Teachings
FA/0255  MATHEMATICS AND ELEMENTS OF STATISTICS
Academic Year 2022/2023
Free text for the University
 Professor

GIACOMO CHERCHI (Tit.)
 Period

First Semester
 Teaching style

Convenzionale
 Lingua Insegnamento

Informazioni aggiuntive
Course  Curriculum  CFU  Length(h) 

[60/76] BIOTECHNOLOGY  [76/20  Ord. 2018] Farmaceutico  7  56 
Objectives
Educational objectives
 Knowledge and understanding
Knowing the elementary algebra of mathematical expressions. Knowing the fundamental geometric entities. Knowing the properties of elementary functions. Knowing the graphs of elementary functions. Knowing the basics of probability. Explore features of the descriptive statistics.
applying knowledge and understanding
Ability to recognize and represent the lines and conics. Ability to describe the qualitative graph of a function. Ability to use elementary statistical functions.
capacity for analysis of experimental data using statistical tools.
 making judgements
Knowing how to recognize when a logical procedure is correct.
communication skills
Learn how to use mathematical language to properly communicate scientific results.
learning skills
Ability to learn how to solve independently complex exercises. Ability to be able to read and understand a text that uses the language of mathematics.
Prerequisites
During the first part of the course and whenever necessary, the teacher will recall some topics which are essential for the understanding of the mathematical methods that will be discussed during the course. However, each student should have a good mastery of the main mathematical concepts studied in the secondary school courses, for instance: properties of powers, radicals and their properties, polynomials factorization , first and second degree equations and inequalities, fractional equations and inequalities, irrational equations and inequalities, systems of equations and inequalities, equation of a line, measure of an angle in degrees and radians, definition of sine, cosine and tangent, relations between the goniometric functions.
It is strongly recommended a continuous and regular attendance to the classes, without which the understanding might become considerably difficult.
Contents
1. Sets and numbers. Intuitive theory of sets: subsets, union, intersection and differences of sets. Numbers. Geometrical representation of real numbers on the line. Powers. Scientific notation. Order of magnitude. Percentages.
2. Further preliminaries. First and second degree. Fractional equations. Irrational equations. First and second degree inequalities. Fractional inequalities. Systems of inequalities. Basic properties of logarithms; change of base. Trigonometry: angles in degrees and radians; sine, cosine, tangent.
3. Basic analytical geometry. Cartesian coordinates. Representation of points and lines. Distance between points. Equation of a line. Geometric interpretation of the angular coefficient; parallelism and orthogonality of lines; circles.
4. Functions. Definition. Real functions. Graph of a function. Composition of two functions. Invertible functions. Increasing and decreasing functions. Some remarkable classes of functions and their applications on life science: linear functions, power functions, exponential functions, logarithmical functions, periodic functions, sine, cosine and tangent function. Determination of the domain of a function.
5. Differential calculus. Limits of a function. Some techniques of solution of indeterminate forms. The notion of derivative. Properties of derivatives: derivative of the sum, of the product and of the quotient of two functions. The second derivative. Maximal and minimum of a function. Qualitative study of a function.
6. Indefinite integrals. Immediate indefinite integrals. Integration by substitution. Integration by parts. Definite integrals. Properties of the definite integral. Mean theorem. Fundamental theorem of integral calculus. LeibenizNewton formula.
7. Statistics. Graphical representations of data. Arithmetic and geometric mean. Median. Mode. Variance. Standard deviation. Linear regression. Correlation coefficient.
Teaching Methods
Lessons will be held simultaneously both in person and remotely (according to the rules established by the University). The method with which the lessons will be carried out is designed to ensure that there are no disparities between students in presence and remotely. Through the use of a graphic tablet and a digital blackboard, projected and shared screen, students will have the opportunity to follow the lessons limiting as much as possible the inconvenience caused by the pandemic situation.
Verification of learning
The student can choose to take two partial written tests (2 h each) or a total written test (3 h). It will be possible to access the second partial test only if a sufficient result has been achieved in the first (grade >=18).
The student can also choose whether to take an oral test to increase the grade of the written / s.
Texts
Main book.
Marco Bramanti, Carlo Domenico Pagani, and Sandro Salsa. Analisi Matematica 1.Zanichelli, 2008.
Other reference book:
M. Abate, Matematica e Statistica. Le basi per le scienze della vita, McGrawHill
D. Benedetto, M. Degli Esposti, C. Maffei, Matematica per le Scienze della vita, CEA
Book for high school math consolidation:
S. Montaldo, A. Ratto, Matematica: 2^3 capitoli per tutti, Liguori, 2011
Exercise books:
 P. Marcellini, C. Sbordone: Esercitazioni di Matematica, Vol. 1, Tomi 12, Ed. Liguori
 A.M. Bigatti, G. Tamone: Elementi di Matematica, esercizi con soluzioni per Scienze e Farmacia, Esculapio
More Information
In addition to the recommended books, it is advisable to consult the teacher's lecture notes.