| Module: GEOMETRY AND COMBINATORICS
(objectives)
The course aims to provide an introduction to those aspects of linear and discrete mathematics needed in science and engineering.
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Code
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20810098-1 |
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Language
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ITA |
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Type of certificate
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Profit certificate
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Credits
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6
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Scientific Disciplinary Sector Code
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MAT/03
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Contact Hours
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54
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Type of Activity
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Basic compulsory activities
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Group: CANALE 1
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Derived from
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20810098-1 GEOMETRY AND COMBINATORICS in Computer science and engineering L-8 CANALE 1 MEROLA FRANCESCA
(syllabus)
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.
(reference books)
Giulia Maria Piacentini Cattaneo
"Matematica discreta"
Edito da Zanichelli.
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Dates of beginning and end of teaching activities
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From 28/09/2020 to 22/01/2021 |
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Delivery mode
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Traditional
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Attendance
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not mandatory
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Evaluation methods
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Written test
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Group: CANALE 2
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Derived from
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20810098-1 GEOMETRY AND COMBINATORICS in Computer science and engineering L-8 CANALE 2 SAMA' MARCELLA
(syllabus)
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.
(reference books)
Giulia Maria Piacentini Cattaneo
"Matematica discreta"
Edito da Zanichelli.
|
|
Dates of beginning and end of teaching activities
|
From 28/09/2020 to 22/01/2021 |
|
Delivery mode
|
Traditional
|
|
Attendance
|
not mandatory
|
|
Evaluation methods
|
Written test
|
|
|
Università Roma Tre