Technologies for Conservation and Restoration of Cultural Heritage

Calculus: Limits and continuous functions, derivatives and optimization, integrals (fundamental theorem of calculus and techniques of integration), differential equations. Probability+statistics: Probability axioms, discrete random variables and discrete models, continuous random variables and continuous models, population and samples, statistical variables, measures of central tendency and dispersion, correlation, regression, statistical tests

Knowledge of basic algebra (polynomials, exponents, logarithms) and trigonometry, at the level of a good high school education.

D'Ancona-Manetti, "Istituzioni di Matematiche" (free pdf version) S. M. Ross, "Introduzione alla statistica", Maggioli Editore, 2023 D. S. Moore: “Statistica di base”, II edizione, APOGEO, 2013

Optional

2 midterms (90%) + weekly homework (10%) + oral exam (adjustment) OR exam (100%) + oral exam (adjustment).

Weekly in person lectures, exercise sessions as time permits, tutoring sessions.

Calculus: Limits and continuous functions, derivatives and optimization, integrals (fundamental theorem of calculus and techniques of integration), differential equations. Probability+statistics: Probability axioms, discrete random variables and discrete models, continuous random variables and continuous models, population and samples, statistical variables, measures of central tendency and dispersion, correlation, regression, statistical tests

Knowledge of basic algebra (polynomials, exponents, logarithms) and trigonometry, at the level of a good high school education.

D'Ancona-Manetti, "Istituzioni di Matematiche" (free pdf version) S. M. Ross, "Introduzione alla statistica", Maggioli Editore, 2023 D. S. Moore: “Statistica di base”, II edizione, APOGEO, 2013

Optional

2 midterms (90%) + weekly homework (10%) + oral exam (adjustment) OR exam (100%) + oral exam (adjustment).

Weekly in person lectures, exercise sessions as time permits, tutoring sessions.

Basic Mathematics. Numbers and algebraic operations; equations and inequalities; geometric representation of real numbers, fundamentals of analytic geometry (cartesian coordinates, distance between points in the cartesian plane). Differential and Integral Calculus. The concept of function, graph and properties of elementary functions: polynomial, exponential, logarithmic, trigonometric functions; asymptotic behavior of sequences and functions (horizontal and vertical asymptotes); the notion of continuity of a function; incremental ratio; fundamentals of differential calculus (definition and geometric meaning of the derivative, derivatives of elementary functions, Leibnitz rule, chain rule); differentiability implies continuity; maxima and minima; fundamental concepts concerning the integral calculus (definition and geometric meaning of integrals; Torricelli-Barrow theorem; integration by parts). Probability Theory. Experiments and sample spaces; events (definition, intersection and union of events, incompatible events); probability of an event; probability of the union of two events; conditioned probability and independent events; elements of combinatorial calculus (dispositions, permutations and combinations); discrete random variables, expectation values and variance, random variables with binomial or Poisson distribution. Continuous random variables (density and distribution, expected value and variance); random variables with uniform, exponential or normal distribution.

It is assumed that students entering the course know the basics of elementary mathematics from the high school. The fact that students actually have the mentioned pre-knowledge is certified by 1) passing the entrance test, or 2) taking the OFA course and passing the relative exam, or 3) taking the present course and passing the relative exam.

[R] S. M. Ross, Introduzione alla statistica. Maggioli Editore, 2014. [M] D. S. Moore: “Statistica di base”, II edizione, APOGEO

Non-mandatory attendance

The exam consists of a written part, to evaluate the ability of the student to solve simple exercises and problems, and of an oral part. The written part, about 120 minutes, contains some open-question problems, possibly with a pre-selection based on multiple-choice questions. The oral part consists in a short colloquium, and defines – together with the written part – the final mark for Part 1.

