Mathematics and Informatics
A.Y. 2023/2024
Learning objectives
The teaching aids to student provides the basic notion of mathematical analisys and descriptive statistics to enable them to develop skills in data processing and modeling. One of the main aims of the course is to develop the ability to analyze the behavior of a real variable function, determining its graph in a system of Cartesian axes through the basic elements of the differential calculation. Another important educational objective pursued by the course is that of acquiring the basic skills in the elaboration of experimental data by introducing the commonly used statistical descriptors.
The Computer Science Course 3CFU provides the basic notions of the computer-science discipline with focus on i) foundations of Computer Science, ii) spreadsheets, iii) information management, and iv) Internet and web. Furthermore, the Course provides skills about the main functionalities of spreadsheet software tools, with focus on the use of formulae, functions, and chart creation.
The Computer Science Course 3CFU provides the basic notions of the computer-science discipline with focus on i) foundations of Computer Science, ii) spreadsheets, iii) information management, and iv) Internet and web. Furthermore, the Course provides skills about the main functionalities of spreadsheet software tools, with focus on the use of formulae, functions, and chart creation.
Expected learning outcomes
The student must know the main notions of mathematical analysis in relation to the study of a real function; in particular the student must know the meaning of domain of a fiction, of continuity of a function in an interval and of derivative of a function in a point. Furthermore the student must demonstrate to know the main statistical descriptors that allow to interpret a series of experimental data. The student must be able to interpret the progress of a function and must be able to describe a series of experimental data on a statistical level. Through the use of acquired notions, he must be able to interpret the tendency of the behavior of variables object of his research.
For the Computer Science Course 3CFU The student will acquire a mix of Knowledge and Skills.
Knowledge: the student will learn about i) foundations of Computer Science, ii) spreadsheets, iii) information management, and iv) Internet and web. The part about the foundations of Computer Science includes: historical notions about the computer-science discipline, physical structure and organization of computers, information coding, units of measure of information, definition of algorithm and program, digital representation of text, audio, and video contents, classification of software tools, security issues and risks concerned with the use of digital technologies. The part about spreadsheets includes: spreadsheet definition and structure, functions in Microsoft Excel, statistical functions in Microsoft Excel, chart creation in Microsoft Excel. The part about information management includes: definition of data and information, databases, relational model of databases, database systems, similarities and differences between spreadsheets and relational databases, database languages, query composition, web databases. The part about Internet and web includes: basic notions of computer networks, standard and protocols of computer networks, history and structure of the Internet, web architecture, HTML language, design and structure of search engines.
Skills: the student will acquire the following skills: Creation and organization of data in a spreadsheet; Dragging of formulae in a spreadsheet; Cell formatting in a spreadsheet; Use of general and statistical functions in Microsoft Excel; Chart creation in Microsoft Excel.
For the Computer Science Course 3CFU The student will acquire a mix of Knowledge and Skills.
Knowledge: the student will learn about i) foundations of Computer Science, ii) spreadsheets, iii) information management, and iv) Internet and web. The part about the foundations of Computer Science includes: historical notions about the computer-science discipline, physical structure and organization of computers, information coding, units of measure of information, definition of algorithm and program, digital representation of text, audio, and video contents, classification of software tools, security issues and risks concerned with the use of digital technologies. The part about spreadsheets includes: spreadsheet definition and structure, functions in Microsoft Excel, statistical functions in Microsoft Excel, chart creation in Microsoft Excel. The part about information management includes: definition of data and information, databases, relational model of databases, database systems, similarities and differences between spreadsheets and relational databases, database languages, query composition, web databases. The part about Internet and web includes: basic notions of computer networks, standard and protocols of computer networks, history and structure of the Internet, web architecture, HTML language, design and structure of search engines.
Skills: the student will acquire the following skills: Creation and organization of data in a spreadsheet; Dragging of formulae in a spreadsheet; Cell formatting in a spreadsheet; Use of general and statistical functions in Microsoft Excel; Chart creation in Microsoft Excel.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
- Equations and inequalities.
- Logarithms and exponentials.
- Concept of function and its graph. Domain and codomain. Function properties: injective; surjective; bijective. Inverse function and compound function.
- Graphs of elementary functions, in particular: straight lines, powers, absolute value, parables, exponentials, logarithms and protractor functions.
- Translations, symmetries and dilations starting from the graph of elementary functions.
- Concept of limit. Limits of elementary functions. Infinity ladder.
- Continuous functions.
- Notion of derivative in a point and its geometric meaning. Line tangent to the graph of a function at a point.
