universit\300 degli studi

Degrees in Mathematics
The Second Part of the Bulletin (Notiziario)
COURSES
PROGRAMME
Academic Year 2009/2010
I Semester:
Thursday 1, October - Saturday 16, January
II Semester:
Monday 1, March - Saturday 12, June
♥♦♣♠
♥♦♣♠
Notes
The new 3+2 degree courses give a bachelor degree (or a first
level degree) after 3 years, and a master's degree (or a
second level degree) after a further 2 years.
1 CFU is earned by attending 8 hours of lectures.
All lectures are held in Italian language.
Attendance of the lectures is warmly recommended.
Table 1 - A. A. 2009/10
Courses at the first level (bachelor): Mathematics
The first 4 semesters belong to the new degree
Year I – Semester I
Year I – Semester II
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Table 2 - A. A. 2009/10
Courses at the first level (bachelor): Mathematics
Name
Year Semester Sector Hours
Didattica della
III
II Sem MAT/04 60
Matematica 1
Fisica 2
III
II Sem FIS/01
60
Geometria 4
III
II Sem MAT/03 60
Geometria Superiore 1 III
I Sem MAT/03 60
Lab. di
Sperimentazione di
III
II Sem FIS/01
36
Fisica 1
Matematiche
III
II Sem MAT/04 60
Complementari 1
Matematiche
III
I Sem MAT/04 60
Elementari p.v.s. 1
Meccanica Razionale 1 III
I Sem MAT/07 60
Storia delle
III
II Sem MAT/04 60
Matematiche 1
Topologia 1
III
I Sem MAT/03 60
CFU
Lecturer
7,5
E. UGHI
7,5
7,5
7,5
G. IMMIRZI
L. GUERRA
L. GUERRA
4,5
A. SANTUCCI
7,5
P. ZAPPA
7,5
F. CONTI
7,5
M.C. NUCCI
7,5
M. C. NUCCI
7,5
A. CATERINO
Table 3 - A. A. 2009/10
Courses at the first level (bachelor): Mathematics for the Applications
Name
Year Semester Sector. Hours CFU
Algebra Superiore 1
III
I Sem
MAT/02
Analisi Numerica 2
III
I Sem
MAT/08
Equazioni Differenziali 1
Fisica Matematica con
laboratorio 1
Geometria Combinatoria 1
Lab. di Program. e Calcolo 1
Lab. di Program. e Calcolo 2
Matematica Applicata 1
Metodi Matematici per
l'Economia 1
III
Lecturer
60
8
II Sem MAT/05
G. FAINA
GERACE,
60 4+3,5
F. MARTINELLI
60
7,5 T. CARDINALI
III
I Sem
MAT/07
64
8
III
III
III
III
II Sem MAT/03
II Sem INF/01
II Sem INF/01
I Sem MAT/07
60
36
24
24
7,5
4,5
3
3
R. VINCENTI
R. BICOCCHI
P.T. MELACCI
B. IANNAZZO
III
I Sem
MAT/05
60
7,5
R. FILIPPUCCI
Statistica Matematica 1
III
II Sem MAT/06
60
7,5
Teoria delle Decisioni 1
III
II Sem MAT/06
60
7,5
A. CAPOTORTI (4,5
CFU)
G. REGOLI (3 CFU)
G. COLETTI
M.C. SALVATORI
Table 4 - A. A. 2009/10
Courses at the second level (master)
for the first year (new degree)
Year Semester
Algebra 3
I - I Sem
Analisi Matematica 5
I - I Sem
Analisi Matematica 6
I - II Sem
Didattica d. Matematica 1 I - I Sem
Equazioni Differenziali
I - II Sem
Fisica Matematica 2
I - II Sem
Geometria 5
I - I Sem
Informatica 3
I - II Sem
Storia delle Matematiche
I - II Sem
Teoria dell'Informazione 2 I - II Sem
Topologia 2
I- II Sem
Name
Sector
Hours
CFU
MAT/02
MAT/05
MAT/05
MAT/04
MAT/05
MAT/07
MAT/03
INF/01
MAT/04
INF/01
MAT/03
48
96
48
48
48
48
96
48
48
48
60
6
12
6
6
6
6
12
6
6
6
7,5
Lecturer
A. LORENZINI
P. PUCCI
E. VITILLARO
E. UGHI
T. CARDINALI
S. DE LILLO
A. TANCREDI
M. BAIOLETTI
M.C. NUCCI
G. FAINA
M.C. VIPERA
Table 5 - A. A. 2009/10
Courses at the second level (master)
for the second year (old degree)
Year Semester
Analisi Numerica 3
II - I Sem
Analisi Superiore 1
II - I Sem
Elementi di Logica 2
II - I Sem
Geometria Combinatoria 2 II - II Sem
Meccanica Superiore 1
II - I Sem
Probabilità 2
II- II Sem
Topologia 2
II- II Sem
Name
Sector
Hours
CFU
MAT/08
MAT/05
MAT/01
MAT/03
MAT/07
MAT/06
MAT/03
60
60
24
60
60
60
60
5,5
7,5
3
7,5
7,5
7,5
7,5
Lecturer
I. GERACE
D. MUGNAI
M. BAIOLETTI
M. GIULIETTI
M. MAMONE CAPRIA
D.CANDELORO
M.C. VIPERA
Notes for each course
1-the title is maintained in Italian
2-the subtitle describes the content in brief
3-the year suggests the year of the bachelor degree in which the course might
be attended (if nothing else is specified) otherwise I master or II master
suggests the year of the master's degree
4-the semester states in which of the two semesters of the year the course is
held
5-the sector indicates the code/s of the scientific area/s of the content
6-the prerequisites suggest pre-course requirements.
7-the hours are the total number of hours of lessons in the semester in
classroom, inclusive of practice
8- One ECTS is equivalent to 1 CFU (Crediti Formativi Universitari) that
consists of 8 hours in lecture-hall plus 17 hours of individual study.
9-If a course is held in common with the old 4-year degree, the original title of
the course is written in brackets.
Links to further information: http://www.dmi.unipg.it/Matematica
Office hours: http://www.dmi.unipg.it/MatematicaOrarioRicevimento
List of Courses
(in alphabetic order)
ALGEBRA 1 - 12 CFU
Subtitle: Numerical sets, cardinal numbers, groups, rings and fields
Year: I
Semester: II
Sector: MAT/02
Prerequisites: set theory, relations, functions
Hours of lessons: 96
Lecturers: Giuliana Fatabbi, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5020, E-mail: [email protected]
Anna Lorenzini – Dipartimento di Matematica e Informatica,
Telefono: +39 075 585 5020, E-mail: [email protected]
Content
Number sets: construction and algebraic properties. Residue Classes. Cardinality theory. Permutations.
Homomorphisms. Direct products. Cyclic groups. Cauchy’s Theorem and Sylow’s theory. Fundamental
homomorphism theorem for groups and rings. Prime and maximal ideals. Polynomial ring. Ring and field
extensions.
