Course 2024-2025 a.y.

30122 - PRECORSO DI MATEMATICA / MATHEMATICS - PREPARATORY COURSE

Department of Decision Sciences


Student consultation hours
Class timetable
Exam timetable

For the instruction language of the course see class group/s below
Go to class group/s: 1 - 2 - 3 - 4 - 5 - 6 - 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 25 - 27 - 40 - 41 - 42 - 43 - 44 - 45
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.)
Docenti responsabili delle classi:
Classe 1: ENRICO MORETTO, Classe 2: ZELINDA CACCIA, Classe 3: FABIO TONOLI, Classe 4: MAURO D'AMICO, Classe 5: FEDERICA ANDREANO, Classe 6: FRANCESCA SIANESI

Classe/i impartita/e in lingua italiana

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: definizione, esempi. Funzioni suriettive, iniettive, biunivoche. Funzioni reali di una variabile reale: definizione, grafico cartesiano, 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 trigonometriche e loro grafici. Funzione arcotangente e suo grafico. Funzioni definite a tratti. Funzione modulo. Trasformazioni di funzioni elementari. Funzioni limitate, funzioni monotone. Funzioni reali di n variabili reali. Funzioni reali di due variabili reali: definizione, grafico cartesiano, curve di livello, esempi.
  • Funzioni reali di una variabile reale: rapporto incrementale, derivata; derivate delle funzioni elementari; algebra delle derivate; derivata della funzione composta; equazione della retta tangente. Funzioni reali di due variabili reali: derivate parziali.
  • 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

DETTAGLI

Lezioni frontali: nulla da specificare.

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    
  • Valutazione all'interno del corso di matematica di primo anno, primo semestre
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 (2024).
Modificato il 22/05/2024 15:30
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

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

DETTAGLI

Lezioni frontali: niente da specificare.

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    
  • Valutazione all'interno del corso di matematica di primo anno, primo semestre
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 22/05/2024 15:45

Classes: 12 (I sem.)
Instructors:
Class 12: ELISA CAPRARI

Class group/s taught in English

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

  • Lectures

DETAILS

Face-to-face lectures: nothing to specify.

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    
  • Assessment is included in the first year, first semester Mathematics course
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 22/05/2024 15:51
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

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.
  • Real functions 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.
  • Vectors of R^n. Real functions of n real variables. Domain, codomain, and image of a function. Separable functions. 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

  • Lectures

DETAILS

Face-to-face lectures: nothing to specify.

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    
  • Assessment is included in the first year, first semester Mathematics course
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 22/05/2024 16:00
BEMACS (I sem. - P)
Course Director:
GUIDO OSIMO

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

Class group/s taught in English

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:

  • Functions: definition, examples. Surjective, injective, bijective functions. Real functions of one real variable: definition, Cartesian 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. Trigonometric functions and their graphs. The inverse tangent function and its graph. Piecewise defined functions. Absolute value function. Transformation of elementary functions. Bounded, monotone functions. Real functions of n real variables. Real functions of two real variables: definition, Cartesian graph, level curves, examples.
  • Real functions of one real variable: difference quotient, derivative; derivatives of elementary functions; algebra of derivatives; chain rule; equation of the tangent line. Real functions of two real variables: partial derivatives.
  • 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

  • Lectures

DETAILS

Face-to-face lectures: nothing to specify.

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    
  • Assessment is included in the first year, first semester Mathematics course
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 (2024).
Last change 22/05/2024 17:15
BIEM (I sem. - P)
Course Director:
GUIDO OSIMO

Classes: 14 (I sem.) - 15 (I sem.) - 16 (I sem.) - 17 (I sem.) - 18 (I sem.) - 19 (I sem.)
Instructors:
Class 14: JACOPO GIUSEPPE DE TULLIO, Class 15: GUIDO OSIMO, Class 16: DOVID FEIN, Class 17: ELISA TACCONI, Class 18: FEDERICA ANDREANO, Class 19: MARIA BEATRICE ZAVELANI ROSSI

Class group/s taught in English

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:

  • Functions: definition, examples. Surjective, injective, bijective functions. Real functions of one real variable: definition, Cartesian 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. Trigonometric functions and their graphs. The inverse tangent function and its graph. Piecewise defined functions. Absolute value function. Transformation of elementary functions. Bounded, monotone functions. Real functions of n real variables. Real functions of two real variables: definition, Cartesian graph, level curves, examples. 
  • Real functions of one real variable: difference quotient, derivative; derivatives of elementary functions; algebra of derivatives; chain rule; equation of the tangent line. Real functions of two real variables: partial derivatives.
  • 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

  • Lectures

DETAILS

Face-to-face lectures: nothing to specify.

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    
  • Assessment is included in the first year, first semester Mathematics course
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 (2024).
Last change 22/05/2024 16:13
BAI (I sem. - P)
Course Director:
GUIDO OSIMO

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

Class group/s taught in English

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

  • Lectures

DETAILS

Face-to-face lectures: nothing to specify.

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    
  • Assessment is included in the first year Mathematics courses
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 22/05/2024 17:12
BIEF (I sem. - P)
Course Director:
GUIDO OSIMO

Classes: 40 (I sem.) - 41 (I sem.) - 42 (I sem.) - 43 (I sem.)
Instructors:
Class 40: JACOPO GIUSEPPE DE TULLIO, Class 41: DOVID FEIN, Class 42: ENRICO MORETTO, Class 43: ELISA TACCONI

Class group/s taught in English

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:

  • Functions: definition, examples. Surjective, injective, bijective functions. Real functions of one real variable: definition, Cartesian 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. Trigonometric functions and their graphs. The inverse tangent function and its graph. Piecewise defined functions. Absolute value function. Transformation of elementary functions. Bounded, monotone functions. Real functions of n real variables. Real functions of two real variables: definition, Cartesian graph, level curves, examples.
  • Real functions of one real variable: difference quotient, derivative; derivatives of elementary functions; algebra of derivatives; chain rule; equation of the tangent line. Real functions of two real variables: partial derivatives.
  • 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

  • Lectures

DETAILS

Face-to-face lectures: nothing to specify.

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    
  • Assessment is included in the first year, first semester Mathematics course
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 (2024).
Last change 27/05/2024 11:05
BIG (I sem. - P)
Course Director:
GUIDO OSIMO

Classes: 44 (I sem.) - 45 (I sem.)
Instructors:
Class 44: LAURA MARIANO, Class 45: LAURA MARIANO

Class group/s taught in English

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:

A) BIG

  • 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.

B) BIG-HEC

  • Real functions of one real variable: general concepts and examples. Graph of a function. Graphs of elementary functions: linear, power, exponential, and logarithmic functions. Piecewise-defined functions and their graphs. Transformations of elementary functions. Composite and inverse functions.
  • Exponential equations and inequalities. Properties of logarithms. Logarithmic equations and inequalities.
  • More on functions: increasing/decreasing, bounded functions.
  • Behavior of elementary functions at the boundaries of the domain, intuitive idea of limits.
  • The rate of change of a function: the notion of difference quotient, the notion of derivative. Elementary derivatives. Rules on derivatives. The chain rule.
  • Introduction to the mathematical language.
  • Summation symbol. Summation properties.

 


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

  • Lectures

DETAILS

Face-to-face lectures: nothing to specify.

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    
  • Assessment is included in the first year, first semester Mathematics course
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: teaching materials prepared by the instructor.


     
Last change 27/05/2024 11:05