
Course unit
SPECIAL TOPICS IN MATHEMATICS
IN01101595, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
MAT/03 
Geometry 
6.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Prerequisites:

For the successful achievement of the course objectives, basic knowledge of Linear Algebra (linear maps, matrices, eigenvalues and eigenvectors, orthogonality), Cartesian Geometry of the threedimensional space and Calculus (limits, derivatives and integrals in one and two variables, series) is required. 
Target skills and knowledge:

The course aims to introduce familiarity with mathematical structures and related techniques, which can be applied immediately in different engineering areas. In particular objectives are:
 Knowledge of the different algebraic representations of the isometries (displacements) of the Euclidean space.
 Knowledge of the singularvalue decomposition of a real matrix, of the pseudoinverse and their applications to least squares problems.
 Ability to compute probability of events in cases of equally likely outcomes (elementary probability).
 Knowledge of the discrete and continuous random variables, as well as the most common types of them.
 Ability to use double integrals in computing of probabilistic values linked to jointly continuous random variables.
 Knowledge of the main limit theorems. 
Examination methods:

The verification of knowledge and expected skills is carried out with a test divided into a written exam and an oral exam, usually on the same day. The written test consists of four exercises, two of which on the part of Linear Algebra and Geometry and two on Probability. The oral exam takes place through a 1015 minutes exposition to the blackboard. Candidates are asked to present one of about eight topics, announced by the end of the course. This is followed by further questions. 
Assessment criteria:

The evaluation of the written test takes value in large classes (not adequate, adequate, good). The aim of the test is to verify the experience that the student has gained on the exercises proposed in class, or similar ones.
The oral exam verifies the skills acquired by the student on the fundamentals presented by the course. Ability and organization are assessed in presenting both abstract and applied mathematical concepts with appropriate terms. It is also evaluated the ability and responsiveness in dealing with questions of various kinds related to the presented topics. 
Course unit contents:

The special orthogonal group of degree three. Euler's theorem. The skewfield of quaternions and the representation of the rotations by means of the quaternions.
Singularvalue decomposition. Pseudoinverse and least squares.
Combinatorial algebra, permutations, combinations, binomial coefficient, multinomial coefficient, Stirling formula, binomial identities, Newton binomial formula, multinomial theorem. Events. Certain event, impossible event, disjoint events, complementary event. Axioms of probability. Inclusionexclusion principle. Successions of events. Conditional probability. Bayes formula. Independence. Discrete random variables. Expected value and variance. Binomial, Bernoulli, Poisson, and geometric variables. Continuous random variables, density, distribution function. Expected value and variance of a continuous random variable. Exponential, Gamma, normal, and uniform variables. Joint distributions and densities, marginal density, independent variables. Properties of the expected value. Covariance, variance of a sum. De MoivreLaplace theorem. Weak and strong law of large numbers. Central limit theorem. 
Planned learning activities and teaching methods:

Teaching activities include lectures at the blackboard where concepts, methods, exercises, problems and solutions are presented. During the lessons the students are invited to ask questions about the doubts that may have arisen in the presentation by the teacher. 
Additional notes about suggested reading:

All the teaching material presented during the lessons will be made available on the moodle platform.
The study material includes:
 lecture notes,
 the teacher's book in pdf format,
 list of topics for exam,
 tables necessary for the exercises,
 texts for further reading,
 complete archive of the previous written exams. 
Textbooks (and optional supplementary readings) 

Ross, Sheldon M.; Mariconda, Carlo; Ferrante, Marco, Calcolo delle probabilitÃ Sheldon M. Rossedizione italiana a cura di Carlo Mariconda e Marco Ferrante. Milano: Apogeo Education  Maggioli Editore, .

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem based learning
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)