Textbooks
D.Dikranjan, M.S. Lucido, Aritmetica e Algebra, Liguori Editore (2007).
G.M. Piacentini Cattaneo, Algebra: un approccio algoritmico, Decibel-Zanichelli (1996).
ALGEBRA 3
- 7,5 CFU
Subtitle: Commutative and Computational Algebra
Year: I master
Semester: I
Sector: MAT/02
Prerequisites: Basic concepts about rings and ideals and about fields.
Hours of lessons: 60
Lecturer: Anna Lorenzini – Dipartimento di Matematica e Informatica –
Tel. +39 075 585 5020, E-mail: [email protected]
Content
Part 1 - Polynomials in several variables. Monomyal orders. Division algorithm. Dickson's Lemma.
Groebner bases. Noetherian modules. Hilbert basis Theorem. Buchberger criterion and algorithm.
Membership algorithm. Elimination a nd intersection algoritm. Primary decomposition in noetherian
rings.
Part 2 - Affine varieties. Hilbert (affine) Nullstellensatz and the consistency algorithm. Radical
membership algorithm. Homogeneous ideals and projective varieties. Hilbert (projective) Nullstellensatz
and the consistency algorithm. Hilbert function, Hilbert polynomial and the dimension af affine and
projective varieties.
Textbooks
Cox, Little, O’Shea, Ideals, varieties and algorithms, Springer, 1997.
Atiyha-MacDonald, Introduction to commutative algebra, Addison-Wesley (1969).
ALGEBRA SUPERIORE 1
- 8 CFU
Subtitle: Algorithmic Theory of numbers and cryptography
Year: III
Semester: I
Sector: MAT/02
Prerequisites: Linear algebra and elementary discrete mathematics
Hours of lessons: 64
Lecturer: Giorgio Faina, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5009, E-mail:[email protected]
Content
Fundamental algorithms for integer arithmetic, greatest common divisor calculation, modular arithmetic,
and other number theoretic computations. Algorithms are derived, implemented and analyzed for
primality testing and integer factorization. Applications to cryptography are explored including
symmetric and public-key cryptosystems. A cryptosystem will be implemented and methods of attack
investigated.
Textbooks
S. Leonessi – C. Toffalori, Numeri e crittografia, Springer 2006
R. Stinson, Cryptography: Theory and Practice, CRC Press 1995.
Notes will be supplied by the lecturer.
ANALISI MATEMATICA 1 - 12 CFU
Subtitle: Functions in one real variable
Year: I
Semester: I
Sector: MAT/05
Prerequisites: none
Hours of lessons: 96
Lecturer: Marcello Ragni, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5036, e-mail: [email protected]
Content
Basic elements of set theory. Subsets of real numbers. Least upper and greatest lower bounds. Functions
and sequences. Elements of topology in Rn. Limits: properties and calculus. Infinite and infinitesimal
functions. Upper and lower limits. Cauchy sequences. Numerical series, convergence criteria. Properties
of continuous functions. Differentiation: definition and rules. Mean value theorem and main
consequences. Higher order derivatives. Taylor’s theorem. Power series. Primitive functions. The
Riemann integration: main properties and fundamental examples. Improper Riemann integral.
Textbooks
C.Vinti, Lezioni di Analisi Matematica, Galeno Editrice Perugia
G. De Marco, C. Mariconda, Esercizi di calcolo in una variabile per il nuovo ordinamento, Decibel Zanichelli.
G. Marangoni, Successioni e serie numeriche, Cedam.
G. Marangoni, Integrali, Cedam.
F. Casolaro, Integrali, Masson.
ANALISI MATEMATICA 2 - 12 CFU
Subtitle: Differential calculus for functions of several variables and Lebesgue integration in Rn .
Year: II
Semester: I
Sector: MAT/05
Prerequisites: Analisi Matematica 1
Hours of lessons: 96
Lecturer: Tiziana Cardinali, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5042, E-mail: [email protected]
Content
Sequences and series of functions. Power series and Taylor series. Vector functions and curves.
Functions of several variables: continuity, partial derivability, differentiability, maximums and minimums
with and without constraints. Implicit functions. Lebesgue integration in Rn. Integrals on curves. Surfaces
and integrals on surfaces. Differential forms and their integration. Gauss and Green’s theorem.
Divergence theorem. Stokes’ theorem.
Textbooks
V. Barutello, M. Conti, D. L.Ferrario, S. Terracini, G. Verzini, Analisi matematica, vol.2, Apogeo, 2008.
G. Buttazzo, V. Colla, Temi di esame di Analisi Matematica II, Pitagora Ed., 2001
Bacciotti, P. Boieri, D. Farina, Esercizi di Analisi Matematica II, Progetto Leonardo Ed. Esculapio, 1999
M. Amar, A. M. Bersani, Esercizi di Analisi Matematica per i Nuovi Corsi di Laurea, Progetto Leonardo
Ed. Esculapio, 2002.
The lecturer will supply texts about the subject “Lebesgue integration in Rn”.
ANALISI MATEMATICA 3 - 6 CFU
Subtitle: ODEs theory, Fourier series and vectorial calculus
Year: II
Semester: II
Sector: MAT/05
Prerequisites: Analisi Matematica 2
Hours of lessons: 48
Lecturer: Patrizia Pucci, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5038, E-mail: [email protected]
Content
General theory of ODEs and systems of differential equations in the nonlinear and linear cases, with
fundamental examples. Fourier series and applications. Special functions. Differential operators, the
divergence theorem and applications. Convex functions and some applications. For a detailed program and
useful training aids and tools see teacher’s web page.
More details can be found on http://www.dmi.unipg.it/~pucci/clmat/AM3/index.htm
The basic parts of the course are summarized in notes and passed to the students by the teacher.
Textbooks
M. Giaquinta & G. Modica, Analisi Matematica, Vol. 4 e 5, Pitagora Ed., 1999 e 2000.
G. De Marco, Analisi 2. Teoria ed esercizi, Zanichelli, 1999, 2a ed.
F. Morgan, Real analysis and applications. Including Fourier series and the calculus of variations.
American Mathematical Society, Providence, RI, 2005.
G.S. Kantorovitz, Introduction to modern analysis. Oxford Graduate Texts in Mathematics, 8. Oxford
University Press, Oxford, 2003.
