
Course unit
MATHEMATICS WITH ELEMENTS OF STATISTICS
SCN1031961, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Basic courses 
MAT/02 
Algebra 
1.0 
Basic courses 
MAT/03 
Geometry 
1.0 
Basic courses 
MAT/05 
Mathematical Analysis 
2.0 
Basic courses 
MAT/06 
Probability and Mathematical Statistics 
3.0 
Basic courses 
MAT/09 
Operational Research 
2.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
3.5 
42 
45.5 
No turn 
Laboratory 
0.5 
8 
4.5 
No turn 
Lecture 
5.0 
40 
85.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
7 MATEMATICA CON ELEMENTI DI STATISTICA 20182019 
01/10/2018 
30/11/2019 
DE FRANCESCO
CARLA
(Presidente)
DI SUMMA
MARCO
(Membro Effettivo)
PICCIRILLI
MARCO
(Supplente)

6 MATEMATICA CON ELEMENTI DI STATISTICA 2017/2018 
01/10/2017 
25/11/2018 
DE FRANCESCO
CARLA
(Presidente)
FERRANTE
MARCO
(Membro Effettivo)
BARBATO
DAVID
(Supplente)

Prerequisites:

Language of mathematics, basics of logics and set theory;
real, rational and integer numbers;
algebra of polynomials;
linear and quadratic equalities and inequalities, systems of linear equations with two variables;
geometry of plane figures;
cartesian coordinate systems, functions and graphs;
classes of functions: linear, powers, polynomials, exponential and logarithmic, sine and cosine. 
Target skills and knowledge:

Good knowledge of basic techniques of Calculus and Linear Algebra. Basic knowledge of Probability Theory and Statistics.
At the end of the course unit students will be able to use calculus and statistics tools to analyze natural phenomena quantitatively. 
Examination methods:

Written exam, divided in two parts, math and stat. Each part requires the solution of some exercises. Comprehension of the topics and problem solving ability will be evaluated. 
Assessment criteria:

The final grade will be based on Mathematics part (66%) and Statistics part (33%). The grade of each part needs to be sufficient. 
Course unit contents:

Mathematics (6 CFU):
Functions: definition, onetoone functions, inversion and composition of functions, cartesian coordinate systems and function graphs. Symmetries and periodicity of functions.
Classes of functions: linear, quadratic, polynomials, powers, rationals, exponential and logarithmic, trigonometric (sine, cosine and tangent).
Solving exponential, logarithmic and trigonometric equalities and inequalities.
Limits: definition, calculus and proof. Continuity of functions.
Derivatives: definition and geometrical interpretation. Derivatives computation.
Study of functions: local and global minima and maxima, increasing and decreasing functions, convexity and concavity, horizontal and vertical asymptotes.
De l'Hôpital rule for limits.
Integrals: geometric definition and properties of definite integrals, Fundamental Theorem and Formula of calculus, definition and computation of indefinite integrals. Integration by substitution and by parts. Improper integrals.
Applied vectors in threedimensional space: sum of vectors, vectorscalar product, scalar product. Bases and coordinates in a vector space, vector norm. Straight lines in threedimensional space: vector and parametric equation.
Systems of linear equations and Gauss method for their solution.
Matrices: operations with matrices, invertible matrices, inverse matrix, determinant of 2x2 and 3x3 matrices.
Statistics (3 CFU):
Frequency tables. Histograms. Average value, median and sample variance. Quantiles: definitions and examples.
Sample space and events. Probability functions and properties. Inclusion and exclusion principle with applications, product rule and conditioned probability. Independence of events: definition and examples. Bayes formula. Discrete random variables, average value and moments of a discrete random variable. Continuous random variables: definition. Uniform, exponential, normal random variables. T of Student. Percentiles for normal and t of Student r.v.
Point estimator: sample average and its distribution. Sample variance: properties. Sample average and variance with normal r.v. Interval estimator: definition. Confidence interval: definition and examples. Confidence interval for the average value of a normal with known and unknown variance.
Statistical hypothesis test: general definition. Oneway and twoway test: average in case of known σ. Twoway test: average in case of unknown σ. pvalue of a hypothesis test. 
Planned learning activities and teaching methods:

Frontal lectures, trying to stimulate the interactive participation of students.
Most of the time is dedicated to solution and discussion of examples and exercises.
Lists of exercises are given to the students through the elearning page of the course: they can be used for selfassessment. 
Additional notes about suggested reading:

The material is available at: https://elearning.unipd.it/biologia 
Textbooks (and optional supplementary readings) 

Benedetto, Dario; Degli_Esposti, Mirko; Maffei, Carlotta, Matematica per le scienze della vita. Milano: CEA, 2015. terza edizione

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Questioning
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
Sustainable Development Goals (SDGs)

