First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
NATURAL SCIENCE
Course unit
MATHEMATICS WITH ELEMENTS OF STATISTICS
SCN1031961, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course First cycle degree in
NATURAL SCIENCE
SC1161, Degree course structure A.Y. 2008/09, A.Y. 2018/19
N0
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Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination MATHEMATICS WITH ELEMENTS OF STATISTICS
Website of the academic structure http://scienzenaturali.scienze.unipd.it/2018/laurea
Department of reference Department of Biology
E-Learning website https://elearning.unipd.it/biologia/course/view.php?idnumber=2018-SC1161-000ZZ-2018-SCN1031961-N0
Mandatory attendance
Language of instruction Italian
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge CARLA DE FRANCESCO MAT/09
Other lecturers MARCO PICCIRILLI

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 01/10/2018
End of activities 18/01/2019
Show course schedule 2019/20 Reg.2008 course timetable

Examination board
Board From To Members of the board
8 MATEMATICA CON ELEMENTI DI STATISTICA 2019-2020 01/10/2019 27/11/2020 FERRANTE MARCO (Presidente)
DE FRANCESCO CARLA (Membro Effettivo)
FORMENTIN MARCO (Supplente)
7 MATEMATICA CON ELEMENTI DI STATISTICA 2018-2019 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)

Syllabus
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, one-to-one 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 three-dimensional space: sum of vectors, vector-scalar product, scalar product. Bases and coordinates in a vector space, vector norm. Straight lines in three-dimensional 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. One-way and two-way test: average in case of known σ. Two-way test: average in case of unknown σ. p-value 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 e-learning page of the course: they can be used for self-assessment.
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 Cerca nel catalogo

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)
Quality Education Gender Equality