B. P. Demodovitch, Esercizi e Problemi di Analisi Matematica, Editori Riuniti, 2003.
ANALISI MATEMATICA 5 - 12 CFU
Subtitle: Functional Analysis and Sobolev spaces
Year: I master
Semester: I
Sector: MAT/05
Prerequisites: Basic concepts of Mathematical Analysis
Hours of lessons: 96
Lecturer: Patrizia Pucci, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5038, E-mail: [email protected]
Content
Lp( ) spaces: convergences in measure, approximation, compactness, convolution. Hilbert spaces:
general theory, geometry, liner operators, projections, duality, complete orthogonal systems. Normed and
Banach spaces: general theory, the Hahn-Banach Theorem and applications, reflexive spaces, the uniform
boundedness theorem and applications, strong and weak convergences and applications; the open mapping
and closed graph theorems, with applications. Reflexive Banach spaces: general theory. Weak and Weak
star topologies: the Banach-Alaoglu and the Krein-Mil’man theorems. Uniform convex spaces: general
theory and properties. The Sobolev spacesW1, p( ): general theory, Sobolev embeddings, the RellichKondrachov theorem, the Poincaré inequality. The Sobolev spaces W1, p0( ).
The basic parts of the course are summarized in notes and passed to the students by the teacher. The
course consists of 60 hours of theory, with several examples and counter-examples, and of 36 hours of
exercises.
http://www.dmi.unipg.it/~pucci/clmat/AM5_12/index.htm
Textbooks
H. Brezis, Analisi funzionale - Teoria e applicazioni, Liguori, Napoli, 1990.
P. Cannarsa & T. D'Aprile, Introduzione alla teoria della misura e all'analisi funzionale, UNITEXT,
Springer, 2008.
L. Tartar, An introduction to Sobolev spaces and interpolation spaces, Lecture Notes of the Unione
Matematica Italiana, 3, Springer, Berlin; UMI, Bologna, 2007.
ANALISI MATEMATICA 6
- 7,5 CFU
Subtitle: The application of Linear Functional Analysis to linear P.D.E.'s.
Year: I master
Semester: II
Sector: MAT/05
Prerequisites: Analisi Matematica 5
Hours of lessons: 60
Lecturer: Enzo Vitillaro, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5045, E- mail: [email protected]
Content
Lax-Milgram Theorem. Compact operators: definition, properties, adjoint operator, Fredholm alternative,
spectrum and spectral decomposition. Elliptic linear problems, existence, uniqueness, multiplicity and
regularity. Maximum principles. Eigenfunctions and eigenvalues. Function spaces for Banach-valued
functions. The energy method for heat and wave equations.
The lectures will be companied by exercises sessions. During them the students will be supposed to solve
on the blackboard the exercises proposed by the teacher.
Textbooks
L.Evans, Partial Differential Equations, Graduate Studies in Mathematics n. 19, American Mathematical
Society, Providence, Rhode Island, 1998.
Notes will supply by the lecturer.
ANALISI NUMERICA 1 - 6 CFU
Subtitle: Basic concepts of numerical linear algebra.
Year: I
Semester: II
Sector: MAT/08
Prerequisites: None
Hours of lessons: 48
Lecturer: Ivan Gerace, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5047, E- mail: [email protected]
Content
Machine numbers. Rounding and truncation. Direct and iterative methods for linear systems. Methods
for computing eigenvalues.
Textbooks
Bini, Capovani Menchi, Metodi numerici per l'algebra lineare, Zanichelli.
Bevilacqua, Bini, Capovani Menchi, Metodi numerici, Zanichelli.
ANALISI NUMERICA 2
- 7,5 CFU
Subtitle: Basic concepts of numerical approximation of continuous problems.
Year: III
Semester: I
Sector: MAT/08
Prerequisites: Analisi Matematica Numerica 1
Hours of lessons: 60
Lecturer: Ivan Gerace, Dipartimento di Matematica e Informatica
Tel. 0755855050, E-mail: [email protected]
Content
Polynomial interpolation. Polynomial approximation. Numerical integration. Iterative methods for nonlinear equations. Numerical methods for solving ordinary differential equations.
Textbooks
Bevilacqua, Bini, Capovani, Menchi, Metodi numerici per l'algebra lineare, Zanichelli, 1996.
ANALISI NUMERICA 3 - 7,5 CFU
Subtitle: Basic concepts of partial differential equation and integral equation discretization.
Year: I master
Semester: II
Sector: MAT/08
Prerequisites: None
Hours of lessons: 60
Lecturer: Ivan Gerace, Dipartimento di Matematica e Informatica
Tel. +39 075 585 5050, E-mail: [email protected]
Content
Partial differential equations. Weak formulation of the problem. Finete element method. Methods of
solving the linear system: conjugate gradient, multi-grid methods.
Fredholm integral equations. Ill-position of the problem. Regularization.
Textbooks
A. Quarteroni, Modellistica numerica per problemi differenziali, Springer,2003 .
ANALISI SUPERIORE 1 - 7,5 CFU
Subtitle: Mathematical models for applied science and their resolution by variational and
topological methods
Year: II master
Semester: I
Sector: MAT/05
Prerequisites: Analisi Matematica 6
Hours of lessons: 60
Lecturer: Dimitri Mugnai, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5043, E-mail: [email protected]
Content
Calculus of Variations. Nemitskij operators. Deformation Lemma. Mountain Pass. Saddle. Linking.
Applications to partial differential equations. Schroedinger equations. Systems of Quantum Mechanics.
Variational inequalities. Bounce inequalities.
Textbooks
A. Ambrosetti & A. Malchiodi, Nonlinear Analysis and Semilinear Elliptic Problems, Cambridge Studies
in Advanced Mathematics 104 (2007).
P. Drábek & J. Milota, Methods of Nonlinear Analysis, Birkhauser Advanced Texts (2007).
M.Willem, Minimax Theorems, Progress in Nonlinear Differential Equations and Their Applications 24
(1996).
M.Schechter, An Introduction to Nonlinear Analysis, Cambridge Studies in Advanced Mathematics 95
(2005).
Further notes will be supplied by the lecturer.
DIDATTICA DELLA MATEMATICA 1 - 7,5 CFU
Subtitle: Hands-on and software approaches in teaching Mathematics
Year: III
Semester: I
Sector: MAT/04
Prerequisites: Algebra 2, Analisi Matematica 2, Geometria 2
Hours of lessons: 60
Lecturer: Emanuela Ughi, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5012, E-mail: [email protected]
Content
The course is focused on studying different teaching approaches on the subject of geometric
transformations, with special interest in hands-on approaches. Geometric software: Cabri geomètre
Textbooks
I.M.Jaglom, Le isometrie, Zanichelli, Bologna, 1983.
Notes will be supplied by the lecturer.
Elementi di Logica 2 - 3
CFU
Subtitle: Basic concepts of logic and computability theory
Year: I master
Semester: I
Sector: MAT/01
Prerequisites: None
Hours of lessons: 24
Lecturer: Marco Baioletti, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5044, E-mail: [email protected]
Content
Propositional logic: syntax, semantics, decision procedures, propositional calculus and its properties.
First-order predicate logic: syntax, semantics, decision procedures, predicate calculus and its properties.
Computability: recursive functions, Turing Machines, Halting theorem, equivalence and Church-Turing
thesis. Recursive and r.e. sets. Limitative results: Gödel’s incompleteness theorems, Church’s theorem.
