A basic algebra course.

Sets. Numbers. Monoids and Groups. Cayley, Lagrange, Homomorphism, Sylow theorems. Rings and Ideals. Rings of polynomials. Factorization criterions. Fundamental Theorem of Algebra. Splitting Fields. Algebraic and transcendent elements.

• GEOMETRIA I (Prof. V. Cristante, Dott. M. Costantini) mark: 22/30

A basic geometry course.

Vector spaces and linear algebra (matrixes, linear systems, determinants). Duality and bilinear forms. Eigenvectors and eigenvalues. Hamilton-Cayley theorem. Jordan theorem. Affine and metric spaces. Projective spaces. Ipersurfaces and Quadrics.

• ANALISI MATEMATICA I (Prof. M. Lanza De Cristoforis, Dott. L. Collauto) mark: 27/30

A basic analysis course.

Real and complex numbers. Metric and Topologic spaces. Limits. Series and infinite sums. Compact and connected spaces. Differential calculus for function with one variable. Elementary theory of integration. Series of functions and uniform convergence.

• FISICA I (Prof. Pisent, Dott. Lotti, Dott. Canton) mark: 30/30

Mechanics and Thermodynamics.

Series of powers. Spaces with norm. Function with vector values and real variable. Differential manifolds. Integrals depending on parameters. Multiples Integrals. Lebesgue Integration. Real differential forms. Functions with complex variable. ODE.

• GEOMETRIA II (Prof. G. Gerotto, Dott. Casnati) mark: 27/30

Projective geometry. Ipersurfaces. Algebraic manifolds. Divisors. Quadrics. Linear Algebra.

• MECCANICA RAZIONALE (Prof. A. Bressan, Dott. M. Motta) mark: 25/30

Mechanics with strictly mathematical point of view.

• FISICA II (Prof. Zumerle, Dott. De Min) mark: 30/30

Electromagnetism and waves.

Complements of group theory. Theory of commutative fields. Galois theory.

• ISTITUZIONI DI ANALISI SUPERIORE (APPL.) mod. A (Prof. Villella Bressan, Dott. P. Soravia) mark: 30/30

Abstract theory of measure and integration. Hilbert spaces. Linear opeators. Adjoint, self-adjoint, compact operators. Spectral theory.

• ISTITUZIONI DI ANALISI SUPERIORE (APPL.) mod. B (Prof. M. Lanza De Cristoforis, Dott. L. Collauto) mark: 30/30

Functional analysis on norm and Banach spaces (Hahn-Banach, Banach-Steinhaus theorems. Duality and weak(*) topology. Lp spaces). Measure theory (Legesgue-Radon-Nykodym theorem). Fourier series. Fourier and Laplace transforms.

• ISTITUZIONI DI GEOMETRIA SUPERIORE mod. A (Prof. Millevoi) mark: 30/30 and honour

Commutative algebra (theory of abelian rings and ideals)

• PROGRAMMAZIONE mod. A (Prof. G. Filè, Dott. M. Bugliesi) mark: 29/30

C programming language. Theory of abstract type of data and algorithms.

• PROGRAMMAZIONE mod. B (Prof. G. Filè, Dott. M. Bugliesi) mark: 27/30

C programming language. Theory of abstract type of data and algorithms.

Errors. Methods for the numerical solution of non linear equations. Interpolation and approximation of functions. Numerical derivative and integration. Numerical linear algebra.

• CALCOLO NUMERICO mod. B (Prof. M. Morandi Cecchi, Dott. M. Vianello, Prof. J. C. Bruch, Jr.) mark: 30/30 and honour

Poisson problem. Heat equation. Waves Equation. Seminar by Prof. J. C. Bruch, Jr. (University of California, Santa Barbara) about Free surface, Moving Boundary (Two-dimensional Dam, Wakes and Cavites, Wet Chemical Etching, Control of Vibrating Structures by Piezoelectrics), application to the parallel computing. Iterative methods for the numerical solution of the linear systems (SOR) and gradient methods. Numerical treatment of the ODEs. Finite Elements method and applications. Finite differences methods.

• ISTITUZIONI DI FISICA MATEMATICA mod. A (Prof. A. Grioli) mark: 28/30

Algebra elements and linear analysis. Tensor calculus. Elements of variation calculus. Riemmann manifolds. Curvature of space. Special type of space. Elements of special and general relativity.

• FONDAMENTI DELL'INFORMATICA mod A. (Prof. G. Filè. Dott. M. Bugliesi) mark: 30/30 and honour

C++ programming language. Theory and algorithms.

• FONDAMENTI DELL'INFORMATICA mod B. (Prof. G. Filè. Dott. M. Bugliesi) mark: 27/30

C++ programming language. Theory and algorithms.

• TEORIA DELLE FUNZIONI mod. A (Prof. A. D'Agnolo) mark: 30/30 and honour

Linear algebra on the ring. Homologic algebra. Categories and Sheaves theory. Hyperfunctions (or Generalized Distributions). D-modules theory. Cauchy-Kowaleski-Kashiwara theorem.

• TEORIA DELLE FUNZIONI mod B (Prof. G. Zampieri) no mark

Multidimensional complex analysis.

• ISTITUZIONI DI ANALISI SUPERIORE (GEN.) mod A+B (Prof. M. Lanza De Cristoforis) marks: 30/30 and honour (mod A.), 28/30 (mod. B)

(A) Abstract Topology. Topological Vector Spaces theory. Abstract functional analysis. Distributions.

(B) Tempered Distributions and Fourier Transform. Interpolation theory of Banach Spaces. Sobolev spaces. Elliptic operators. Elliptic equation with non homogeneous conditions on the border.