Principles of Mathematics and Computer Skills
A.Y. 2024/2025
Learning objectives
The course is aimed at providing the student with fundamentals of mathematical analysis and descriptive statistics. One major goal is to develop the ability to analyze the behavior of a real variable function, determining its graph in a Cartesian system through basic elements of differential calculation. A further important objective is to develop essential skills in experimental data processing by introducing commonly used statistical descriptors. The course is also aimed at providing knowledge in computer science particularly with reference to the fundamentals of the discipline, spreadsheets, information management and the internet and web. Furthermore, it provides the student with skills in the use of the main functionalities of spreadsheet software tools, with a focus on the use of formulae, functions and chart creation.
Expected learning outcomes
Through this course the student will acquire fundamentals of mathematical analysis related to the study of a real function. Particularly, she/he will understand the meaning of domain of a function, continuity of a function in an interval and derivative of a function in a point. The student will have to demonstrate that she/he has gained knowledge of the main statistical descriptors that allow an experimental data set to be interpreted. Moreover, she/he will be able to interpret the progress of a function and describe data on a statistical level. Through application of what has been learned, the student will also manage to interpret the trend of variables that are the subject of her/his research.
Regarding computer science, the student will acquire fundamentals of the discipline and knowledge of spreadsheets, information management as well as the internet and web. Particularly, this knowledge will have to cover the historical foundations of computer science, structure and organization of computers, information coding, units of measurement of information, definition of algorithm and software, digital representation of text, audio and video contents, classification of software tools, security issues and risks related to the use of digital technologies, definition and structure of spreadsheet, calculation functions in Microsoft Excel, definition of data and information, databases, statistical functions and chart creation in Microsoft Excel, databases, relational database model, database systems, similarities and differences between spreadsheets and relational databases, database languages, query composition, web databases, basics 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. Along with knowledge of the above-mentioned topics, the student will acquire skills in organizing data, dragging and dropping formulae and formatting cells in a spreadsheet as well as using general and statistical functions and creating charts in Microsoft Excel.
Regarding computer science, the student will acquire fundamentals of the discipline and knowledge of spreadsheets, information management as well as the internet and web. Particularly, this knowledge will have to cover the historical foundations of computer science, structure and organization of computers, information coding, units of measurement of information, definition of algorithm and software, digital representation of text, audio and video contents, classification of software tools, security issues and risks related to the use of digital technologies, definition and structure of spreadsheet, calculation functions in Microsoft Excel, definition of data and information, databases, statistical functions and chart creation in Microsoft Excel, databases, relational database model, database systems, similarities and differences between spreadsheets and relational databases, database languages, query composition, web databases, basics 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. Along with knowledge of the above-mentioned topics, the student will acquire skills in organizing data, dragging and dropping formulae and formatting cells in a spreadsheet as well as using general and statistical functions and creating charts 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
Mathematics Program
- Review of fundamental prerequisites: number sets, algebra review, equations, inequalities, logarithms, and exponentials.
- Functions and graphs. Domain, codomain and function study. Properties of functions: injective, surjective, and bijective functions. Even and odd functions. Periodic functions. Inverse function and composite function.
- Graphs of elementary functions: lines, powers, parabolas, exponentials, logarithms, and trigonometric functions.
- Concept of limit. Limits of elementary functions. Scale of infinities.
- Continuous and discontinuous functions.
- Derivatives: derivative of a functions at a point and its geometric interpretation. Tangent line to the graph of a function at a point. Points of non-differentiability.
- Differentiation rules. Operations with derivatives: sum, product, quotient, and composition of functions.
- Higher-order derivatives.
- Application of derivatives to the study of the graph of a function.
- Elements of statistics: random variables, measures of central tendency and variability, correlation, and linear regression.
Computer Science Assessment Program
- Fundamentals of computer science
- Introduction to computer science
- Information encoding
- Computer structure
- Programs and software
- Risks of the "Infosphere"
- Spreadsheets
- Introduction to spreadsheets
- Calculation functions in Excel
- Statistical functions in Excel
- Creating charts in Excel
- Information management
- Introduction to information management
- Data storage and databases
- Relational databases
- Creating a database
- Composing queries
- Web databases
- Internet and web
- Computer networks
- The Internet
- Web architecture
- Web standards
- Web content
- Search engines
- Evolution of the web
- Review of fundamental prerequisites: number sets, algebra review, equations, inequalities, logarithms, and exponentials.
- Functions and graphs. Domain, codomain and function study. Properties of functions: injective, surjective, and bijective functions. Even and odd functions. Periodic functions. Inverse function and composite function.
- Graphs of elementary functions: lines, powers, parabolas, exponentials, logarithms, and trigonometric functions.
- Concept of limit. Limits of elementary functions. Scale of infinities.
- Continuous and discontinuous functions.
