Calculus and Statistics

A.Y. 2019/2020
6
Max ECTS
56
Overall hours
SSD
MAT/05
Language
Italian
Learning objectives
The course intends to give both the basic concepts of the theory of univariate functions and the basic concepts.
Expected learning outcomes
At the end of the course, students should be able to:
· use real valued functions and Calculus tools to describe easy models;
· handle basic tools in both Statistics and Probability.
Course syllabus and organization

Linea AL

Lesson period
First semester
Course syllabus
Elements of calculus: sets, number sets, numerical sequences, functions, limits, continuity, differential calculus in one variable, analysis of a function, integral calculus in one variable. 2. Linear Algebra: matrices, matrix operations, invertible matrices, matrix determinant, inverse matrix. Systems of linear equations and the gaussian elimination method. 3. Elements of Statistics: Data and sampling. Graphic presentations. Measures of location: arithmetic mean, geometric mean, median, mode. Measures of dispersion: quartiles, interquartile range, variance and standard deviation. Normal distribution. Coefficient of correlation and linear regression line. Iphotesis test
Prerequisites for admission
Knowledge and skill in the following arguments: equations and inequalities of first and second degrees; the equation of a line; trigonometric functions and main identities; properties of powers and logarithms.
Teaching methods
Frontal lessons using multimedia devices. Exercises
Teaching Resources
Handouts provided by the teacher
Assessment methods and Criteria
The general learning outcome is to develop the students' abstract thought, to provide them with basic mathematical concepts, tools and rigorous language, together with problem solving abilities and the capacity to read and understand simple mathematical texts. To this purpose, the methods of calculus will be illustrated and applied to the analysis of real valued functions in one variable. The matrix methods for solving systems of linear equations will be presented, as well as the basic methods of descriptive statistics in the context of life sciences. In this way the students will become skillful at differential and integral calculus, and statistical data analysis.
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 6
Practicals: 16 hours
Lessons: 40 hours
Professor: Bertini Stefano

Linea MZ

Lesson period
First semester
Course syllabus
1 Calculus
· Real numbers, real field and its properties
· Functions, their properties, graphs.
· Limits, continuity
· Differential calculus and its applications
· Integral calculus

2 Probability and Statistics
· Probability, conditional probability and applications.
· Random variables
· Sampling and descriptive Statistics
· Parameter estimate
· Hypothesis testing
Prerequisites for admission
Good knowledge of high-school Mathematics
Teaching methods
Front lessons, and exercise sessions
Teaching Resources
Handouts
M. Bramanti, C. D.Pagani, S.Salsa: Analisi Matematica 1, Zanichelli
S. Ross: Introduzione alla Statistica, Apogeo
Assessment methods and Criteria
Written exam. Student must solve problems using tools that have been given during the course
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 6
Practicals: 16 hours
Lessons: 40 hours