Further information concerning the course, including the “Lecture Calendar” and a wide selection of problems and exercises, is available through the course website on classroom [p2y2nrw]. [A] M. Abate: "Matematica e Statistica - Le basi per le scienze della vita", The McGraw-Hill, 2017 [VG] V. Villani, G. Gentili, "Matematica - Comprendere e interpretare fenomeni delle scienze della vita", The McGraw-Hill, 2022 [BMD] D. Benedetto, C. Maffei, M. Degli Esposti: “Matematica per le scienze della vita”, II edizione, CEA [C] C. Cammarota: Elementi di Calcolo e di Statistica - Libreria Scientifica Dias [LMN1] L. Lamberti, L. Mereu, A. Nanni. Nuovo Lezioni di Matematica, vol. D . Etas RCS, Milano, 2012 [LMN2] L. Lamberti, L. Mereu, A. Nanni. Nuovo Lezioni di Matematica, vol. E . Etas RCS, Milano, 2012 [R] S. M. Ross, Probabilità e statistica per l'ingegneria e per le scienze. Apogeo, Milano, 2003 [M] D. S. Moore: “Statistica di base”, II edizione, APOGEO

The course includes lectures and exercise sessions. Lectures aim to transfer to students the fundamental concepts of the discipline, while exercise sessions focus on the application of the abstract knowledge to the solution of concrete problems emerging in natural sciences.

Basic Mathematics. Numbers and algebraic operations; equations and inequalities; geometric representation of real numbers, fundamentals of analytic geometry (cartesian coordinates, distance between points in the cartesian plane). Differential and Integral Calculus. The concept of function, graph and properties of elementary functions: polynomial, exponential, logarithmic, trigonometric functions; asymptotic behavior of sequences and functions (horizontal and vertical asymptotes); the notion of continuity of a function; incremental ratio; fundamentals of differential calculus (definition and geometric meaning of the derivative, derivatives of elementary functions, Leibnitz rule, chain rule); differentiability implies continuity; maxima and minima; fundamental concepts concerning the integral calculus (definition and geometric meaning of integrals; Torricelli-Barrow theorem; integration by parts). Probability Theory. Experiments and sample spaces; events (definition, intersection and union of events, incompatible events); probability of an event; probability of the union of two events; conditioned probability and independent events; elements of combinatorial calculus (dispositions, permutations and combinations); discrete random variables, expectation values and variance, random variables with binomial or Poisson distribution. Continuous random variables (density and distribution, expected value and variance); random variables with uniform, exponential or normal distribution.

It is assumed that students entering the course know the basics of elementary mathematics from the high school. The fact that students actually have the mentioned pre-knowledge is certified by 1) passing the entrance test, or 2) taking the OFA course and passing the relative exam, or 3) taking the present course and passing the relative exam.

[R] S. M. Ross, Introduzione alla statistica. Maggioli Editore, 2014. [M] D. S. Moore: “Statistica di base”, II edizione, APOGEO

Non-mandatory attendance

The exam consists of a written part, to evaluate the ability of the student to solve simple exercises and problems, and of an oral part. The written part, about 120 minutes, contains some open-question problems, possibly with a pre-selection based on multiple-choice questions. The oral part consists in a short colloquium, and defines – together with the written part – the final mark for Part 1.

Further information concerning the course, including the “Lecture Calendar” and a wide selection of problems and exercises, is available through the course website on classroom [p2y2nrw]. [A] M. Abate: "Matematica e Statistica - Le basi per le scienze della vita", The McGraw-Hill, 2017 [VG] V. Villani, G. Gentili, "Matematica - Comprendere e interpretare fenomeni delle scienze della vita", The McGraw-Hill, 2022 [BMD] D. Benedetto, C. Maffei, M. Degli Esposti: “Matematica per le scienze della vita”, II edizione, CEA [C] C. Cammarota: Elementi di Calcolo e di Statistica - Libreria Scientifica Dias [LMN1] L. Lamberti, L. Mereu, A. Nanni. Nuovo Lezioni di Matematica, vol. D . Etas RCS, Milano, 2012 [LMN2] L. Lamberti, L. Mereu, A. Nanni. Nuovo Lezioni di Matematica, vol. E . Etas RCS, Milano, 2012 [R] S. M. Ross, Probabilità e statistica per l'ingegneria e per le scienze. Apogeo, Milano, 2003 [M] D. S. Moore: “Statistica di base”, II edizione, APOGEO

The course includes lectures and exercise sessions. Lectures aim to transfer to students the fundamental concepts of the discipline, while exercise sessions focus on the application of the abstract knowledge to the solution of concrete problems emerging in natural sciences.