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Credits  Dept.  Type  Requirements 

9.0 (7.2 ECTS)  MAT 

AL
 Prerequisite for DIE , DCSYS , DCSFW 
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The overall aim of this subject is to introduce students to the concepts and techniques involved in discrete mathematics and algebra that, due to their ubiquity in the world of new technologies, form part of the basic training of any engineer in information technology.
Estimated time (hours):
T  P  L  Alt  Ext. L  Stu  A. time 
Theory  Problems  Laboratory  Other activities  External Laboratory  Study  Additional time 

T  P  L  Alt  Ext. L  Stu  A. time  Total  

7,0  7,0  0  0  0  19,0  0  33,0  
Partial fractions. Successions and generating functions. Linear recurrences. Catalan names. Partitions. Exponential generating function. Disarrangements. Stirling numbers and Bell numbers.


T  P  L  Alt  Ext. L  Stu  A. time  Total  

8,0  8,0  0  0  0  21,0  0  37,0  
Definitions. Isomorphism. Eulerian graphs and matching lemma. Circuits, paths, distance, connections and connectedness. Operations with graphs. Eulerian graphs. Hamiltonian graphs. Matricial representation of a graph.


T  P  L  Alt  Ext. L  Stu  A. time  Total  

6,0  7,0  0  0  0  18,0  0  31,0  
Definition and characterisation of trees. Tree generators. Obtention through broad and indepth searches. Number of tree generators in a graph. Minimal tree generators. Kruskal"s algorithm and Prim"s algorithm.


T  P  L  Alt  Ext. L  Stu  A. time  Total  

7,0  8,0  0  0  0  20,0  0  35,0  
Z_p rings of residue class modules of an integer prime. Polynomials rings with Z_p coefficients.
Greatest common divisor and Bezout"s identity. Irreducible polynomials and unique factorisation. Roots. Polynomial module quotients. Construction of finite bodies. Discrete logarithms. Polynomials over finite fields. 
Total per kind  T  P  L  Alt  Ext. L  Stu  A. time  Total 
36,0  38,0  0  0  0  99,0  0  173,0  
Avaluation additional hours  7,0  
Total work hours for student  180,0 
Theory classes will take the form of lectures, which may include the use of an overhead slide projector or computer demonstrations.
The classes of problems will be of a participatory nature, with students explaining previously set problems and discussing other previously set problems in class.
The evaluation is continuous, based on the following three exams:
P1: covering the initial part of the course,
P2: covering the middle part of the course,
P3: covering the final part of the course.
The final grade is N= 0.2*P1+0.4*P2+0.4*P3 (where P1,P2,P3
are grades over 10).
The students who do not want to follow the continuous evaluation or wish
to renounce to it, must take an exam covering the whole course, and
their final grade will be the one obtained in this exam. The student
must inform the coordinator about the renounce by the end of the
classes, following the procedure that will be posted on the Raco.
Understand operations with and relationships in sets: union, intersection, difference, Cartesian product, inclusion.
Understand the various applications of sets.
Ability to count combinations and permutations (with and without repetition).
Understand the basic properties of binomial numbers and how to calculate them.
Know how to calculate the GCD (Greatest Common Denominator) of integers and Bezout identity coefficients using Euclides" algorithm.
Know how to calculate the products of matrices and how to calculate determinants.
AL is a prerequisite for taking this course.