- Rules of derivation; sum, product, quotient and composition of functions.
- Higher order derivatives.
- Application of derivatives to the study of the graph of a function.
- Discrete random variables.
- Average value, variance, mean square deviation, standard deviation.
- Linear regression (least squares method).
[Program for non-attending students]:
- Real numbers, coordinates on the straight line and in the plane. Form of a real number.
- Notable products. Equations and inequalities.
- Concept of function and its graph. Domain and codomain. Function properties: injective; surjective; bijective. Inverse function and compound function.
- Graphs of elementary functions, in particular: straight lines, powers, absolute value, parables, exponentials, logarithms and protractor functions.
- Translations and symmetries starting from the graph of elementary functions.
- Concept of limit. Limits of elementary functions. Infinity ladder.
- Continuous functions.
- Notion of derivative in a point and its geometric meaning. Line tangent to the graph of a function at a point.
- Rules of derivation; sum, product, quotient and composition of functions.
- Higher order derivatives.
- Application of derivatives to the study of the graph of a function.
- Discrete random variables.
- Average value, variance, mean square deviation, standard deviation.
- Linear regression (least squares method).
The Computer Science Course 3CFU program is focused on the following topics:
o Foundations of Computer Science
o Introduction to Computer Science
o Information coding
o Computer structure
o Programs and software
o The "Infosphera" risks
o Spreadsheets
o Introduction to spreadsheets
o General functions in Excel
o Statistical functions in Excel
o Chart creation in Excel
o Information management
o Introduction to information management
o Data storing and databases
o Relational databases
o Database creation
o Query composition
o Web databases
o Internet and web
o Computer networks
o The Internet network
o Web architecture
o Web standards
o Web contents
o Search engines
o Web evolutions
- Logarithms and exponentials.
- Concept of function and its graph. Domain and codomain. Function properties: injective; surjective; bijective. Inverse function and compound function.
- Graphs of elementary functions, in particular: straight lines, powers, absolute value, parables, exponentials, logarithms and protractor functions.
- Translations, symmetries and dilations starting from the graph of elementary functions.
- Concept of limit. Limits of elementary functions. Infinity ladder.
- Continuous functions.
- Notion of derivative in a point and its geometric meaning. Line tangent to the graph of a function at a point.
- Rules of derivation; sum, product, quotient and composition of functions.
- Higher order derivatives.
- Application of derivatives to the study of the graph of a function.
- Discrete random variables.
- Average value, variance, mean square deviation, standard deviation.
- Linear regression (least squares method).
[Program for non-attending students]:
- Real numbers, coordinates on the straight line and in the plane. Form of a real number.
- Notable products. Equations and inequalities.
- Concept of function and its graph. Domain and codomain. Function properties: injective; surjective; bijective. Inverse function and compound function.
- Graphs of elementary functions, in particular: straight lines, powers, absolute value, parables, exponentials, logarithms and protractor functions.
- Translations and symmetries starting from the graph of elementary functions.
- Concept of limit. Limits of elementary functions. Infinity ladder.
- Continuous functions.
- Notion of derivative in a point and its geometric meaning. Line tangent to the graph of a function at a point.
- Rules of derivation; sum, product, quotient and composition of functions.
- Higher order derivatives.
- Application of derivatives to the study of the graph of a function.
- Discrete random variables.
- Average value, variance, mean square deviation, standard deviation.
- Linear regression (least squares method).
The Computer Science Course 3CFU program is focused on the following topics:
o Foundations of Computer Science
o Introduction to Computer Science
o Information coding
o Computer structure
o Programs and software
o The "Infosphera" risks
o Spreadsheets
o Introduction to spreadsheets
o General functions in Excel
o Statistical functions in Excel
o Chart creation in Excel
o Information management
o Introduction to information management
o Data storing and databases
o Relational databases
o Database creation
o Query composition
o Web databases
o Internet and web
o Computer networks
o The Internet network
o Web architecture
o Web standards
o Web contents
o Search engines
o Web evolutions
Prerequisites for admission
Basics of arithmetic and algebra: literal calculation, first and second degree numerical equations in R; first and second degree inequalities in R.
The Course Computer Science Course 3CFU does not have prerequisites
The Course Computer Science Course 3CFU does not have prerequisites
Teaching methods
Frontal and participatory lesson in class with multimedia aid.
The Computer Science Course 3CFU is provided as a blended-learning course.
