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Course 2023-2024 a.y.

30122 - PRECORSO DI MATEMATICA / MATHEMATICS - PREPARATORY COURSE

Department of Decision Sciences

For the instruction language of the course see class group/s below

Go to class group/s: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 15 - 16 - 17 - 18 - 21 - 22 - 23 - 25 - 27

CLEAM (I sem. - P)
Course Director:
GUIDO OSIMO

Classi: 1 (I sem.) - 2 (I sem.) - 3 (I sem.) - 4 (I sem.) - 5 (I sem.) - 6 (I sem.) - 7 (I sem.) - 8 (I sem.)
Docenti responsabili delle classi:
Classe 1: ENRICO MORETTO, Classe 2: FEDERICA ANDREANO, Classe 3: ZELINDA CACCIA, Classe 4: MAURO D'AMICO, Classe 5: GUIDO OSIMO, Classe 6: LAURA MARIANO, Classe 7: FABIO TONOLI, Classe 8: ELISA TACCONI

Classe/i impartita/e in lingua italiana

Synchronous Blended: Lessons in synchronous mode in the classroom (for a maximum of one hour per credit in remote mode)

Mission e Programma sintetico
MISSION

Il precorso di matematica ha l’obiettivo di consolidare alcuni argomenti di matematica a livello pre-universitario, per permettere allo studente di iniziare gli studi universitari con serenità e competenza. Negli studi universitari questi argomenti sono dati per noti e non sono ripetuti. Il precorso è erogato in modalità blended learning, ovvero in parte on-line e in parte in presenza. La parte on-line è accessibile a partire dall’estate che precede il primo anno di studi universitari. La parte in presenza tratta argomenti diversi dalla parte on-line, si articola su 12 ore di corso e si svolge interamente durante la Welcome Week del primo anno. È preferibile che gli studenti fruiscano della parte on-line prima dell’inizio della parte in presenza. La conoscenza dei contenuti della parte on-line e della parte in presenza è un elemento importante per ottenere buoni risultati nei primi esami di matematica previsti nel piano di studi.

PROGRAMMA SINTETICO

Parte online:

  • Insiemi. Operazioni tra insiemi. Insiemi numerici. Rappresentazione degli insiemi numerici sulla retta.
  • Potenze a esponente intero. Radici. Potenze a esponente razionale e a esponente reale.
  • Calcolo letterale.
  • Equazioni di primo e secondo grado. Equazioni di grado superiore al secondo. Equazioni frazionarie. Sistemi di equazioni.
  • Coordinate cartesiane nel piano. Rette. Parabole. Altre curve.
  • Elementi di trigonometria.
  • Disequazioni di primo e secondo grado. Disequazioni di grado superiore al secondo. Disequazioni frazionarie. Sistemi di disequazioni. Equazioni e disequazioni con termini in valore assoluto.

Parte in presenza:

  • Funzioni reali di una variabile reale: definizione, grafico, esempi. Funzioni suriettive, iniettive, biunivoche. Funzione composta. Funzione inversa. Funzioni potenza e loro grafici. Funzioni esponenziali e loro grafici. Introduzione ai logaritmi. Proprietà dei logaritmi. Funzioni logaritmiche e loro grafici. Funzioni trigonometriche e loro grafici. Funzioni definite a tratti. Funzione modulo. Trasformazioni di funzioni elementari. Funzioni limitate, crescenti, decrescenti.
  • Rapporto incrementale, derivata. Derivate delle funzioni elementari. Algebra delle derivate. Derivata della funzione composta. Equazione della retta tangente.
  • La matematica come sistema assiomatico: nozioni primitive e definizioni, assiomi e teoremi. Terminologia di base sui teoremi. Esempi di dimostrazioni e di tecniche dimostrative. Congetture: dimostrazioni e controesempi. Implicazione, equivalenza. Condizione sufficiente, condizione necessaria, condizione necessaria e sufficiente. La negazione di una proposizione. Esempi di dimostrazioni per assurdo. Esempi di dimostrazioni per contronominale.

Risultati di Apprendimento Attesi (RAA)
CONOSCENZA E COMPRENSIONE
Al termine dell'insegnamento, lo studente sarà in grado di...

  

CAPACITA' DI APPLICARE CONOSCENZA E COMPRENSIONE
Al termine dell'insegnamento, lo studente sarà in grado di...