- Derivatives: derivative of a functions at a point and its geometric interpretation. Tangent line to the graph of a function at a point. Points of non-differentiability.
- Differentiation rules. Operations with derivatives: sum, product, quotient, and composition of functions.
- Higher-order derivatives.
- Application of derivatives to the study of the graph of a function.
- Elements of statistics: random variables, measures of central tendency and variability, correlation, and linear regression.
Computer Science Assessment Program
- Fundamentals of computer science
- Introduction to computer science
- Information encoding
- Computer structure
- Programs and software
- Risks of the "Infosphere"
- Spreadsheets
- Introduction to spreadsheets
- Calculation functions in Excel
- Statistical functions in Excel
- Creating charts in Excel
- Information management
- Introduction to information management
- Data storage and databases
- Relational databases
- Creating a database
- Composing queries
- Web databases
- Internet and web
- Computer networks
- The Internet
- Web architecture
- Web standards
- Web content
- Search engines
- Evolution of the web
Prerequisites for admission
Basic knowledge of arithmetic and algebra: literal calculations, first and second-degree numerical equations in R; first and second-degree inequalities in R.
For the Computer Science assessment (3 CFU), no preliminary knowledge is required.
For the Computer Science assessment (3 CFU), no preliminary knowledge is required.
Teaching methods
Interactive lectures.
For the Computer Science assessment, students must consult the program content via e-learning through the online course of the subject. The contents are organized into learning paths such as: G) fundamentals of computer science, F) spreadsheets, B) information management, I) Internet and web. Each path is divided into thematic modules, each ending with a self-assessment test. Initially, students only have access to an introductory module. Access to subsequent modules is gradual and conditional upon the progressive passing of the self-assessment tests of the accessible modules.
Additionally, two laboratory sessions in the computer room are scheduled for exercises aimed at acquiring the skills covered by the course. Participation in the exercises is not mandatory but highly recommended.
For the Computer Science assessment, students must consult the program content via e-learning through the online course of the subject. The contents are organized into learning paths such as: G) fundamentals of computer science, F) spreadsheets, B) information management, I) Internet and web. Each path is divided into thematic modules, each ending with a self-assessment test. Initially, students only have access to an introductory module. Access to subsequent modules is gradual and conditional upon the progressive passing of the self-assessment tests of the accessible modules.
Additionally, two laboratory sessions in the computer room are scheduled for exercises aimed at acquiring the skills covered by the course. Participation in the exercises is not mandatory but highly recommended.
Teaching Resources
Any high school mathematics textbook that mainly covers topics from the fourth and fifth years of secondary school.
The teaching materials for the Computer Science assessment are available in the online course at: https://3cfuinformatica.unimi.it
The teaching materials for the Computer Science assessment are available in the online course at: https://3cfuinformatica.unimi.it
Assessment methods and Criteria
Mathematics Written Test: Exercises to be completed in 120 minutes on the practical and theoretical aspects discussed in the lessons. Evaluation is expressed in thirtieths.
The assessment of basic computer skills is carried out through a centralized UNIMI service. Evaluation is expressed in thirtieths.
The final grade is the average of the individual positive evaluations obtained.
For the Computer Science Assessment 3 CFU, the learning assessment occurs in two distinct phases. The first assessment is a self-evaluation within the online course dedicated to the subject through the completion of multiple-choice tests related to the thematic modules that make up the learning paths. Completing all self-evaluation tests is a necessary condition to access the subsequent learning assessment (final exam).
The second assessment (final exam) takes place in the computer room and consists of a one-hour computer test with multiple-choice questions on all the topics covered in the subject program. The questions aim to verify the acquisition of the knowledge and skills expected from the course. During the test, it will not be possible to use paper materials or access web resources other than those explicitly enabled on the computer used for the test.
The assessment of basic computer skills is carried out through a centralized UNIMI service. Evaluation is expressed in thirtieths.
The final grade is the average of the individual positive evaluations obtained.
For the Computer Science Assessment 3 CFU, the learning assessment occurs in two distinct phases. The first assessment is a self-evaluation within the online course dedicated to the subject through the completion of multiple-choice tests related to the thematic modules that make up the learning paths. Completing all self-evaluation tests is a necessary condition to access the subsequent learning assessment (final exam).
The second assessment (final exam) takes place in the computer room and consists of a one-hour computer test with multiple-choice questions on all the topics covered in the subject program. The questions aim to verify the acquisition of the knowledge and skills expected from the course. During the test, it will not be possible to use paper materials or access web resources other than those explicitly enabled on the computer used for the test.
INF/01 - INFORMATICS - University credits: 3
MAT/01 - MATHEMATICAL LOGIC - University credits: 3
MAT/01 - MATHEMATICAL LOGIC - University credits: 3
Basic computer skills: 18 hours
Lessons: 24 hours
Lessons: 24 hours
Professor:
Biasibetti Luca
Educational website(s)
Professor(s)