For acquisition of expected knowledge, a student has to browse the program contents on the online course according to an e-learning modality. Contents are organized into the following training courses: G) Foundations of Computer Science, F) Spreadsheets, B) Information management, and I) Internet and web. A training course is then articulated into thematic modules. Students have to pass a self-evaluation test at the end of each thematic module. Initially, a student can access just an introductory module. The access to subsequent modules is progressively enabled when the test of available modules is successfully passed. For acquisition of expected skills, a student can attend two exercise sessions in a computer-science room. Each exercise session is three hours long. The attendance to exercise sessions is not a mandatory requirement for successfully pass the Course and obtain the credits, however students are strongly encouraged to attend the exercise sessions.
The Computer Science Course 3CFU is provided as a blended-learning course.
For acquisition of expected knowledge, a student has to browse the program contents on the online course according to an e-learning modality. Contents are organized into the following training courses: G) Foundations of Computer Science, F) Spreadsheets, B) Information management, and I) Internet and web. A training course is then articulated into thematic modules. Students have to pass a self-evaluation test at the end of each thematic module. Initially, a student can access just an introductory module. The access to subsequent modules is progressively enabled when the test of available modules is successfully passed. For acquisition of expected skills, a student can attend two exercise sessions in a computer-science room. Each exercise session is three hours long. The attendance to exercise sessions is not a mandatory requirement for successfully pass the Course and obtain the credits, however students are strongly encouraged to attend the exercise sessions.
Teaching Resources
Any commercially available Mathematics text adopted in high school, which mainly covers topics discussed in the fourth and fifth years of high school.
Assessment methods and Criteria
Written test: 8 exercises to be completed in 120 minutes related to the practical and theoretical aspects discussed in class.
Evaluation expressed in thirtieths.
The assessment of basic IT skills is detected through a centralized UNIMI service. The evaluation is expressed in thirtieths.
The final evaluation is given by the arithmetic average of the single positive evaluations obtained.
Computer Science Course 3CFU: The examination is articulated in two distinct evaluation steps.
The first evaluation step consists in the successful completion of self-evaluation tests related to all the thematic modules that constitute the training courses. The tests are composed of choice questions on the whole Course program. The completion of all the expected self-evaluation tests is a mandatory requirement for accessing to the subsequent evaluation step (final exam).
The second evaluation step (final exam) consists successfully pass a test in a computer-science room. The test one hour long and it is based on choice questions on the whole Course program. The questions aim to evaluate the expected acquisition of both knowledge and skills. During the test, it is not possible to use paper stuff and to access web resources that are not explicitly authorized. The final exam result is expressed in thirtieths. The Academic Exam System (SIFA) is exploited by students for subscription to the final exam.
Evaluation expressed in thirtieths.
The assessment of basic IT skills is detected through a centralized UNIMI service. The evaluation is expressed in thirtieths.
The final evaluation is given by the arithmetic average of the single positive evaluations obtained.
Computer Science Course 3CFU: The examination is articulated in two distinct evaluation steps.
The first evaluation step consists in the successful completion of self-evaluation tests related to all the thematic modules that constitute the training courses. The tests are composed of choice questions on the whole Course program. The completion of all the expected self-evaluation tests is a mandatory requirement for accessing to the subsequent evaluation step (final exam).
The second evaluation step (final exam) consists successfully pass a test in a computer-science room. The test one hour long and it is based on choice questions on the whole Course program. The questions aim to evaluate the expected acquisition of both knowledge and skills. During the test, it is not possible to use paper stuff and to access web resources that are not explicitly authorized. The final exam result is expressed in thirtieths. The Academic Exam System (SIFA) is exploited by students for subscription to the final exam.
Informatics
MAT/09 - OPERATIONS RESEARCH
MAT/08 - NUMERICAL ANALYSIS
MAT/07 - MATHEMATICAL PHYSICS
MAT/06 - PROBABILITY AND STATISTICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/03 - GEOMETRY
MAT/02 - ALGEBRA
MAT/01 - MATHEMATICAL LOGIC
INF/01 - INFORMATICS
MAT/08 - NUMERICAL ANALYSIS
MAT/07 - MATHEMATICAL PHYSICS
MAT/06 - PROBABILITY AND STATISTICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/03 - GEOMETRY
MAT/02 - ALGEBRA
MAT/01 - MATHEMATICAL LOGIC
INF/01 - INFORMATICS
Basic computer skills: 18 hours
Mathematics
MAT/01 - MATHEMATICAL LOGIC
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
INF/01 - INFORMATICS
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
INF/01 - INFORMATICS
Lessons: 32 hours
Professor:
De Paoli Camilla
Educational website(s)
Professor(s)
Reception:
by appointment
Teams