  


Modalità didattiche
  • Lezioni frontali
  • Lezioni online
DETTAGLI

Lezioni online: la prima parte del precorso si svolge online, sulla piattaforma didattica Bboard.


Metodi di valutazione dell'apprendimento
  Accertamento in itinere Prove parziali Prova generale
  • Partecipazione in aula (virtuale, fisica)
  • x x x
    STUDENTI FREQUENTANTI E NON FREQUENTANTI

        La valutazione dell'apprendimento avviene all'interno del corso di matematica di primo anno, con le modalità definite da quel corso.


    Materiali didattici
    STUDENTI FREQUENTANTI E NON FREQUENTANTI
    • Parte online: tutti i materiali didattici sono disponibili sulla piattaforma Bboard.
    • Parte in presenza: sarà utilizzato il testo Corso preparatorio in Matematica, Guido Osimo, EGEA (2019), ISBN 978-88-7534-186-2.
    Modificato il 02/06/2023 11:45

    CLEF (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classi: 9 (I sem.) - 10 (I sem.)
    Docenti responsabili delle classi:
    Classe 9: JACOPO GIUSEPPE DE TULLIO, Classe 10: FRANCESCA SIANESI

    Classe/i impartita/e in lingua italiana

    Synchronous Blended: Lessons in synchronous mode in the classroom (for a maximum of one hour per credit in remote mode)

    Mission e Programma sintetico
    MISSION

    Il precorso di matematica ha l’obiettivo di consolidare alcuni argomenti di matematica a livello pre-universitario, per permettere allo studente di iniziare gli studi universitari con serenità e competenza. Negli studi universitari questi argomenti sono dati per noti e non sono ripetuti. Il precorso è erogato in modalità blended learning, ovvero in parte on-line e in parte in presenza. La parte on-line è accessibile a partire dall’estate che precede il primo anno di studi universitari. La parte in presenza tratta argomenti diversi dalla parte on-line, si articola su 12 ore di corso e si svolge interamente durante la Welcome Week del primo anno. È preferibile che gli studenti fruiscano della parte on-line prima dell’inizio della parte in presenza. La conoscenza dei contenuti della parte on-line e della parte in presenza è un elemento importante per ottenere buoni risultati nei primi esami di matematica previsti nel piano di studi.

    PROGRAMMA SINTETICO

    Parte online:

    • Insiemi. Operazioni tra insiemi. Insiemi numerici. Rappresentazione degli insiemi numerici sulla retta.
    • Potenze a esponente intero. Radici. Potenze a esponente razionale e a esponente reale.
    • Calcolo letterale.
    • Equazioni di primo e secondo grado. Equazioni di grado superiore al secondo. Equazioni frazionarie. Sistemi di equazioni.
    • Coordinate cartesiane nel piano. Rette. Parabole. Altre curve.
    • Elementi di trigonometria.
    • Disequazioni di primo e secondo grado. Disequazioni di grado superiore al secondo. Disequazioni frazionarie. Sistemi di disequazioni. Equazioni e disequazioni con termini in valore assoluto.

    Parte in presenza:

    • Funzioni reali di una variabile reale: definizione, grafico, esempi. Funzioni suriettive, iniettive, biunivoche. Funzione composta. Funzione inversa. Funzioni potenza e loro grafici. Funzioni esponenziali e loro grafici. Introduzione ai logaritmi. Proprietà dei logaritmi. Funzioni logaritmiche e loro grafici. Funzioni trigonometriche e loro grafici. Funzioni definite a tratti. Funzione modulo. Trasformazioni di funzioni elementari. Funzioni limitate, crescenti, decrescenti.
    • Rapporto incrementale, derivata. Derivate delle funzioni elementari. Algebra delle derivate. Derivata della funzione composta. Equazione della retta tangente.
    • La matematica come sistema assiomatico: nozioni primitive e definizioni, assiomi e teoremi. Terminologia di base sui teoremi. Esempi di dimostrazioni e di tecniche dimostrative. Congetture: dimostrazioni e controesempi. Implicazione, equivalenza. Condizione sufficiente, condizione necessaria, condizione necessaria e sufficiente. La negazione di una proposizione. Esempi di dimostrazioni per assurdo. Esempi di dimostrazioni per contronominale.