Textbooks
C. Toffalori, P. Cintioli, Logica Matematica, McGraw-Hill, 2000
Notes will be supplied by the lecturer.
EQUAZIONI DIFFERENZIALI 1 - 7,5 CFU
Subtitle: Differential equations and applications
Year: III
Semester: II
Sector: MAT/05
Prerequisites: Analisi Matematica 4
Hours of lessons: 60
Lecturer: Tiziana Cardinali, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5042, E-mail: [email protected]
Content
Fixed point theory for functions and multifunctions with applications to the existence of equilibriums for
deterministic or random abstract economies. Selections theorems for multifunctions. Existence theorems
for problems involving differential equations or differential inclusions.
Textbooks
S. Singh, B. Watson, P. Srivastava, Fixed Point Theory and Best Approximation. The KKM-map
Principle, Kluwer Academic Publisher, 1997.
J.M. A. Toledano, T. D. Benavides, G. L. Acedo, Measures of Noncompactness in Metric Fixed Point
Theory, Birkhauser, 1997.
M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publishers, 1991.
C. Piccinini, G. Stampacchia,G. Vidossich, Equazioni differenziali ordinarie in Rn, Ed. Liguori, 1978.
Some texts will be supplied by the lecturer
FISICA 1 - 9 CFU
Subtitle: Mechanics and Thermodinamics
Year: I
Semester: II
Sector: FIS/01
Prerequisites: Vectors, operations with vectors. Derivatives and integrals of one variable
functions.
Hours of lessons: 72
Lecturer: Maurizio Biasini, Dipartimento di Fisica,
Tel. +39 075 585 2774, E-mail: [email protected]
Content
Experimental method. Kinematics. Principles of dynamics. Energy and Work. Forces in nature.
Dynamics of systems. Rigid body. Armonic oscillator. Elastic properties of solids. Mechanics of fluid.
Heat and temperature. Principles of thermodynamics. Kinetic theory. Waves.
Textbooks
Mazzoldi, Nigro, Voci, Fisica, Volume I, Meccanica – Termodinamica, EdiSES.
D.Halliday, R.Resnick, J.Walker, Fondamenti di Fisica (IV Edizione), Meccanica Termologia, Casa
Editrice Ambrosiana
FISICA 2
- 7,5 CFU (nota: nel notiziario sono indicati 6 CFU....)
Subtitle: Electromagnetism and optics
Year: III
Semester: I
Sector: FIS/01
Prerequisites: None
Hours of lessons: 60
Lecturer: Giorgio Immirzi, Dipartimento di Fisica,
Tel. +39 075 585 2770, E-mail: [email protected]
Content
General introduction, Coulomb law, electric field. Gauss theorem; dielectrics and conductors; electrostatic
potential, electrostatic energy. Steady currents, magnetic field, Ampere equivalence principle, Ampere law,
magnetic materials. Time varying magnetic fields, Faraday's law, alternating currents, applications. The
Maxwell term, the Maxwell equations, wave equation; plane and spherical electromagnetical waves,
polarization; emission of electromagnetic waves. The superposition principle, interference; the Huyghens
principle, diffraction. Mirrors, lenses, optical instruments.
Textbooks
P. Mazzoldi, M. Nigro, C. Voci, Fisica, vol. II (Elettromagnetismo - Onde), EdiSES
D. J. Griffith, Introduction to electrodynamics.
FISICA MATEMATICA CON LABORATORIO 1
- 8 CFU
Subtitle: Mathematics methods and models for applications
Year: III
Semester: I
Sector: MAT/07
Prerequisites: None
Hours of lessons: 64
Lecturer: Maria Cesarina Salvatori Dartimento di Matematica e Informatica,
Tel. +39 075 585 5064, E-mail: [email protected]
Content
Partial differential equations. Linear and quasi-linear equations. First and second order equations. Initial
and boundary value problems. Hyperbolic, parabolic and elliptic equations. Classical exact and
approximate solutions. Mathematical models concernig PDE studies. Exercises with Maple.
Textbooks
Tyn-Mynt, U. and L. Debnath, Partial Differential Equations for Scientist and Engineer, North Holland.
W. E. Boyce and R. C. Diprima, Elementary Differential Equations and Boundary Value Problems, John
Wiley & Sons
Salsa, Equazioni a derivate parziali, Springer Verlag, Collana UNITEXT
Salsa, Verzini, Equazioni a derivate parziali. Complementi ed esercizi, Springer Verlag, Collana
UNITEXT
Notes will be supplied by the lecturer
FISICA MATEMATICA 2
- 6 CFU
Subtitle: Nonlinear partial differential equations
Year: I master
Semester: II
Sector: MAT/07
Prerequisites: Analisi Matematica 4, Geometria 2
Hours of lessons: 48
Lecturer: Silvana de Lillo, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5048, E-mail: [email protected]
Content
Introduction to the theory and applications of Introduction to the theory of nonlinear partial differential
equations.
Textbooks
Tyn-Myint-U and L.Debnath, Partial Differential Equations for Scientists and Engineers, North Holland,
1987.
GEOMETRIA 1
- 12 CFU
Subtitle: Basic linear algebra, affine and euclidean geometry
Year: I
Semester: I
Sector: MAT/03
Prerequisites: None
Hours of lessons: 96
Lecturer: Rita Vincenti, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5022, E-mail: [email protected]
http://www.dmi.unipg.it/~alicew
Content
Basic algebra. Basic affine geometry of dimension 2 and 3 over the real field R. Vector spaces over a
field K. Linear systems over R. Geometry of the affine plane and of the 3-dimensional affine space over
R. Generalization. Linear applications. Groups of linear transformations and affinities.
Basic euclidean geometry of dimension 2 and 3 over the real field R. Euclidean spaces. Groups of
euclidean transformations.
Textbooks
A. Basile, Algebra lineare e geometria cartesiana, Margiacchi-Galeno Editore, Perugia, 1997.
M. Stoka-V.Pipitone, Esercizi e problemi di geometria, Vol.I, Cedam, Padova, 1995.
Notes will be supplied by the lecturer.
GEOMETRIA 2
- 6 CFU
Subtitle: Basic concepts of quadratic forms, projective spaces and conics
Year: II
Semester: I
Sector: MAT/03
Prerequisites: Geometria 1
Hours of lessons: 48
Lecturer: Alessandro Caterino, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5013, E-mail: [email protected] http://www.dmi.unipg.it/~caterino
Content
Eigenvalues and eigenvectors. Diagonalization. Quadratic forms. Reduction of a quadratic form to
canonical form. Projective spaces. Hyperquadrics. Conics and their projective, affine and euclidean
classification.
Textbooks
M. Stoka, Corso di geometria, Cedam, Padova, 1995.
M.Stoka, V.Pipitone, Esercizi e problemi di geometria, Vol.I, Cedam, Padova, 1995.
E.Sernesi, Geometria 1, Boringhieri, 1992.
