This subject has two parts. In the first part we focus on propositional and predicate logic and mathematical reasoning that are needed for the curriculum. The second part deals with the basic concepts of integer arithmetic, such as divisibility and congruence relations.
Person in charge
Rafel Farré Cirera (
Fernando Martínez Sáez (
Francesc Prats Duaygues (
Guillermo González Casado (
Jose Luis Ruiz Muñoz (
Common technical competencies
CT1 - To demonstrate knowledge and comprehension of essential facts, concepts, principles and theories related to informatics and their disciplines of reference.
- To interpret, select and value concepts, theories, uses and technological developments related to computer science and its application derived from the needed fundamentals of mathematics, statistics and physics. Capacity to solve the mathematical problems presented in engineering. Talent to apply the knowledge about: algebra, differential and integral calculus and numeric methods; statistics and optimization.
- To use properly theories, procedures and tools in the professional development of the informatics engineering in all its fields (specification, design, implementation, deployment and products evaluation) demonstrating the comprehension of the adopted compromises in the design decisions.
G9 [Avaluable] - Capacity of critical, logical and mathematical reasoning. Capacity to solve problems in her study area. Abstraction capacity: capacity to create and use models that reflect real situations. Capacity to design and perform simple experiments and analyse and interpret its results. Analysis, synthesis and evaluation capacity.
- Critical, logical and mathematical reasoning capacity. Capacity to understand abstraction and use it properly.
To understand the importance of language in scientific communication and the need to refine it and define it to avoid, as far as possible, the ambiguity.
To understand what a mathematical proof is and to know the main types of proofs which the student may meet
Understanding the language of sets as an essential tool in mathematical communication and also as an instrument
Understanding the language of mappings as a way to define and to study correspondences and rules
To understand that we cannot prove that a certain property is valid for infinitely many numbers by testing the property one number at a time but that we must use some principle that makes possible the proof
To understand the properties of the divisibility of integers, to calculate the greatest common divisor using Euclid's algorithm and to write Bézout's identity of two integers. To calculate small prime numbers and to understand the difficulty of performing integer factorization.
To u nderstand the concept of congruence and to be able of computing with congruences. To apply the language of congruences to solve arithmetic problems.
The principle of induction
Induction. Complete induction.
Sets and elements, the membership relation. Elementary operations with sets. Relations. Equivalence relations and quotient set.
Functions. Injectivity and surjectivity. Inverse function. Image and pre-imaging. Composition.
Divisibility of integers
The divisibility relation in the set of integers. The division theorem. Primes. Infinitude of primes. Sieve of Eratosthenes. Greatest common divisor and least common multiple. Euclidean algorithm. Bézout's identity. Gauss Lemma.
Congruences of integers
The relation of congruence. Operations with congruences. Modular inverse: calculation. Congruence classes and the quotient group Zn. Operations with congruence classes.
Applications of congruences
Modular exponentiation. Linear equations in congruences. The chinese remainder theorem. The RSA cryptography systgem.
* There are two partial exams, not in classtime, (20% each one). Rating: P1 and P2 (both over 10).
* There is be a final exam, not in classtime, (40%). Rating: F (over 10)
* The achievement of objectives in the workshop sessions will be also considered (20%). Rating: T (over 10)
Moreover, there is the possibility to improve the partial marks during the final exam by answering and additional task. Say that RP1 and RP2 are the marks corresponding to those additional parts. Then the mark for the course is computed as:
0.20 * T + 0.20*max(P1,RP1) + 0.20*max(P2,RP2) + 0.40*F
All the students who want to do the additional task in the final exam to improve the partial marks have to say so in advance.
The participation in less than 30% by weight of evaluating sessions will be considered as non evaluated.
Due to the particularities of the subject, the grade for the cross competition will be calculated from the course grade as follows:
* between 0 and 4.9 : D
* between 5 to 6.9 : C
* between 7 and 8.4 : B
* between 8.5 and 10 : A
¿La Dama o el tigre? y otros pasatiempos lógicos : incluyendo una novela matemática que presenta el gran descubrimiento de Gödel -
Smullyan, R.M, Cátedra ,
ISBN: 9788437604145 http://cataleg.upc.edu/record=b1510243~S1*cat
The kind of abilities that a student that has succesfully passed his/her secondary studies is supposed to have
L'unic canvi, per raons de calendari, és que donarem menys pes a la inducció completa.
Algunes classes de teoria es faran de manera no presencial mitjançant sessions de Meet. Cada setmana farem una de les tres hores de teoria amb Meet. La resta de la docència no canvia.
Hi haurà dues proves de taller que puntuaran un 10% cada una.
Hi haurà un primer parcial fora d'hores de classe que puntuarà un 35%.
Hi haurà un segon parcial fora d'hores de classe que puntuarà un 35%.
La resta de la nota, un 10% s'obtindrà responent diversos qüestionaris Atenea.
La nota per parcials N s'obté amb la fórmula:
Els que suspenguin per parcials, podran optar a un final i aprovar el curs amb aquest examen.
La nota de curs es: max( N, F )
T1,T2 tallers. P1,P2 parcials. A Atenea. F final.
Els exàmens parcials i el final tindran una part amb Qüestionaris Atenea i una part escrita.
Totes les classes es faran amb Meet, respectant els grups i els horaris.
Les avaluacions dels parcials es faran mitjançant qüestionaris Atenea, respectant continguts, pesos de les proves i horaris en la mesura del possible.
Where we are
B6 Building Campus Nord
C/Jordi Girona Salgado,1-3
08034 BARCELONA Spain
Tel: (+34) 93 401 70 00