The course aims to provide an introduction to those aspects of linear and discrete mathematics needed in science and engineering.
Curriculum
Canali
teacher profile teaching materials
Elements of propositional logic, truth tables. Equivalence and order relations.
Combinatorics. Binomial coefficients and binomial theorem. Permutations. The Integers: divisibility, GCD and Euclidean algorithm, Bézout identity, linear congruences.
Baiscs of algebraic structures: permutation groups, abstract groups, polynomials and finite fields.
Elements of graph theory.Lattices and Boolean algebras
Matematica discreta e applicazioni
Zanichelli 2008
Programme
Elements of set theory. Maps between sets: invective, surjective, bijective maps.Elements of propositional logic, truth tables. Equivalence and order relations.
Combinatorics. Binomial coefficients and binomial theorem. Permutations. The Integers: divisibility, GCD and Euclidean algorithm, Bézout identity, linear congruences.
Baiscs of algebraic structures: permutation groups, abstract groups, polynomials and finite fields.
Elements of graph theory.Lattices and Boolean algebras
Core Documentation
Giulia Maria Piacentini CattaneoMatematica discreta e applicazioni
Zanichelli 2008
Reference Bibliography
Giulia Maria Piacentini Cattaneo Matematica discreta e applicazioni Zanichelli 2008Type of delivery of the course
Class teaching and exercise classesAttendance
Attending classes is strongly advisedType of evaluation
During the COVID-19 emergency, the exam rules will follow the art.1 of Decreto Rettorale n°. 703 of 5 May 2020 A midterm exam is generally held. In the exam, both exercises and theory questions are present. teacher profile teaching materials
Union, intersection, Cartesian product, set subtraction, complementary set, cardinality.
2. Set functions.
Domain, codomain, Range. Injective, surjective, bijective functions. Inverse function, Identity, Permutations.
3. Elements of logic.
Propositional calculus, Operations between propositions.
4. Relations.
Reflexive, symmetric, antisymmetric, transitive. Order and equivalence relations. Examples.
5. Partially ordered sets.
Equivalence relations and classes. Quotient set.
6. Integer numbers.
Division and its properties. Greatest common divisor.
7. Euclidean algorithm.
Introduction and application.
8. Prime numbers.
Fundamental theorem of arithmetic.
9. Congruence mod n.
Basic modular arithmetic. Sum and multiplication in Zn. Linear congruence. Description of linear congruence solutions. Euler's totient function. Small Fermat Theorem, Euler’s Theorem
10. Combinatory algebra.
Dispositions and combinations with and without repetitions, binomial coefficient. Properties. Tartaglia's triangle.
11. Partially ordered sets
Hasse Diagram. Maximum and minimum, Sup and inf.
12. Reticular formations. Properties of inf e sup.
13. Boolean algebra.
Introduction. The Boolean operators AND, OR and NOT.
"Matematica discreta"
Edito da Zanichelli.
Programme
1. Elements of Set Theory.Union, intersection, Cartesian product, set subtraction, complementary set, cardinality.
2. Set functions.
Domain, codomain, Range. Injective, surjective, bijective functions. Inverse function, Identity, Permutations.
3. Elements of logic.
Propositional calculus, Operations between propositions.
4. Relations.
Reflexive, symmetric, antisymmetric, transitive. Order and equivalence relations. Examples.
5. Partially ordered sets.
Equivalence relations and classes. Quotient set.
6. Integer numbers.
Division and its properties. Greatest common divisor.
7. Euclidean algorithm.
Introduction and application.
8. Prime numbers.
Fundamental theorem of arithmetic.
9. Congruence mod n.
Basic modular arithmetic. Sum and multiplication in Zn. Linear congruence. Description of linear congruence solutions. Euler's totient function. Small Fermat Theorem, Euler’s Theorem
10. Combinatory algebra.
Dispositions and combinations with and without repetitions, binomial coefficient. Properties. Tartaglia's triangle.
11. Partially ordered sets
Hasse Diagram. Maximum and minimum, Sup and inf.
12. Reticular formations. Properties of inf e sup.
13. Boolean algebra.
Introduction. The Boolean operators AND, OR and NOT.
Core Documentation
Giulia Maria Piacentini Cattaneo"Matematica discreta"
Edito da Zanichelli.
Type of delivery of the course
Lessons and exam simulations.Attendance
Attending class is recommended.Type of evaluation
During the COVID-19 emergency the exam will follow art. 1 of the D.R. n°703 of 5th may 2020Canali
teacher profile teaching materials
Elements of propositional logic, truth tables. Equivalence and order relations.