A.Basile,, Algebra lineare e geometria cartesiana, Margiacchi-Galeno Editore, Perugia, 1997.
Notes will be supplied by the lecturer.
GEOMETRIA 3 - 12 CFU
Subtitle: Analytic functions of complex variable
Year: II
Semester: II
Sector: MAT/03
Prerequisites: Affine and Euclidean geometry, linear algebra, vector functions of a vector variable
Hours of lessons: 96
Lecturer: Giuliana Fatabbi, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5020, E-mail: [email protected]
Content
Local theory of curves: definition, arc length, curvature and torsion. Elementary topology in euclidean
space: open sets, closed sets, connected sets and arch -wise connected sets, compact sets. Local theory of
surfaces: definition, differentiable functions, tangent plane. Curvature: first and second fundamental
form, normal curvature, principal curvatures, Gaussian and mean curvature, theorem of Gauss. Analytic
functions of one complex variable. Cauchy integral formula and its applications.
The students should acquire the fundamental concepts of the differential geometry of curves and surfaces in
three-dimensional Euclidean ant they should be able to apply these concepts either to study particular
curves and surfaces or to solve specific problems.
The students should also acquire basic knowledge about analytic functions of on e complex variable in order
to face either further study of analytic functions of one variable or analytic functions of several complex
variables.
Textbooks
M. Abate, F. Tovena, Curve e superfici, Springer, 2006
M. Lipschutz, Schaum'S outlines. Differential Geometry, McGraw-Hill, 1969
GEOMETRIA 4
- 7,5 CFU
Subtitle: Elementary algebraic geometry
Year: III
Semester: II
Sector: MAT/03
Prerequisites: Geometria 2, Algebra 2
Hours of lessons: 60
Lecturer: Lucio Guerra, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5014, E-mail: [email protected]
Content
Polynomials. Algebraically closed fields. Algebraic plane curves, affine and projective. Conics. Local
study of plane curves, multiplicity and tangents. Intersections, Bézout's theorem. Flexes, the Hessian
curve. Projective cubics, classification, the group law.
Textbooks
C. G. Gibson, Elementary geometry of algebraic curves, Cambridge University Press, 1998
E. Sernesi, Geometria 1, Boringhieri 1998
GEOMETRIA 5 – 12 CFU
Subtitle: Basic knowledge of the differentiable manifolds.
Year: I master
Semester: I
Sector: MAT/03
Prerequisites: Linear algebra. Point-set topology. Multivariate calculus.
Hours of lessons: 96
Lecturer: Alessandro Tancredi, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5007, E-mail: [email protected]
Content
Smooth manifolds. Vector bundles. Smooth vector fields. Differential forms. Integration on manifolds.
De Rham cohomology. Riemannian manifolds. Tubular neighborhoods. Isotopy.
Textbooks
T. Bröcker, K. Jänich, Einführung in die Differentialtopologie. Springer 1990
L. W. Tu, An introduction to manifolds. Springer 2008
GEOMETRIA 6 - 6 CFU
Subtitle: Algebraic approximations
Year: I master
Semester: II
Sector: MAT/03
Prerequisites: Geometria 5
Hours of lessons: 48
Lecturer: Alessandro Tancredi, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5007, E-mail: [email protected]
Content
Analytic and Nash functions. Algebraic and Nash sets. Algebraic approximations.
Textbooks
J. Bochnak, M. Coste, M. F. Roy, Real algebraic geometry. Springer 1998
J. M. Ruiz, The basic theory of power series. Vieweg 1993
GEOMETRIA COMBINATORIA 1
- 7,5 CFU
Subtitle: Galois Geometries and algebraic-geometric codes
Year: III
Semester: II
Sector: MAT/03
Prerequisites: Algebra 1, Algebra 2, Geometria 1, Geometria 2.
Hours of lessons: 60
Lecturer: Rita Vincenti, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5022, +39 347 27 095 28, E-mail: [email protected]
http://www.dmi.unipg.it/~alicew
Content
The geometry PG(r, q), r 1. Linear projective groups. Desargues, Pappus, Pascal Theorems.. Projective
varieties. Quadrics in PG(r, q). Grassmannians. Rational normal curves. Applications. Linear codes.
Projective systems. Permutation Deconding.
Textbooks
A. Beutelspacher, U.Rosenbaum, Projective Geometry: from foundations to applications, Cambridge
University Press, 1998.
G. Tallini, Geometria di Galois e Teoria dei Codici, CISU, Roma, 1995.
Notes will be supplied by the lecturer.
GEOMETRIA COMBINATORIA 2 - 7,5 CFU
Subtitle: Finite Geometry with applications to digital communications and IT security
Year: I master
Semester: II
Sector: MAT/03
Prerequisites: Geometria 4.
Hours of lessons: 60
Lecturer: Massimo Giulietti, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5021, E-mail: [email protected]
Content
Linear codes and multisets in finite projective spaces. Basic inequalities: Singleton, Hamming, Plotkin,
Gilbert-Varshamov.
Plane algebraic curves over finite fields. Algebraic function fields, divisors, Riemann-Roch Theorem.
Rational maps between curves. Algebraic geometric codes as a generalization of Reed-Solomon Codes
and BCH codes. One-point codes. Hermitian codes.
The main conjecture on MDS Codes. Lemma of tangents. Segre's Theorem. Focused and Hyperfocused
arcs with applications to Secret Sharing Schemes.
Elliptic curve cryptography. The group law. Isogenies. The Weil pairing and the MOV attack to ECC.
Textbooks
M.A. Tsfasman and S.G. Vladut, Algebraic-Geometric Codes, Kluwer, 1991.F. Blake, G. Seroussi and
N.P. Smart, Elliptic curves in cryptography, Cambridge University Press 1999.
GEOMETRIA SUPERIORE 1 - 7,5 CFU
Subtitle: Algebraic curves
Year: III
Semester: I
Sector: MAT/03
Prerequisites: Geometria 3, Geometria 4
Hours of lessons: 60
Lecturer: Lucio Guerra, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5014, E-mail: [email protected]
Content
Algebraic plane curves, conics and cubics. Algebraic varieties, affine and projective. Irreducible
components. Tangent space and dimension, smooth and singular points. Rational maps and morphisms.
Nonsingular curves. Differentials and canonical divisors, the genus of a curve. Introduction to the
Riemann-Roch theorem.
Textbooks
W. Fulton, Algebraic Curves, Benjamin, 1969.
M. Reid, Undergraduate Algebraic Geometry, Cambridge Univ. Press, 1988.
C.G. Gibson, Elementary geometry of algebraic curves, Cambridge Univ. Press, 1998.
