Tribunal titular

Cargo

Departamento

Profesor

Presidente

MATEMATICAS

GRANJA BARON , ANGEL

Secretario

MATEMATICAS

LOPEZ CABECEIRA , MONTSERRAT

Vocal

MATEMATICAS

PISABARRO MANTECA , MARIA JESUS

Tribunal suplente

Cargo

Departamento

Profesor

Presidente

MATEMATICAS

TROBAJO DE LAS MATAS , MARIA TERESA

Secretario

MATEMATICAS

MAZCUñAN NAVARRO , EVA MARIA

Vocal

QUIROS CARRETERO , ALICIA

Description

Qualification

Mixed tests

Two written exams, where problems are proposed to be solved by applying the theoretical contents studied in the classroom. Aspects to be evaluated, among others: the correct use of the mathematical and logical language, the rigorous explanation of all steps of the solutions, as well as the numerical results obtained. Each exam is worth 45% of the total grade, and may be re-evaluated in the second call.

90%

Others

Works, assignments and online questionnaries will be evaluated. These activities are not re-evaluated in the second call.

10%

Other comments and second call

In all tests: the use of mobile phones and other electronic devices is strictly forbidden, and will result in grade zero. Only the material specifically allowed by the instructors may be used.

Second call. Students may choose between these two options:

- maintain/preserve the grades obtained in all works and assignments (10%) and repeat one or both written tests. If either of the parts is not repeated in the second call, the grade corresponding to that part obtained in the first call will be maintained in the second call.

- remove/withdraw all works and assigments from the calculation of the final grade, in this case each of the written tests will be worth 50%.

Code
A18117
B5618
B5619
B5623
B5624
B5625
C1	CMECES1 That students have demonstrated possession and understanding of knowledge in an area of study that is based on general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study
C4	CMECES4 That students can transmit information, ideas, problems and solutions to both a specialised and non-specialised audience
C5	CMECES5 That students have developed those learning skills necessary to undertake further studies with a high degree of autonomy

	Competences
1. The students understand the main concepts of discrete mathematics and logics, and they apply them in solving mathematical problems appearing in engineerings.	A18117	B5618	C1
2. Students show skills and abilities in analysis, synthesis, critical reasoning and decision making.		B5623 B5624
3. Students apply the studied concepts in the elaboration of correct argumentations and reasonings. They are able to face up with situations where they need new mathematical knowledge and techniques. They have developed their autonomous learning skills.		B5619	C5
4. Students are able to communicate mathematical ideas and information in oral and written form.		B5619 B5625	C4

Topic	Sub-topic
Part I: INTRODUCTION TO FORMAL LOGIC	Fundamentals of Logic. Proof techniques.
PART II: SETS, CORRESPONDENCES, FUNCTIONS AND RELATIONS	Intuitive set theory. Correspondences and functions. Relations.
PART III: COUNTING TECHNIQUES	Combinatorics and counting techniques. Induction, recursion and recurrence relations.
PART IV: BOOLEAN ALGEBRA AND OTHER ALGEBRAIC STRUCTURES	Boolean Algebra. Groups, semigroups, rings and fields.

Methodologies :: Tests
	Class hours	Hours outside the classroom	Total hours
Lecture	25	25	50


Problem solving, classroom exercises	30	45	75

Mixed tests	5	20	25

(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

	Description
Lecture	Classical expository lectures.
Problem solving, classroom exercises	Solving problems and exercises in the classroom.

Basic	Meng, K.K., Guan, T.E., Counting, World Scientific, 2002 Anderson, I., Introducción a la Combinatoria, Vicens Vives, 1993 Biggs, N.L., Matemática discreta, Vicens Vives, 1994 García Merayo, F., Matemática Discreta, Thomson, 2005 W.K. Grassmann, J.P. Tremblay, Matemática discreta y Lógica. Una perspectiva desde la Ciencia de la Computación, Prentice Hall, 1997 Rosen, K.H., Matemática discreta y sus aplicaciones, McGraw-Hill, Interamericana de España, 2004 Grimaldi, R.P., Matemáticas discreta y combinatoria : una introducción con aplicaciones, Addison Wesley, 1998 Lipschutz, S., Lipson, M., Matemáticas discretas, McGraw-Hill, Interamericana de España, 2009

Complementary	Schumacher, C., Chapter zero : fundamental notions of abstract mathematics, Addison-Wesley Pub. Co., 1997 Y. Nievergelt, Foundations of Logic and Mathematics. Applications to Computer Science and Cryptography, Birkhäuser, 2002 P.R. Halmos, Naive set theory, Springer, 1974 P.T. Johnstone, Notes on logic and set theory, Cambridge, 1996 Cameron, P.J., Sets, logic and categories, Springer, 1999 D.E. Knuth, The Art of Computer Programming. Volume 1. Fundamental Algorithms, Addison-Wesley, 1997 D.E. Knuth, The Art of Computer Programming. Volume 2. Seminumerical Algorithms, Addison-Wesley, 1998 D.E. Knuth, The Art of Computer Programming. Volume 3. Sorting and Searching, Addison-Wesley, 1998 D.E. Knuth, The Art of Computer Programming. Volume 4A. Combinatorial Algorithms, Addison-Wesley, 2011