    Risultati di Apprendimento Attesi (RAA)
    CONOSCENZA E COMPRENSIONE
    Al termine dell'insegnamento, lo studente sarà in grado di...

      

    CAPACITA' DI APPLICARE CONOSCENZA E COMPRENSIONE
    Al termine dell'insegnamento, lo studente sarà in grado di...

      


    Modalità didattiche
    • Lezioni frontali
    • Lezioni online
    DETTAGLI

    Lezioni online: la prima parte del precorso si svolge online, sulla piattaforma didattica Bboard.


    Metodi di valutazione dell'apprendimento
      Accertamento in itinere Prove parziali Prova generale
  • Partecipazione in aula (virtuale, fisica)
  • x x x
    STUDENTI FREQUENTANTI E NON FREQUENTANTI

       La valutazione dell'apprendimento avviene all'interno del corso di matematica di primo anno, primo semestre, con le modalità definite da quel corso.


    Materiali didattici
    STUDENTI FREQUENTANTI E NON FREQUENTANTI
    • Parte online: tutti i materiali didattici sono disponibili sulla piattaforma Bboard.
    • Parte in presenza: sarà utilizzato il testo Corso preparatorio in Matematica, Guido Osimo, EGEA (2019), ISBN 978-88-7534-186-2.
    Modificato il 02/06/2023 11:48

    CLEACC (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classi: 11 (I sem.)
    Docenti responsabili delle classi:
    Classe 11: ELISA CAPRARI

    Classe/i impartita/e in lingua italiana

    Synchronous Blended: Lessons in synchronous mode in the classroom (for a maximum of one hour per credit in remote mode)

    Mission e Programma sintetico
    MISSION

    Il precorso di matematica ha l’obiettivo di consolidare alcuni argomenti di matematica a livello pre-universitario, per permettere allo studente di iniziare gli studi universitari con serenità e competenza. Negli studi universitari questi argomenti sono dati per noti e non sono ripetuti. Il precorso è erogato in modalità blended learning, ovvero in parte on-line e in parte in presenza. La parte on-line è accessibile a partire dall’estate che precede il primo anno di studi universitari. La parte in presenza tratta argomenti diversi dalla parte on-line, si articola su 12 ore di corso e si svolge interamente durante la Welcome Week del primo anno. È preferibile che gli studenti fruiscano della parte on-line prima dell’inizio della parte in presenza. La conoscenza dei contenuti della parte on-line e della parte in presenza è un elemento importante per ottenere buoni risultati nei primi esami di matematica previsti nel piano di studi.

    PROGRAMMA SINTETICO

    Parte online:

    • Insiemi. Operazioni tra insiemi. Insiemi numerici. Rappresentazione degli insiemi numerici sulla retta.
    • Potenze a esponente intero. Radici. Potenze a esponente razionale e a esponente reale.
    • Calcolo letterale.
    • Equazioni di primo e secondo grado. Equazioni di grado superiore al secondo. Equazioni frazionarie. Sistemi di equazioni.
    • Coordinate cartesiane nel piano. Rette. Parabole. Altre curve.
    • Disequazioni di primo e secondo grado. Disequazioni di grado superiore al secondo. Disequazioni frazionarie. Sistemi di disequazioni. Equazioni e disequazioni con termini in valore assoluto.

    Parte in presenza:

    • Funzioni reali di una variabile reale: definizione, grafico, esempi. Funzione composta. Funzione inversa. Funzioni potenza e loro grafici. Funzioni esponenziali e loro grafici. Introduzione ai logaritmi. Proprietà dei logaritmi. Funzioni logaritmiche e loro grafici. Funzioni definite a tratti. Funzione modulo. Trasformazioni di funzioni elementari.
    • Equazioni e disequazioni esponenziali/logaritmiche. Semplici equazioni e disequazioni irrazionali.

    Risultati di Apprendimento Attesi (RAA)
    CONOSCENZA E COMPRENSIONE
    Al termine dell'insegnamento, lo studente sarà in grado di...

       

    CAPACITA' DI APPLICARE CONOSCENZA E COMPRENSIONE
    Al termine dell'insegnamento, lo studente sarà in grado di...

       


    Modalità didattiche
    • Lezioni frontali
    • Lezioni online
    DETTAGLI

    Lezioni online: la prima parte del precorso si svolge online, sulla piattaforma didattica Bboard.