INFORMATICA 1 - 6 CFU
Subtitle: Basic information theory and programming, multimedia laboratory
Year: I
Semester: I
Sector: INF/01
Prerequisites: None
Hours of lessons: 48
Lecturer: Pietro Tito Melacci, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5047, E-mail: [email protected]
Content
Introduction computer systems, fundamentals on computer architectures, digital information processing
systems, data representation, processing data. Software programming and development, creating
computer programs, programming languages (PASCAL). Using Operating Systems (UNIX,
GNU/Linux), Unix shell, main commands, scripts, using Pascal compiler: simple programs and code
generation. Working with application software (MAPLE, MATHEMATICA, OPEN Source), software
for mathematical applications (numerical calculations, symbolic computation, visualization for functions
and data, graphics, language). Applying Internet technologies (WWW, HTML).
Textbooks
Notes will be supplied by the lecturer in electronic version.
INFORMATICA 3 - 6 CFU
Subtitle: Basic concepts of logic and theoretical computer science. Fundamentals of Object and
functional programming.
Year: I
Semester: II
Sector: INF/01
Prerequisites: Basic concepts of computer science and programming
Hours of lessons: 48
Lecturer: Marco Baioletti, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5049, E-mail: [email protected]
Content
Propositional logic: syntax, semantics, decision procedures, propositional calculus. First-order predicate
logic: syntax, semantics, decision procedures, predicate calculus. Theoretical computer science:
Recursive functions, Lambda Calculus, Register machines Turing Machines, , Halting theorem,
equivalence and Church-Turing thesis. Recursive and r.e. sets.
Functional programming: general concepts, CaML syntax, recursion, lists, higher-order functions.
Object-oriented programming: basic concepts of imperative programming, object oriented programming,
syntax and semantics of C++ languages, numerical and other mathematical applications.
Textbooks
C. Toffalori, P. Cintioli, Logica Matematica, McGraw-Hill, 2000
M. Cialdea Mayer, C. Limongelli, Introduzione alla Programmazione Funzionale. Esculapio 2002
C. Horstmann. Fondamenti di C++. McGraw-Hill, 2003
LABORATORIO DI PROGRAMMAZIONE E CALCOLO 1 - 4,5 CFU
Subtitle: Pascal language, representation of data abstract types acting on them.
Year: III
Semester: II
Sector: INF/01
Prerequisites: None
Hours of lessons: 36
Lecturer: Rosanna Bicocchi, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5047, E-mail: [email protected]
Content
PASCAL programming language, Data type, Loops and Control structures, Procedures and Functions,
Recursion, Array, Records, Pointers and Dynamic allocation. Introduction to the programming language
C. Sorting. Abstract data types and Data structures. Lists, Binary trees, Hash tables, Binary search trees,
Graphs: Implementation and Algorithms.
Textbooks
N. Wirth, K. Jensen, Il manuale del Pascal, Gruppo Editoriale Jackson, 1981
C. Batini, L. Carlucci Aiello, M. Lenzerini, A. Marchetti Spaccamela, A. Miola, Fondamenti di
programmazione dei calcolatori elettronici, Franco Angeli, Milano, 1990.
LABORATORIO DI PROGRAMMAZIONE E CALCOLO 2 - 3 CFU
Subtitle: Applications by MATHEMATICA
Year: III
Semester: II
Sector: INF/01
Prerequisites: None
Hours of lessons: 24
Lecturer: Pietro Tito Melacci, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5047, E-mail: [email protected]
Content
Working with application software (MATHEMATICA). Mathematica interfaces, Front ends, Built-in
functions, Packages, Numerical computation, Algebra and Calculus, Solving equations, Lists, Matrices,
Mathematica function definition, Recursive functions, Symbolic computation, Graphics, two- and threedimensional graphics, The Mathematica language, Programming, Loops and Control structures, Modules
and Local variables, Files and External operations.
The lessons will be held in the Laboratorio di Informatica.
Textbooks
Stephen Wolfram, The Mathematica Book, 4th ed., Wolfram Media - Cambridge University Press, 1999
Notes from the lessons in electronic version.
LABORATORIO DI SPERIMENTAZIONE DI FISICA 1
– 4,5 CFU
Subtitle: Laboratory of Mechanics
Year: II
Semester: II
Sector: FIS/01
Prerequisites: Analisi Matematica 1, Fisica 1
Hours of lessons: 36
Lecturer: Aldo Santucci, Dipartimento di Fisica
Tel. +39 075 5852717, E-mail: [email protected]
Content
Systems of measurement units, fundamental quantities - Measurement errors - Functional relationships
between physical quantities- Introduction to the use of graphs. - Laboratory experiences: measurements of
mass, time and length
Textbooks
G. Cannelli, Introduzione alla Esperimentazione fisica, Ed. EDISES (Napoli).
Notes will be supplied by the lecturer
LINGUA INGLESE 1-
3 CFU
Subtitle: The English language in studying the Maths degree courses.
Year: I
Semester: II
Sector: L-LIN/12
Prerequisites: none
Hours of lessons: 24
Lecturer: Hilary Giles - Centro Linguistico d'Ateneo,
Tel 075 585 6804, E-mail: [email protected]
Lecturer: Nancy Hutchinson, Dipartimento di Biologia Cellulare e Molecolare,
Tel. +39 075 585 5741, E-mail: [email protected]
Content
A "placement test" is realized at the beginning to establish the level of each student, then students follow
the defined levels.
Textbooks
Consult the lecturers.
MATEMATICA APPLICATA 1 -
3 CFU
Subtitle: Maths models
Year: III
Semester: I
Sector: MAT/05-08
Prerequisites: Some familiarity with problems and concepts of numerical analysis.
Hours of lessons: 24
Lecturer: Bruno Iannazzo, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5050, E-mail: [email protected]
webpage: http://poisson.phc.unipi.it/%7emaxreen/bruno/
Content
Some mathematical models based on numerical tools will be developed: search engines for the
Internet, curves in vector graphics, fast Fourier transform and its applications to the multimedia.
The arguments will be decided during the course following the wishes of the students.
Textbooks
R. Bevilacqua, D. Bini, M. Capovani e O. Menchi, Metodi numerici, Zanichelli.
Notes will be supplied by the lecturer
MATEMATICHE COMPLEMENTARI 1
- 7,5 CFU
Subtitle: Numbers: theoretical aspects and didactic difficulties.
Year: III
Semester: II
Sector: MAT/04
Prerequisites: Basic Algebra and Analysis.
Hours of lessons: 60
Lecturer: Paolo Zappa, Dipartimento di Matematica,
Tel. +39 075 585 5016, E-mail: [email protected]
Content
Peano-Dedekind axioms for natural numbers. The constructions of integers and rationals. Continued
fractions. The main approaches to the definition of the real numbers. Finally one and only one of these
two subjects a-Ordinals and cardinals. b- Introduction to the non-standard analysis.
Textbooks
H. D.Ebbinghaus e altri, Numbers, GTM 123, Sprinter-Verlag, 1990.
K. J. Devlin, The Joy of Sets: fundamentals of contemporary set theory, UTM, Springer-Verlag, 1993.
H. J. Keisler, Fundation of infinitesimal calculus, Prindle, Webber & Schmidt.
MATEMATICHE ELEMENTARI DA UN PUNTO DI VISTA SUPERIORE 1 - 7,5 CFU
Subtitle: Maths didactic and Maths foundations.
