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Credits  Dept.  Type  Requirements 

9.0 (7.2 ECTS)  MAT 

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Others:  () 
The overall objective of this subject is to introduce students to basic aspects of whole number arithmetic, combinatorics, linear algebra and geometry. Throughout the subject, emphasis is placed on the techniques of mathematical reasoning.
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  

6,0  6,0  0  0  0  10,0  0  22,0  
Propositional Logic. Sets. Applications. Successions.


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

6,0  6,0  0  0  0  10,0  0  22,0  


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

6,0  6,0  0  0  0  10,0  0  22,0  
Demonstration methods. Induction principle.


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

20,0  20,0  0  0  0  40,0  0  80,0  

Total per kind  T  P  L  Alt  Ext. L  Stu  A. time  Total 
42,0  42,0  0  0  0  78,0  0  162,0  
Avaluation additional hours  6,0  
Total work hours for student  168,0 
Theory classes will take the form of lectures.
Problem classes will be of a participative nature.
Continuous evaluation:
Assessment will be based on:
a part exam (P) (only the first part)
a class exam (E) (only intermediate part)
and a final exam (F) (only on the final part)
The final grade will be calculated in accordance to the following formula:
N=N=0.3P+0.25E+0.45F
Non continuous evaluation:
The final examination consists of the part F (45%) and an extra part EXT (55%), covering the first and intermediate part of the subject.
It is possible to decide if this non continuous evaluation is applied at the moment of the final examination (F). If any exercise of part EXT is solved, non continuous avaluation will be choosen. Resignment of continuous avaluation can not be partial.
Any attempt of fraud during the course will entail the application of the UPC's general academic normative and the beginning of a disciplinary process.
Basic notions of sets and their application.
Ability to work with inequalities:
Knowledge of integers and the properties of operations.
Operating with matrices: sum, multiply, invert. Ability to calculate the rank of a matrix and its determinants.
Ability to resolve linear systems using the GaussJordan method.
Ability to find equations for R^2 i R^3 straightlines and planes. Recognise the relative positions between straight lines and R^3 planes. Solving basic 2D and 3D metric problems.
Ordinary scalar product and vectorial product. Module.