    Metodi di valutazione dell'apprendimento
      Accertamento in itinere Prove parziali Prova generale
  • Partecipazione in aula (virtuale, fisica)
  • x x x
    STUDENTI FREQUENTANTI E NON FREQUENTANTI

      La valutazione dell'apprendimento avviene all'interno del corso di matematica di primo anno, primo semestre, con le modalità definite da quel corso.


    Materiali didattici
    STUDENTI FREQUENTANTI E NON FREQUENTANTI
    • Parte online: tutti i materiali didattici sono disponibili sulla piattaforma Bboard.
    • Parte in presenza: materiali didattici a cura del docente.
    Modificato il 02/06/2023 11:50

    Classes: 12 (I sem.)
    Instructors:
    Class 12: LAURA MARIANO

    Class group/s taught in English

    Synchronous Blended: Lessons in synchronous mode in the classroom (for a maximum of one hour per credit in remote mode)

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 12 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

    Classroom part:

    • Real functions of one real variable: definition, graph, examples. Composite function. Inverse function. Power functions and their graphs. Exponential functions and their graphs. Introduction to logarithms. Properties of logarithms. Logarithmic functions and their graphs. Piecewise defined functions. Absolute value function. Transformation of elementary functions.
    • Exponential/logarithmic equations and inequalities. Simple irrational equations and inequalities.

    Intended Learning Outcomes (ILO)
    KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

      

    APPLYING KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

      


    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

    Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.


    Assessment methods
      Continuous assessment Partial exams General exam
  • Active class participation (virtual, attendance)
  • x x x
    ATTENDING AND NOT ATTENDING STUDENTS

       Assessment is included in the first year, first semester Mathematics course, with the methods used for that course.


    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: teaching materials prepared by the instructor.
    Last change 02/06/2023 11:51

    BESS-CLES (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classes: 13 (I sem.)
    Instructors:
    Class 13: MAURO D'AMICO

    Class group/s taught in English

    Synchronous Blended: Lessons in synchronous mode in the classroom (for a maximum of one hour per credit in remote mode)

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 12 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • Elements of trigonometry.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

    Classroom part:

    • Introduction to propositional logic. Basic logical connectives, truth tables. Tautology and contradiction. De Morgan’s laws. Conditional and biconditional statements. Contrapositive and converse statements. Predicates. Universal quantifiers. Negating quantified statements.

    • Sets. Operations on sets and logical connectives. Properties. Power set. Set of natural, integer, rational and irrational numbers. Factorial of a number. Binomial coefficient. Sum and product of numbers.
    • Meaning of the following terms: definition, theorem, proposition, lemma, corollary, and proof. Direct and contrapositive proofs. Proofs by contradiction. Special forms of the premise or of the conclusion. Proof by induction.
    • Order structure of R. Intervals. Lower and upper bounds. Bounded sets. Maxima and minima. Supremum and infimum. Least upper bound principle. The extended real line. Short review of powers and logarithms.
    • Notion of real function of one real variable. Domain, codomain, and image of a function. Surjective, injective, and bijective functions. Bounded functions. Elementary functions. Geometric notion of derivative of a function at a point. Derivatives of elementary functions. Algebra of derivatives. Introduction to the calculation of partial derivatives.

     


    Intended Learning Outcomes (ILO)
    KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

      

    APPLYING KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

      


    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

    Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.


    Assessment methods
      Continuous assessment Partial exams General exam
  • Active class participation (virtual, attendance)
  • x x x
    ATTENDING AND NOT ATTENDING STUDENTS

     Assessment is included in the first year, first semester mathematics course, with the methods used for that course.


    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: teaching materials prepared by the instructor.
    Last change 02/06/2023 11:53

    BEMACS (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classes: 25 (I sem.)
    Instructors:
    Class 25: FABIO TONOLI

    Class group/s taught in English

    Synchronous Blended: Lessons in synchronous mode in the classroom (for a maximum of one hour per credit in remote mode)

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 12 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Number systems.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • Elements of trigonometry.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

    Classroom part:

    • Introduction to proofs. Connectives, quantifiers. Demonstration techniques: direct, contrapositive and indirect (or by contradiction). Principle of induction.
    • Real functions of one real variable: definition, graph, examples. Surjective, injective, bijective functions. Composite function. Inverse function. Bounded and unbounded functions. Increasing and decreasing functions. Global extrema of a function. Concave and convex functions. Operations with functions (sum, difference, product and quotient). Linear combination of functions. Odd and even functions. Periodic functions. Elementary functions and their graphs: constant, linear, affine linear, power, exponential and logarithm. Piecewise defined functions. Elementary notion of continuity.
    • Derivative. Derivatives of elementary functions. Algebra of derivatives. Chain rule. Equation of the tangent line. Stationary points. Second derivative.