Combinatorics. Binomial coefficients and binomial theorem. Permutations. The Integers: divisibility, GCD and Euclidean algorithm, Bézout identity, linear congruences.
Baiscs of algebraic structures: permutation groups, abstract groups, polynomials and finite fields.
Elements of graph theory.Lattices and Boolean algebras
Matematica discreta e applicazioni
Zanichelli 2008
Mutuazione: 20810098-1 GEOMETRIA E COMBINATORIA I MODULO in Ingegneria informatica L-8 CANALE 1 MEROLA FRANCESCA
Programme
Elements of set theory. Maps between sets: invective, surjective, bijective maps.Elements of propositional logic, truth tables. Equivalence and order relations.
Combinatorics. Binomial coefficients and binomial theorem. Permutations. The Integers: divisibility, GCD and Euclidean algorithm, Bézout identity, linear congruences.
Baiscs of algebraic structures: permutation groups, abstract groups, polynomials and finite fields.
Elements of graph theory.Lattices and Boolean algebras
Core Documentation
Giulia Maria Piacentini CattaneoMatematica discreta e applicazioni
Zanichelli 2008
Type of delivery of the course
Class teaching and exercise classesAttendance
Attending classes is strongly advisedType of evaluation
During the COVID-19 emergency, the exam rules will follow the art.1 of Decreto Rettorale n°. 703 of 5 May 2020 A midterm exam is generally held. In the exam, both exercises and theory questions are present. teacher profile teaching materials
Union, intersection, Cartesian product, set subtraction, complementary set, cardinality.
2. Set functions.
Domain, codomain, Range. Injective, surjective, bijective functions. Inverse function, Identity, Permutations.
3. Elements of logic.
Propositional calculus, Operations between propositions.
4. Relations.
Reflexive, symmetric, antisymmetric, transitive. Order and equivalence relations. Examples.
5. Partially ordered sets.
Equivalence relations and classes. Quotient set.
6. Integer numbers.
Division and its properties. Greatest common divisor.
7. Euclidean algorithm.
Introduction and application.
8. Prime numbers.
Fundamental theorem of arithmetic.
9. Congruence mod n.
Basic modular arithmetic. Sum and multiplication in Zn. Linear congruence. Description of linear congruence solutions. Euler's totient function. Small Fermat Theorem, Euler’s Theorem
10. Combinatory algebra.
Dispositions and combinations with and without repetitions, binomial coefficient. Properties. Tartaglia's triangle.
11. Partially ordered sets
Hasse Diagram. Maximum and minimum, Sup and inf.
12. Reticular formations. Properties of inf e sup.
13. Boolean algebra.
Introduction. The Boolean operators AND, OR and NOT.
"Matematica discreta"
Edito da Zanichelli.
Mutuazione: 20810098-1 GEOMETRIA E COMBINATORIA I MODULO in Ingegneria informatica L-8 CANALE 2 SAMA' MARCELLA
Programme
1. Elements of Set Theory.Union, intersection, Cartesian product, set subtraction, complementary set, cardinality.
2. Set functions.
Domain, codomain, Range. Injective, surjective, bijective functions. Inverse function, Identity, Permutations.
3. Elements of logic.
Propositional calculus, Operations between propositions.
4. Relations.
Reflexive, symmetric, antisymmetric, transitive. Order and equivalence relations. Examples.
5. Partially ordered sets.
Equivalence relations and classes. Quotient set.
6. Integer numbers.
Division and its properties. Greatest common divisor.
7. Euclidean algorithm.
Introduction and application.
8. Prime numbers.
Fundamental theorem of arithmetic.
9. Congruence mod n.
Basic modular arithmetic. Sum and multiplication in Zn. Linear congruence. Description of linear congruence solutions. Euler's totient function. Small Fermat Theorem, Euler’s Theorem
10. Combinatory algebra.
Dispositions and combinations with and without repetitions, binomial coefficient. Properties. Tartaglia's triangle.
11. Partially ordered sets
Hasse Diagram. Maximum and minimum, Sup and inf.
12. Reticular formations. Properties of inf e sup.
13. Boolean algebra.
Introduction. The Boolean operators AND, OR and NOT.
Core Documentation
Giulia Maria Piacentini Cattaneo"Matematica discreta"
Edito da Zanichelli.
Type of delivery of the course
Lessons and exam simulations.Attendance
Attending class is recommended.Type of evaluation
During the COVID-19 emergency the exam will follow art. 1 of the D.R. n°703 of 5th may 2020