Mathematics I and Information Tecnology
A.Y. 2023/2024
Learning objectives
Modulo Mathematic I
Learning the basic facts about real functions of a real variable and of linear algebra
Applying knowledge and understanding
Given an exercise, to choose the right part of the theory to solve it, and to apply it in the correct way
Modulo informatica:
To supply fundamentals of computer science, balancing practical aspects related to usage of computers with basic theoretical notions on information management and computer networks.
Learning the basic facts about real functions of a real variable and of linear algebra
Applying knowledge and understanding
Given an exercise, to choose the right part of the theory to solve it, and to apply it in the correct way
Modulo informatica:
To supply fundamentals of computer science, balancing practical aspects related to usage of computers with basic theoretical notions on information management and computer networks.
Expected learning outcomes
Modulo Mathematic I:
To be able to talk about mathematics explaining both concepts and reasoning.
Learning skills
Given a mathematical problem, to find the right part of a book needed to solve it.
Modulo di Informatica:
Knowledge of the fundamentals of computer science. Structure and behavior of computer networks and Web. Usage of search engines for information retrieval. Usage of spreadsheets for creation of formulas and generation of graphs. Basic notions regarding databases and related tools for management and storage of information.
To be able to talk about mathematics explaining both concepts and reasoning.
Learning skills
Given a mathematical problem, to find the right part of a book needed to solve it.
Modulo di Informatica:
Knowledge of the fundamentals of computer science. Structure and behavior of computer networks and Web. Usage of search engines for information retrieval. Usage of spreadsheets for creation of formulas and generation of graphs. Basic notions regarding databases and related tools for management and storage of information.
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
Prerequisites for admission
There are no prerequisites
Assessment methods and Criteria
The exam of the Mathematics module consists of a written test with some exercises and theorical questions. The oral test is not mandatory. The exam of this part ends with a final mark on 30 points.
The examination of the Computer Science module is a laboratory test with final mark "Approved/Not approved".
The examination of the Computer Science module is a laboratory test with final mark "Approved/Not approved".
Matematica I
Course syllabus
1) Rational numbers, real numbers: operations, comparison and reference system on the straight line. Maximum, minimum of a set of real numbers.
2) Real functions of real variable, composition and inverse functions. Elementary functions: powers, exponentials, logarithms and trigonometric; their properties and their graphs.
Equations and inequalities: algebraic, irrational, exponential, logarithmic and trigonometric.
3) Limits of functions: definitions and main properties (uniqueness, permanence of the sign, comparison). Remarkable limits. Comparison between infinites and infinitesimals. Continuity of functions: definition and discontinuity. Main properties: Weierstrass, zero and intermediate value theorems.
4) Differential calculus: definition of derivative, derivatives of elementary functions, derivation rules. Derivative of composition of functions. Absolute and relative extremes, stationary points. Fermat and Lagrange theorems and their consequences. Higher order derivatives. Concave and convex functions. Taylor formula with remainder according to Peano. Study of the graph of a function.
5) Integral calculation. Indefinite integral and integration methods. Defined integral: definition and geometric meaning of the definite integral. Integral function, theorem and fundamental formula of integral calculus. Integral mean theorem. Improper or generalized integrals.
6) Linear algebra: matrices and determinants. Inverse matrix of an invertible matrix. Rank of a matrix. Eigenvalues and eigenvectors of a matrix. Diagonalization of a symmetric matrix.
7) Linear systems and their matrix representation. Linear systems solution: Cramer and Rouché-Capelli theorems.
2) Real functions of real variable, composition and inverse functions. Elementary functions: powers, exponentials, logarithms and trigonometric; their properties and their graphs.
Equations and inequalities: algebraic, irrational, exponential, logarithmic and trigonometric.
3) Limits of functions: definitions and main properties (uniqueness, permanence of the sign, comparison). Remarkable limits. Comparison between infinites and infinitesimals. Continuity of functions: definition and discontinuity. Main properties: Weierstrass, zero and intermediate value theorems.
4) Differential calculus: definition of derivative, derivatives of elementary functions, derivation rules. Derivative of composition of functions. Absolute and relative extremes, stationary points. Fermat and Lagrange theorems and their consequences. Higher order derivatives. Concave and convex functions. Taylor formula with remainder according to Peano. Study of the graph of a function.
5) Integral calculation. Indefinite integral and integration methods. Defined integral: definition and geometric meaning of the definite integral. Integral function, theorem and fundamental formula of integral calculus. Integral mean theorem. Improper or generalized integrals.
6) Linear algebra: matrices and determinants. Inverse matrix of an invertible matrix. Rank of a matrix. Eigenvalues and eigenvectors of a matrix. Diagonalization of a symmetric matrix.
7) Linear systems and their matrix representation. Linear systems solution: Cramer and Rouché-Capelli theorems.
Teaching methods
Frontal lessons with the projection of previously prepared beamers, examples and exercises carried out on the blackboard.
Teaching Resources
Matematica Assistita" - theory lessons, exercises and exercise solutions.
All the material is available (in italian) on the e-learning platform of the University "Ariel"
All the material is available (in italian) on the e-learning platform of the University "Ariel"
Informatica
Course syllabus
The Course program is focused on the following topics:
· Foundations of Computer Science
o Introduction to Computer Science
o Information coding
o Computer structure
o Programs and software
o The "Infosphera" risks
· Spreadsheets
o Introduction to spreadsheets
o General functions in Excel
o Statistical functions in Excel
o Chart creation in Excel
· Information management
o Introduction to information management
o Data storing and databases
o Relational databases
o Database creation
o Query composition
o Web databases
· 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
· Foundations of Computer Science
o Introduction to Computer Science
o Information coding
o Computer structure
o Programs and software
o The "Infosphera" risks
· Spreadsheets
o Introduction to spreadsheets
o General functions in Excel
o Statistical functions in Excel
o Chart creation in Excel
· Information management
o Introduction to information management
o Data storing and databases
o Relational databases
o Database creation
o Query composition
o Web databases
· 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
Teaching methods
The Course 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 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.
Teaching Resources
The teaching stuff is online at https://3cfuinformatica.unimi.it
Informatica
INF/01 - INFORMATICS - University credits: 3
Basic computer skills: 18 hours
Matematica I
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
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
Practicals: 36 hours
Lessons: 24 hours
Lessons: 24 hours
Professors:
Cavaterra Cecilia, Salvatori Maura Elisabetta
Educational website(s)
Professor(s)
Reception:
appointment via email
Dipartimento di Matematica, Via Saldini 50 - ufficio n. 2060