Mathematics I and Information Tecnology
A.Y. 2019/2020
Learning objectives
The course of the module "Matematica" provides the basic notions of Calculus. In particular it is focused on: the real number system, real functions and their properties, a basic on linear algebra. Furthermore the course gives practical skills to solve exercises as an application of the theoretical part.
The course of the module "Matematica" provides the basic notions of Calculus. In particular it is focused on: the real number system, real functions and their properties, a basic on linear algebra. Furthermore the course gives practical skills to solve exercises as an application of the theoretical part.
The course of the module "Matematica" provides the basic notions of Calculus. In particular it is focused on: the real number system, real functions and their properties, a basic on linear algebra. Furthermore the course gives practical skills to solve exercises as an application of the theoretical part.
Expected learning outcomes
Module "Matematica". The student will have knowledge of the topics covered the the program. In particular she/he will know definitions, examples, and the principal theorems and results in the program. Furthermore, the student will show skills in th choice and use of the appropriate theoretical stuff in order to solve mathematical exercises.
Module "Informatica". 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,
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
Module "Informatica". 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,
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 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.
The examination of the Computer Science module is a laboratory test.
The course is passed when both modules have been passed. The final mark, expressed in the range 0-30, is obtained, starting from the one obtained in the Mathematics module by adding a delta which can be -1, 0, +1.
To the math mark -1 is added if the result of the Computer Science module is 18/30 or 19/30, while +1 is added if the Computer Science result is at least 27/30.
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.
The course is passed when both modules have been passed. The final mark, expressed in the range 0-30, is obtained, starting from the one obtained in the Mathematics module by adding a delta which can be -1, 0, +1.
To the math mark -1 is added if the result of the Computer Science module is 18/30 or 19/30, while +1 is added if the Computer Science result is at least 27/30.
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.
Mathematics I
Course syllabus
1) Rational numbers, real numbers: operations, comparison and reference system on the straight line. Maximum, minimum, sup and inf of a set of real numbers.
2) Real functions of real variable, composition and inverse functions. Elementary functions: powers, exponentials, logarithms and trigonometric and their properties.
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 and inverse 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 and their properties.
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 and inverse 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"
Information Tecnology
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 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.
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
The teaching stuff is online at https://3cfuinformatica.unimi.it
Information Tecnology
INF/01 - INFORMATICS - University credits: 3
Basic computer skills: 18 hours
Mathematics 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
Professor:
Salvatori Maura Elisabetta
Shifts:
-
Professor:
Salvatori Maura ElisabettaProfessor(s)