Year: III
Semester: I
Sector: MAT/04
Prerequisites: Algebra 2, Geometria 4
Hours of lessons: 60
Lecturer: Francesca Conti, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5023, E-mail: [email protected]
Content
Formalization of Geometry: from an axiomatic theory non-definetively formal to a formal axiomatic
theoery (Euclid, Hilbert, Choquet). Non-Euclidean Geoemtries and their models. The thoery of metric
planes. Learning-teaching Maths: problems and expectations. In choosing and using Maths tools for
teaching.
Textbooks
Euclide, Gli Elementi, Classici UTET, 1970.
Hilbert D., Fondamenti di Geometria, Feltrinelli, 1970.
Choquet, L’insegnamento della Geometria, Feltrinelli, 1967.
Resnick L.B, Ford W.W., Psicologia della matematica e apprendimento scolastico, SEI, Torino, 1991.
Spagnolo, Insegnare matematica nella scuola secondaria, La Nuova Italia, 1999.
D’Amore B., Didattica della Matematica, Pitagora Editrice, Bologna, 2001.
Papers from specialized reviews in Maths Didactic will be supplied by the lecturer.
MECCANICA RAZIONALE
- 9 CFU
Subtitle: Mechanicals models and Lagrange equations.
Year: II
Semester: II
Sector: MAT/07
Prerequisites: Analisi Matematica 2, Geometria 2, Fisica 1
Hours of lessons: 72
Lecturer: Silvana De Lillo, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5048, E-mail: [email protected]
Content
Elements of Newtonian Mechanics. Motion in a Central Force Field. Lagrangian Mechanics. Hamiltonian
Mechanics. Kynematics and Dynamics of Rigid Bodies. Hamilton Jacobi Equation.
Textbooks
H. Goldstein, Classical Mechanics, Addison-Wesley (1980).
MECCANICA RAZIONALE 1
- 7,5 CFU
Subtitle: Basic concepts of analytical mechanics
Year: III
Semester: I
Sector: MAT/07
Prerequisites: Analisi Matematica 4, Geometria 4, Fisica 1
Hours of lessons: 60
Lecturer: Maria Clara Nucci, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5018, E-mail: [email protected]
Content
Newtonian Mechanics: principles. Lagrangian Mechanics: constrained and generalized coordinates,
Hamilton's principle, Lagrangian equations, motion of rigid bodies, Lie's and Noether's symmetries.
Hamiltonian Mechanics: Hamiltonian equations, Poisson brackets, canonical transformations, HamiltonJacobi theory.
Textbooks
H. Goldstein, Meccanica Classica, II ed. italiana, Zanichelli, 2004;
G. Grioli, Lezioni di Meccanica Razionale, Libreria Cortina;
V. I. Arnold, Mathematical Methods of Classical Mechanics, II ed., Springer-Verlag, 1989.
The lecturer will also supply some notes.
MECCANICA SUPERIORE 1 - 7,5 CFU
Subtitle: Basics of theory of relativity
Year: II
Semester: I
Sector: MAT/07
Prerequisites: Analisi Matematica 4, Geometria 4, Fisica 1
Hours of lessons: 60
Lecturer: Marco Mamone Capria, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5006, E-mail: [email protected]
Content
The principle of relativity in classical physics, Newtonian space-time, the origins of special relativity,
Minkowski space-time, relativistic physics.
Textbooks
O. Costa De Beauregard, La théorie de la Relativité restreinte, Masson, 1949.
R. D’Inverno, Introducing Einstein’s Relativity, Cambridge Univ. Press, 1992.
M. Mamone Capria (a cura di), Physics Before and After Einstein, IOS, 2005.
A. Sudbery, Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians,
Cambridge Univ. Press 1986.
Notes by the Lecturer.
METODI MATEMATICI PER L’ECONOMIA 1 - 7,5 CFU
Subtitle: Optimization theory applied to macroeconomics
Year: III
Semester: I
Sector: MAT/05
Prerequisites: Analisi Matematica 4
Hours of lessons: 60
Lecturer: R. Filippucci, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5033, E- mail: [email protected]
Content
Free optimization theory, optimization theory with equality and inequality constraints, Lagrange
multipliers, homotetic, concave, quasiconcave, pseudoconcave functions. Applications to demand and
consumer theory, Pareto's optima. Walrasian equilibria and welfare economy theorems.
Textbooks
J C. P. Simon e L.E. Blume, Matematica 2, Università Bocconi Editore, 2002
E. Castagnoli, L. Peccati, Matematica in azienda 1: calcolo finanziario con applicazioni. Egea
E. Castagnoli, M. Cigola, L. Peccati, Matematica in azienda 2: complementi di analisi. Egea.
PROBABILITÀ E STATISTICA - 7,5 CFU
Subtitle: Basic notions and methodologies of probability and statistical inference.
Year: II
Semester: I
Sector: MAT/06
Prerequisites: Analisi Matematica 1, Geometria 1, Algebra 1, Informatica 1
Hours of lessons: 60
Module 1 - 4,5 CFU - Lecturer: Giuliana Regoli, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5022, E-mail: [email protected]
Module 2 - 3 CFU - Lecturer: Andrea Capotorti, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5011, E-mail: [email protected]
Content
Module 1 - Events and random variables (r.v.). Conditional and joint probability. Stochastic
independence. Real random variables. Distribution function, probability function density function.
Expected value, variance, moments. Common univariate probability distributions. Multivarate random
variables: joint and marginal distributions, conditional distributions. Independence of r.v. Relations
among random variables; transforms of random variables. Approximations. Convergence of r.v. Law of
large numbers. Central limit Theorem.
Module 2 - Basic notions of descriptive Statistics. Simple linear models. Parametric estimation.
Confidence intervals. Hypothesis tests.
Textbooks
P.Baldi, Introduzione alla Probabilità con elementi di Statistica. McGraw-Hill ed., 2003.
P.Erto, Probabilità e Statistica per le scienze e l'ingegneria. McGraw-Hill ed., 2004.
S.Antonelli, G.Regoli, Probabilità discreta: Esercizi con richiami di Teoria, Liguori editore, 2005
S.M.Iacus, G.Masarotto, Laboratorio di statistica (with R.), McGraw-Hill.
Additional material will be given by lecturers.
PROBABILITÀ 2
- 7,5 CFU
Subtitle: Introduction to stocastic processes
Year: II
Semester: II
Sector: MAT/06
Prerequisites: Probabilità 1, Analisi Matematica 3
Hours of lessons: 60
Lecturer: Domenico Candeloro, Dipartimento di Matematica e Informatica,
Tel. +39 075 5852936, or +39 075 585 5034, E-mail: [email protected]
Content
Generalities on Stochastic Processes. Random Walks. Markov Chains, classification of states. Birth-death
processes. Discrete-time martingales, convergence theorem. Stationary processes, ergodic theorem.
