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1015376 - MATHEMATICAL ANALYSIS II |
Knowledge and understanding: Successful students will have a deep comprehension of the main concepts of mathematical analysis for functions of several variables, with particular attention to differential calculus, invertibility, integration theory, integration of differential forms, and the fundamental theorems of divergence and Stokes.Skills and attributes: Successful students will be able to employ various techniques of differential calculus to functions of several variables. In particular they will be able to compute integrals of functions of two and three variables, and to apply calculus techniques to compute the solution to various problems like the search of unconstrained and constrained optima, the determination of the primitive of a differential form and the area of a surface.
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First semester |
9 |
MAT/05 |
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1035136 - GENERAL PHYSICS I |
Knowledge and understanding:Successful students will be able to deal with basic topics concerning Mechanics and Thermodynamics. They will become proficient and acquainted with subjects such as work, energyand conservation laws.Skills and attributes:Successful students will be able to solve problems of mechanics and thermodynamics by applying the main laws of Physics.
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First semester |
9 |
FIS/02 |
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1051667 - Algebra I |
General objectives: to acquire basic knowledge of Algebra.
Specific objectives:
Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results related to:
1) Modular arithmetic.
2) Group Theory.
3) Ring Theory.
4) Field Theory and their extensions.
Apply knowledge and understanding: at the end of the course the student will be able to autonomously handle the initial techniques of abstract algebra and to solve simple problems in the context of the acquired concepts.
Critical and judgmental skills: the student will have the basis to analyze the similarities and relationships with concepts acquired in the first year courses with particular reference to topics concerning linear algebra and the resolution of algebraic equations in the real and complex field.
Communication skills: The learner will have the ability to communicate rigorously the ideas and contents shown in the course.
Learning skills: the acquired knowledge will allow a study, individual or given in a subsequent course in order to acquire more advanced concepts related to the main algebraic structures.
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First semester |
12 |
MAT/02 |
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1023149 - GEOMETRY II |
General objectives: to acquire basic knowledge in general topology, with an introduction to
algebraic topology and differential geometry.
Specific objectives:
Knowledge and understanding. At the end of the course the student will have acquired the concepts and the results
basic general topology, with various possible approaches to the notions of topological space,
continuous application, homeomorphism; then constructions of topologies on subspaces, products and
quotients, topological properties of separation, numerability, compactness, and connection
connection for arches. The student will also have acquired the notion of fundamental group and the its use together with the relevant calculation techniques, and the fundamental elements of the theory of topological coatings. Finally, the student will have acquired the basics of geometry differential of curves and surfaces in three-dimensional Euclidean space.
Apply knowledge and understanding. At the end of the course the student will be able to solve
simple topology problems, even with the use of elementary algebraic topology. He will also know use the notion of curvature in the contexts of the differential geometry of the curves and of the surfaces.
Critical and judgmental skills. The student will have the basis for analyzing the similarities and relations between
the topics covered and the fundamental notions of the theory of continuity and differentiability,
also with tools that have historically led to the solution of classical problems.
Communication skills. Ability to expose the contents in the oral part of the verification and in the any theoretical questions present in the written test.
Learning ability. The acquired knowledge will allow a study, individual or
given in a subsequent three-year or master's degree course, related to more advanced aspects of geometry.
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Second semester |
9 |
MAT/03 |
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1001746 - RATIONAL MECHANICS |
General targets: To acquire basic knowledge in classical mechanics.
Specific targets:
Knowledge and understanding: Students who have passed the exam will be able to construct
mathematical models not only for problems of mechanical nature, and to use analytic and
qualitative methods of ordinary differential equations to deal with them.
Applying knowledge and understanding: Students who have passed the exam will be able: i) to
perform the qualitative analysis on the phase space for one-dimensional conservative systems and
to obtain quantitative estimates; ii) to study problems of stability of equilibrium points elementary
methods of Liapunov; iii) to calculate frequencies of normal modes around stable equilibria; iv) to
choose properly Lagrangian coordinates for particular configuration manifolds (like Euler angles
for SO(3), spherical coordinates, etc.); iv) to recognize the variational nature of Lagrange equations
and their implications; v) to use specific criteria for searching prime integrals in Lagrange
equations and to perform the subsequent reduction to a smaller number of degrees of freedom.
Making judgements: Students who have passed the exam will have the basis to analyze the
similarities between the topics covered in the course and the already acquired knowledges in
analysis and geometry; they will also acquire important tools and ideas that have historically led to
the solution of fundamental problems of classical mechanics.
Communication skills: Students who have passed the exam will have gained the ability to
communicate concepts, ideas and methodologies of analytical mechanics.
Learning skills: The acquired knowledge will allow students who have passed the exam to face the
study, at an individual level or in a master’s degree course, of specialized aspects of classical
mechanics and, more generally, of the theory of dynamical systems.
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Second semester |
9 |
MAT/07 |
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1032750 - GENERAL INFORMATICS |
Knowledge and understanding:
At the end of this course the students will
know fundamental methodologies for the design and analysis of
iterative/recursive algorithms, fundamental data structures and sorting
algorithms, and basic implementations of dictionaries.
Skills and attributes:
At the end of this course the students:
will be able to explain the behavior of the most important data
structures, to analyze their running times, and to design new variants
for specific problems;
will be able to describe and to analyze the most important sorting
algorithms, and to apply the same design techniques to
different problems;
will be able to compare asymptotically execution times of the studied
algorithms;
will be able to design and analyze recursive algorithms.
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Second semester |
9 |
INF/01 |
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1022367 - REAL ANALYSIS |
General objectives: to acquire basic knowledge in measure and integration theory, L ^ p spaces, Fourier series and complex variables.
Specific objectives:
Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results related to the Theory of the Abstract Measure, the construction of the Lebesgue Measure, the Integration Theory, the Convergence Theorems under the sign of integral, the spaces L ^ p, to the Hilbert spaces and the Fourier series, to the basic properties of differential and integral calculus for complex variable functions.
Apply knowledge and understanding: at the end of the course the student will be able to understand the concept of measure and integral in abstract spaces, to integrate strongly discontinuous functions, to work with different notions of convergence in L ^ p, to use the Fourier series in L ^ 2 to approximate solutions of some equations to partial derivatives, to apply the Residual Theorem in a complex field.
Critical and judgmental skills: the student will have the basis to deal with some problems of applied mathematics, in particular those based on the study of suitable partial differential equations. He will also be able to undertake the study of more advanced disciplines, such as the Geometric Measure Theory or the Calderon-Zygmund Singular Integral Theory.
Communication skills: ability to expose the contents in the oral part of the verification and in any theoretical questions present in the written test.
Learning skills: the acquired knowledge will allow a study, individual or
given in an LM course, related to more specialized aspects concerning the real and complex variable.
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Second semester |
9 |
MAT/05 |
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Abilità informatiche |
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