    Intended Learning Outcomes (ILO)
    KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

        

    APPLYING KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

        


    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

    Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.


    Assessment methods
      Continuous assessment Partial exams General exam
  • Active class participation (virtual, attendance)
  • x x x
    ATTENDING AND NOT ATTENDING STUDENTS

        Assessment is included in the first year, first semester Mathematics course, with the methods used for that course.


    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: teaching materials prepared by the instructor.
    Last change 02/06/2023 11:54

    BIEM (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classes: 15 (I sem.) - 16 (I sem.) - 17 (I sem.) - 18 (I sem.)
    Instructors:
    Class 15: JACOPO GIUSEPPE DE TULLIO, Class 16: DOVID FEIN, Class 17: MARIA BEATRICE ZAVELANI ROSSI, Class 18: FEDERICA ANDREANO

    Class group/s taught in English

    Synchronous Blended: Lessons in synchronous mode in the classroom (for a maximum of one hour per credit in remote mode)

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 12 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • Elements of trigonometry.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

    Classroom part:

    • Real functions of one real variable: definition, graph, examples. Surjective, injective, bijective functions. Composite function. Inverse function. Power functions and their graphs. Exponential functions and their graphs. Introduction to logarithms. Properties of logarithms. Logarithmic functions and their graphs. Trigonometric functions and their graphs. Piecewise defined functions. Absolute value function. Transformation of elementary functions. Bounded, increasing, decreasing functions.
    • Difference quotient, derivative. Derivatives of elementary functions. Algebra of derivatives. Chain rule. Equation of the tangent line.
    • Mathematics as an axiomatic system: primitive notions and definitions, axioms and theorems. Basic terminology on theorems. Examples of proofs and demonstration techniques. Conjectures: proofs and counterexamples. Implication, equivalence. Sufficient condition, necessary condition, necessary and sufficient condition. The negation of a proposition. Examples of proofs by contradiction. Examples of proofs by contrapositive.

    Intended Learning Outcomes (ILO)
    KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

      

    APPLYING KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

      


    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

    Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.


    Assessment methods
      Continuous assessment Partial exams General exam
  • Active class participation (virtual, attendance)
  • x x x
    ATTENDING AND NOT ATTENDING STUDENTS

       Assessment is included inside the first year, first semester mathematics course, with the methods used for that course.


    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: we use the textbook Preparatory Course in Mathematics, Guido Osimo, EGEA (2020), ISBN 978‐88‐7534‐200‐5.
    Last change 02/06/2023 11:56

    BAI (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classes: 27 (I sem.)
    Instructors:
    Class 27: GUIDO OSIMO

    Class group/s taught in English

    Synchronous Blended: Lessons in synchronous mode in the classroom (for a maximum of one hour per credit in remote mode)

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 15 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

       

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • Elements of trigonometry.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

     

    Classroom part:

    • Cartesian product. Relations. Equivalence relations, order relations. Functions. Surjective, injective, bijective functions. Internal operations, external operations. 
    • Real functions of one real variable. Composite function. Inverse function. Power functions and their graphs. Exponential functions and their graphs. Introduction to logarithms. Properties of logarithms. Logarithmic functions and their graphs. Trigonometric functions and their graphs. Inverse trigonometric functions and their graphs. Piecewise defined functions. Absolute value function. Transformations of elementary functions. Positive part and negative part of a function. Graphical solution of equations. Bounded functions. Increasing, decreasing, monotonic functions. Global maxima, global minima. 
    • Mathematics as an axiomatic system: axioms and theorems, primitive notions and definitions. Basic terminology on theorems. Examples of proofs and proving techniques. Conjectures: proofs and counterexamples. Implication, equivalence. Sufficient condition, necessary condition, necessary and sufficient condition. The negation of a proposition. Proofs by contradiction. Proofs by contrapositive. Proofs by induction.
    • Elements of combinatorics. Permutations, combinations. Binomial coefficients, Pascal's triangle, binomial theorem.

