Mathematics I and Information Tecnology
A.Y. 2022/2023
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 cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
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 and an oral test 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 course is passed when both modules have been passed. The final mark, expressed in the range 0-30, is the one obtained in the Mathematics part.
The written exam in the Mathematics module contains multiple choice and open exercises and aims to value the student's ability to solve exercises close the topics covered in the course.
The written test can be replaced by two ongoing tests during the year. Students with written exam almost sufficient are allowed to do the compulsory oral exam.
Starting from the contents of the written part, the oral exam focuses on the definitions of the concepts and on the fundamental theorems and their applications.
For the Computer Science module, 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 Course evaluation is expressed through an "Approved" - "Not approved" result. The Academic Exam System (SIFA) is exploited by students for subscription to the final exam and for getting the results of taken exams.
The examination of the Computer Science module is a laboratory test with final mark "Approved/Not approved".
The course is passed when both modules have been passed. The final mark, expressed in the range 0-30, is the one obtained in the Mathematics part.
The written exam in the Mathematics module contains multiple choice and open exercises and aims to value the student's ability to solve exercises close the topics covered in the course.
The written test can be replaced by two ongoing tests during the year. Students with written exam almost sufficient are allowed to do the compulsory oral exam.
Starting from the contents of the written part, the oral exam focuses on the definitions of the concepts and on the fundamental theorems and their applications.
For the Computer Science module, 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 Course evaluation is expressed through an "Approved" - "Not approved" result. The Academic Exam System (SIFA) is exploited by students for subscription to the final exam and for getting the results of taken exams.
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
Frontal lessons with the projection of previously prepared beamers, examples and exercises carried out on the blackboard.
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
Professor(s)
Reception:
appointment via email
Dipartimento di Matematica, Via Saldini 50 - ufficio n. 2060