Brownian Motion. Stochastic integration and calculus (elementary notions).
Textbooks
Billingsley, Probability and measure, John Wiley and Sons (1995)
Grimmett-Stirzaker, Probability and random processes (Second edition, 1992) - The Clarendon Press,
Oxford University Press, New York.
Additional notes will be supplied by the lecturer
STATISTICA MATEMATICA 1 - 7,5 CFU
Subtitle: Advanced notions and methodologies of statistical inference.
Year: III
Semester: II
Sector: MAT/06
Prerequisites: Probabilità e Statistica, Probabilità 1, Analisi Matematica 1, Analisi Matematica 2,
Analisi Matematica 3, Geometria 1, Algebra 1.
Hours of lessons: 60
Module 1- 4,5 CFU - Lecturer: Andrea Capotorti, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5011, E-mail: [email protected]
Module 2 - 3 CFU - Lecturer: Giuliana Regoli, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5022, E-mail: [email protected]
Content
Module 1 - Distributions of sample statistics. Sufficient principle: sufficient statististics, minimal
sufficient statistics, ancillary statistics, complete statistics. Point Estimation: Method of Moments,
Maximum Likelihood Estimators. Methods of evaluating estimators. Hypothesis Testing: methods of
finding tests, methods of evaluating tests. Interval estimation. The Analysis of Variance: Introduction.
The oneway analysis of variance. Chi-squared tests.
Module 2 - Bayesian inference. Subjective probability as coherent approach to the inference. Bayes'
Theorem; Prior and Posterior Distributions. Coniugate Analysis. Decision Theory. Parametric point
estimation; Test of Hypotheses. Exchangeability and the de Finetti's representation theorem. Predictive
inference.
Textbooks
Casella G., Berger, R. L., Statistical inference, Duxbury Press, 2002
Cifarelli, D. M., Muliere, P. Statistica Bayesiana : appunti ad uso degli studenti, Iuculano, Pavia, 1989
and as integration:
Cicchitelli G., Probabilità e Statistica, Maggioli ed., 2001.
Berger,J.O., Statistical decision theory and Bayesian Analysis, 2nd ed New York [etc.]:SpringerVerlag,1985
STORIA DELLE MATEMATICHE 1- 7,5 CFU
Subtitle: Basic concepts of history of mathematics.
Year: III
Semester: II
Sector: MAT/04
Prerequisites: none
Hours of lessons: 60
Lecturer: Maria Clara Nucci, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5018, E-mail: [email protected]
Content
Ancient Mathematics. The Beginnings of Mathematics in Greece. Archimedes and Apollonius.
Mathematical Methods in Hellenistic Times. The Final Chapters of Greek Mathematics. The
Mathematics of Islam. Mathematics in Medieval Europe. Algebra in the Renaissance.
Textbooks
C.B. Boyer and U. C. Merzbach, A History of Mathematics, II ed., Wiley, 1991.
V. J. Katz, A History of Mathematics, II ed., Addison Wesley, 1998.
J. Fauvel, J. Gray (ed.), The History of Mathematics – A Reader, MacMillan
Press, 1987.
The lecturer will supply copies of the original works (or their translations),
and papers from the American Mathematical Monthly, Archive of History of Exact
Sciences, Bollettino di Storia delle Scienze Matematiche, Bullettino di
Bibliografia e Storia delle Scienze Matematiche e Fisiche, Centaurus, Endeavour,
Historia Mathematica, ISIS, Mathematics Teacher, Scripta Mathematica.
TEORIA DELLE DECISIONI 1 - 7,5 CFU
Subtitle: Decisional models in the presence of certainty, uncertainty and risk.
Year: III
Semester: II
Sector: MAT/06
Prerequisites: Algebra 1, Analisi Matematica 2, Probabilità e Statistica
Hours of lessons: 60
Lecturer: Giulianella Coletti, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5019, E-mail: [email protected]
Content
Foundations of the theory of measurements. Utility theory on a certain ambit. Comparative uncertainty
measures. Comparative probability. Expected Utility theory (Morgstern-von Neuman and Savage model).
Some recent models generalizing the Expected Utility one. The social choice.
Textbooks
G.Coletti, R.Scozzafava, Probabilistic Logic in a Coherent Setting, Kluwer A.P.
Dordrecht/Boston/London (2002)
References will be supplied by the lecturer.
TEORIA DELL’INFORMAZIONE 2 - 6 CFU
Subtitle: Principles of information theory and coding.
Year: I master
Semester: II
Sector: INF/01
Prerequisites: Elementary Probability Theory, Linear Algebra, Calculus.
Hours of lessons: 48
Lecturer: Giorgio Faina, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5009, E-mail: [email protected]
Content
Information, uncertainty and entropy. Entropy for discrete memoryless sources. Source coding. Mutual
information and channel capacity. Shannon's theorem on channel coding. Channel coding. Linear block
codes. Applications. Coding for compact disk systems.
Textbooks
R. Togneri – C.J. De Silva, Fundamentals of Information Theory and Coding Design, Chapman-Hall,
London, 2003.
Notes will be supplied by the lecturer
TOPOLOGIA 1-
7,5 CFU
Subtitle: Basic concepts of topological spaces and topological properties.
Year: III
Semester: I
Sector: MAT/03
Prerequisites: Geometria 3, Analisi Matematica 2
Hours of lessons: 60
Lecturer: Alessandro Caterino, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5013, E-mail: [email protected]
Content
Topological spaces and continuous functions. Subspaces, product spaces and quotient spaces. Separation
and countability axioms. Compactness and weak compactness. Local compactness. Paracompactness and
partition of unity. Metrizability. Connectedness. Local connectedness. Arcwise connectedness.
Textbooks
J. R. Munkres, Topology: a first course, Prentice-Hall, 1975.
S.Willard, General Topology, Addison-Wesley Publishing, 1970.
TOPOLOGIA 2 -
7,5 CFU
Subtitle: Advanced topics in General Topology. Basic concepts in Algebraic topology.
Year: II master
Semester: II
Sector: MAT/03
Prerequisites: Basic notions of General Topology.
Hours of lessons: 60
Lecturer: Cristina Vipera, Dipartimento di Matematica e Informatica,
Tel. +39 075 585 5012, E-mail: [email protected]
Content
Connectedness. Cardinal and ordinal numbers. Cardinal invariants (weight, density, character, etc.).
Locally compact spaces. Function spaces. Compactifications. The Stone-Cech Compactification. Nets
and filters. Homotopy, Retracts, Fundametal Group. Coverings. Theorem of Van Kampen.
Textbooks
R. Engelking, General Topology, Heldermann Verlag, Berlino
C. Kosniowski, Introduzione alla Topologia Algebrica, Zanichelli.
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