2-4 days it was around 30 Euros a day but drivers under 25 have to pay an extra fee.
Aquilasmus is a student association, part of ESN (Erasmus Student Network). Aquilasmus offers several services to Erasmus students, like organizing parties, trips, international dinners, cineforums and more. Take a look at their website and join their Facebook group to get to know other international students and be involved in their activities.
Check this article to see more information about cinemas, theathers, music, bars, restaurants,pubs & clubs, discos.
Free time and nightlife
Aquilasmus is a student association, part of ESN (Erasmus Student Network). Aquilasmus offers several services to Erasmus students, like organizing parties, trips, international dinners, cineforums and more. Take a look at their website and join their Facebook group to get to know other international students and be involved in their activities.
Cinemas
Theatres
Music
Before the 2009 earthquake most people and students used to gather at the many cafes and bars in L'Aquila city centre. Now, while most buildings there are still to be reconstructed and great part of the area is not yet accessible to people, a bunch of bars have proudly reopened their doors. You will find lots of students hanging out mostly on Thursday nights (typically, university night) and Saturday nights. Just ask the taxi/bus driver to drop you at "Fontana Luminosa" (the big fountain near the castle) and walk into the main road "Corso Federico II". You'll see that most people gather in that small square or head right into via Garibaldi. As a consequence of the earthquake, several other good pubs and clubs have had to move to other areas of the city. So, take a look at the rest of list, too.
City centre
Viale della Croce Rossa
After the earthquake several pubs moved from the city centre, which was off-limits for several months, to this road which connects the "Fontana Luminosa" to Viale Corrado IV
Between the train station and Viale Corrado IV
Viale Corrado IV (main road connecting Hotel Amiternum to the city centre)
Other areas
For informantion on popular excursions you can make around L'Aquila (ski resorts, beaches and more), read here.
Check these articles for more info about shoping in L'Aquila or shops in Pizzoli.
As for fashion or souvenirs there are many shops in Roma or Pescara on various price level.
Many collective sports like rugby, football as well as tennis can be played in student organisations. Check the map below for University Sports Centre (CUS - Centi Colella), where students have reduced fee. It should be the bus stop s.s.17
Please mind that in Italy it is necessary to have a health check certificate from a 'family doctor' ( = the general doctor) before joining any sport facility (f.e. a gym). Feel free to e-mail us in case you have difficulties getting one.
Thanks to the great geographical location, both, L'Aquila and Pizzoli offer great oportunities to hike or just go for a nice walk into the mountains or woods.
All Pizzoli hikes start at the 'Pizzoli castle' when you continue up the road and after you pass few houses you will find yourself in the nice Abruzzo woodland.
As for L'Aquila hikes, you may pick any hill you see from the center
It is quite likely to meet horses, cheep, cows or even some wild animals on your way - all being more scared than yourself and therefore harmless. Sometime you may stumble across cheep dogs that might look angry but if you don't show any signs of agression and simply ignore them they will gladly return the favore.
Dispite having no cycle paths in L'Aquila, it is possible to cycle on the road, however, this is on everyones own responsibility. You can get propper cycling stufff in Decathlon in Laquilone or other cycling shops in L'Aquila. There is also an active cycling club that occasionally organises bike events in Gran Sasso .
there is a big stable in Paganica, check AMA busses to see. One lecture costs 10 Euros and it is possible to prepay 10 lectures. Mind, the transportation from L'Aquila can take a while.
there are few gyms in L'Aquila and in Pizzoli as well. Please see the map above for precise location and this article about sporting facilities in L'Aquila for more information.
If you are interested in Yoga classes or similar, there used to be some in Asilo Occupato but we recommend to ask Laquilasmus.
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