    Intended Learning Outcomes (ILO)
    KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

          

    APPLYING KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

          


    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

        Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.


    Assessment methods
      Continuous assessment Partial exams General exam
  • Active class participation (virtual, attendance)
  • x x x
    ATTENDING AND NOT ATTENDING STUDENTS

             Assessment is included in the first year mathematics courses, with the methods used for those courses.


    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS

        

    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: we use the textbook BAI Preparatory Course in Mathematics, Guido Osimo, EGEA (2022), ISBN 978-88-6407-473-3.
    Last change 02/06/2023 12:00

    BIEF (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classes: 21 (I sem.) - 22 (I sem.)
    Instructors:
    Class 21: ENRICO MORETTO, Class 22: ELISA CAPRARI

    Class group/s taught in English

    Synchronous Blended: Lessons in synchronous mode in the classroom (for a maximum of one hour per credit in remote mode)

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 12 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • Elements of trigonometry.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

    Classroom part:

    • Real functions of one real variable: definition, graph, examples. Surjective, injective, bijective functions. Composite function. Inverse function. Power functions and their graphs. Exponential functions and their graphs. Introduction to logarithms. Properties of logarithms. Logarithmic functions and their graphs. Trigonometric functions and their graphs. Piecewise defined functions. Absolute value function. Transformation of elementary functions. Bounded, increasing, decreasing functions.
    • Difference quotient, derivative. Derivatives of elementary functions. Algebra of derivatives. Chain rule. Equation of the tangent line.
    • Mathematics as an axiomatic system: primitive notions and definitions, axioms and theorems. Basic terminology on theorems. Examples of proofs and demonstration techniques. Conjectures: proofs and counterexamples. Implication, equivalence. Sufficient condition, necessary condition, necessary and sufficient condition. The negation of a proposition. Examples of proofs by contradiction. Examples of proofs by contrapositive.

    Intended Learning Outcomes (ILO)
    KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

      

    APPLYING KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

      


    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

    Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.


    Assessment methods
      Continuous assessment Partial exams General exam
  • Active class participation (virtual, attendance)
  • x x x
    ATTENDING AND NOT ATTENDING STUDENTS

       Assessment is included in the first year, first semester mathematics course, with the methods used for that course.


    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: we use the textbook Preparatory Course in Mathematics, Guido Osimo, EGEA (2020), ISBN 978‐88‐7534‐200‐5.
    Last change 02/06/2023 11:58

    BIG (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classes: 23 (I sem.)
    Instructors:
    Class 23: BARBARA GATTI

    Class group/s taught in English

    Synchronous Blended: Lessons in synchronous mode in the classroom (for a maximum of one hour per credit in remote mode)

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 15 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

    Classroom part:

    • Real functions of one real variable: general concepts and examples. Composite and inverse functions. Graph of a function. Graphs of elementary functions: linear, power, exponential, and logarithmic functions. Piecewise-defined functions and their graphs. Transformations of elementary functions.
    • Exponential equations and inequalities. Properties of logarithms. Logarithmic equations and inequalities.

    • More on functions: increasing/decreasing, concave/convex, and bounded functions. Global and local extrema of a function.

    • Behavior of elementary functions at the boundaries of the domain. Hierarchy of infinite functions.

    • Graph of a function: domain, behavior at the boundaries, zeros (or x-intercepts), y-intercept, sign, monotonicity, points of maximum and minimum, concavity and convexity.

    • Summation symbol and remarkable sums. Summation properties. 

    • Limits: an intuitive idea.

    • Basic language and examples of differential and integral calculus.


    Intended Learning Outcomes (ILO)
    KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

      

    APPLYING KNOWLEDGE AND UNDERSTANDING
    At the end of the course student will be able to...

      


    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

    Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platfor


    Assessment methods
      Continuous assessment Partial exams General exam
  • Active class participation (virtual, attendance)
  • x x x
    ATTENDING AND NOT ATTENDING STUDENTS

     Assessment is included in the first year, first semester mathematics course, with the methods used for that course.


    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: teaching materials prepared by the instructor.
    Last change 02/06/2023 11:59