AIMS AND CONTENT

LEARNING OUTCOMES

Module MATEMATICS: The course aims at giving the basic mathematics necessary for the scientific language. Therefore the student is supplied with the capability of handling calculus, algebra and geometry.

Module INFORMATICS: To understand the complete set of subjects (even somewhat differentiated) that form the actual informatics matter. To be able to use, with a correct level of knowledge, most of the tools that the computer science have developed at present.

TEACHING METHODS

Frontal lessons and exercises.

Any Student with documented Specific Learning Disorders (SLD), or with any special needs, should contact the Lecturer(s) and to the dedicated SLD Representative in the Department before class begins, in order to liaise and arrange the specific teaching methods so that the learning aims and outcomes may be met.

SYLLABUS/CONTENT

Module MATHEMATICS

The programme will be taught in 24 lessons, each lasting 2 hours.

1.     References on numerical sets and arithmetic, properties of real numbers and their consequences.
2.     Approximation of real numbers with decimal numbers having a finite number of digits, propagation of errors with the sum and with the product. Elementary set theory: union, intersection and applications.
3.     Elementary set theory : Injective, surgettive, invertible functions; function graph in a real variable: definition, properties and applications.
4.     Polynomials: divisibility and roots; equations and sequences with polynomial fractions: algebraic calculation and graphical representations.
5.     Elementary functions: trigonometric functions (sen x, cos x, tan x, arcsen x, arccos x, arctan x): definitions, properties, graphs, applications.
6.     References to analytical geometry in the plane, cartesian and parametric equations of lines, intersection of two lines, angles between two lines, polar coordinates.
7. Elementary functions: power and root n-th functions, exponential functions and logarithm functions: definitions, properties, graphs, applications.
8. Use of exponential and logarithm in science: definition of pH, definition of decibel for noise measurement, decibel sum formula, models for the evolution of a population such as bacteria in a culture or cells in an organism’s tissue.
9. Functions of a real variable: definition domain, growth, decay, maximum and minimum (absolute), composition of elementary functions and their graph.
10. Limits: definitions, properties, calculation rules, order of infinity and infinitism, graphical aspects, oblique asymptotes.
11. Continuous functions: definition, properties, zero theorem, approximation of the zeroes of a function (for example, of the roots of a polynomial) by bisection.
12. Continuous functions: existence of maximum and minimum over a closed and limited range. Composition of elementary functions and their graph, considering definition domain, limits to the extremes of the definition domain, growth and decline, maximum and minimum.
13. Derivative (first): definition, geometric meaning, properties and rules of derivation, the derivatives of elementary functions, calculation of derivatives.
14. Use of the first derivative in the study of a graph of a derivable function: lines tangent to the graph, growth and decline, calculation of relative maximums and minima, L'Hopital theorems for calculating limits of indeterminate forms.
15.  Second derivative, study of concavity and flexes.
16.  Successive derivatives and Taylor polynomials to approximate a function locally, local study of graphs of functions for which it is not possible to study the properties of the derivatives globally.
17. Taylor’s polynomial and Lagrange rest to estimate the approximation error, approximate calculation of function values.
18. Integral: definition, properties, calculation of areas, approximation with the trapezoid method.
19. Primitive of a function; fundamental theorem of integral calculus: use of the primitives for the calculation of integrals; integration of elementary functions, integration by substitution, integrals of fractions of polynomials (with a degree denominator at most 2).
20. Simple integration methods (integrative function primitive search): method for substitution and part; use of approximation methods for the calculation of integrals (defined) of functions for which it is difficult or impossible to find the primitive as compositions of elementary functions; improper integrals.
21. Linear systems of m equations in n unknown, algebraic and geometric meaning (with particular attention to the cases n=2 and n=3), their solution by Gauss reduction by making appropriate linear combinations between the equations.
22. Linear system solutions with the Gauss algorithm, various cases.
23. Matrices: product, determinant (of square matrix), characteristic or rank.

Calculation of the determinant or rank by appropriate linear combinations on rows or columns. Matrices associated with linear systems.

Module INFORMATICS

• Data abstraction:
  • Basis concepts
  • Data structure implementation
  • Classes and objects
• Database structures:
  • Level based approach to the development of databases
  • Relational model
  • Database integrity management
• Software engineering:
  • Software life cycle
  • Testing
  • Documentation
• Artificial Intelligence:
  • Perception
  • Artificial neural networks
  • Robotics
• Computational Theory
  • Turing machine
  • Universal programming language
  • Private key cryptography
• Practical examples:
  • Use of spreadsheet as data collection tool
  • Migration from spreadsheet to database management system
  • Use of internet for scientific and bibliographic research

RECOMMENDED READING/BIBLIOGRAPHY

Module MATEMATICS

• M. Bianchi, E. Paparoni; Matematica per le Scienze; Pearson Education 2007.

Libro consigliato:

• D. Benedetto, M. Degli Esposti, C. Maffei; Matematica per le Scienze della Vita; Casa Editrice Ambrosiana 2012.

Module INFORMATICS

• J. Glenn Brookshear “Informatica: Una panoramica generale” 9° Ed, Pearson Milano 2006.

TEACHERS AND EXAM BOARD

Exam Board

NORBERT MAGGI (President)

Anna Maria MASSONE (President)

PAOLA FERRARI

ISABELLA FURCI

MAURO GIACOMINI

LESSONS

LESSONS START

I semester, in October.

Class schedule

MATHEMATICS AND INFORMATICS

EXAMS

EXAM DESCRIPTION

Written and oral.

ASSESSMENT METHODS

Module MATHEMATICS: During the course, two interim tests will be conducted to ensure learning, they may replace a part of the written exam. The exam consists of a written test followed by an oral exam. On the written exam there will be some exercises related to the topics discussed in the course, not only the result will be evaluated, but also the performance and analysis of the result. At the oral examination, any mistakes made in the written test will be discussed and it will be ensured that adequate mastery of the concepts and methodologies outlined in the course has been acquired.

Module INFORMATICS: Written examination and oral exam on the topics discussed.

Exam schedule