Overview:
Organic Unit
Escola Superior de Tecnologia e Gestão
Academic Year 2013/2014
Study Cicle
Engenharia Informática
Degree
Licenciatura
Curricular Unit
Matemática Discreta
ECTS
6
Scientific Area
Base Sciences
Type
Obrigatório
Work Load
162
T 0
TP 75
PL 0
TC 0
S 0
E 0
OT 5
T - Theoretical; TP - Theoretical and Practical; PL - Practical and Laboratorial; TC - Field Work; S - Seminar; E - Trining; OT - Tutorial
Responsible academic staff member:
Diogo Pedro Ferreira Nascimento Baptista ( 125,00 horas semanais de contacto: TP: 75,00; TP: 50,00; )
Conceição Veloso Nogueira ( 76,50 horas semanais de contacto: TP: 50,00; TP: 25,00; OT: 1,50; )
Ana Isabel Gonçalves Mendes ( 1,50 horas semanais de contacto: OT: 1,50; )
Prerequisites:
It does not apply.
Language:
Português
Outline:
The Discrete Mathematics can be seen as part of mathematics that studies the structures that led to modern
computers and therefore, even these days, the practice provides the necessary foundation for a good performance in
many areas of computer science; such as structured data, the development of algorithms, databases, automata,
formal languages, compilers, computer security, operating systems, among others. Therefore, this course will
transmit knowledge of elementary logic, set theory, functions, relationships, and some concepts of abstract algebra
and number theory. It is also expected to acquire skills to a higher level (solving problems and implementing
solutions) with regard to topics such as combinatory and graph theory or computation theory.
Learning outcomes:
C1. Knowledge and understanding - To know and understand the concepts of discrete mathematics and its
properties.
C2. Knowledge and understanding application - To interconnect different contents; To model problems involving the
concepts of discrete mathematics; To solve abstract problems using algebraic structures contents; Ability to apply
contents of discrete mathematics in modeling and solving computer science problems.
C3. Making judgments - To use a critical analysis of the results.
C4. Communication skills - Ability to use mathematical symbols; Ability to achieve greater accuracy and clarity of
thought and language.
C5. Learning Skills – Ability of teamwork; Ability of self-learning.
Syllabus:
Syllabus:
1. Sets, functions, relations and algorithms
2. Logic and Propositional Calculus
3. Techniques of Counting
4. Directed Graphs
5. Binary trees
6. Properties of the integers
7. Languages, Grammars and Machines
8. Ordered Sets and Lattices
9. Boolean Algebra
Demonstration of the syllabus coherence with the curricular unit’s intended learning outcomes:
1. Set Theory; Relations; Functions and Algorithms - objectives C1, C2, C3, C4 and C5
2. Logic and Propositional Calculus - objectives C1, C2, C3, C4 and C5
3. Counting Techniques - objectives C1, C2, C3, C4 and C5
4. Directed Graphs - objectives C1, C2, C3, C4 and C5
5. Binary Trees - objectives C1, C2, C3, C4 and C5
6. Properties of the Integers - objectives C1, C2, C3, C4 and C5
7. Languages, Grammars and Machines - objectives C1, C2, C3, C4 and C5
8. Ordered Sets and Lattices - objectives C1, C2, C3, C4 and C5
9. Boolean Algebra - objectives C1, C2, C3, C4 and C5
Teaching/Learning methodologies:
In Class:
1. Theoretical and practical teaching (The contents will be described, with several examples and exercises resolutions;
Interaction with the students in the resolution of the exercises and answering their doubts)
2. Tutorial orientation (Sessions of personal orientation, in order to lead the learning of the class; including guiding the work of
the student’s and answer student’s doubts.)
Autonomous:
1. Autonomous Learning
1.1. Home-study ( Reading parts of the bibliography; Solving exercises)
2. E-learning (Looking material concerning Discrete Mathematics;Interaction with teaching staff to clarify doubts)
Specific Resources:
1. Theoretical and practical teaching / classes - Classroom with white board, computer with the software Matlab and projector
2. Tutorial orientation - classroom or teacher’s office
Evaluation:
Description:
Assessment:
Periodic Assessment (PA):
• 3 individual written tests: PE1, PE2 e PE3
• there is no minimum for PE1 and PE2
• minimum 7.0 values for PE3
Final Classification = 0.25*PE1 + 0.25*PE2+0.5*PE3
Final Assessment:
One final individual written exam.
Number of elements in the final evaluation:
1
Number of elements for continuous evaluation:
3
Demonstration of the teaching methodologies coherence with the curricular unit’s intended
learning outcomes:
Contact teaching
1. Theoretical and practical teaching
1.1 The contents will be described, with several examples and exercises resolutions – objectives C1, C2, C3
1.2 Interaction with the students in the resolution of the exercises and answering their doubts - objectives C2, C3, C4, C5
2. Tutorial orientation
2.1 Sessions of personal orientation, in order to lead the learning of the class; including
guiding the work of the student’s and answer student’s doubts – objectives C1, C2, C3, C4, C5
Autonomous Learning
1. Home-study
1.1 Reading parts of the bibliography of the course – objectives C1, C2, C5
1.2 Resolution of exercises – objectives C2, C3, C4, C5
2. E-learning – objective C5
Bibliography:
Main Bibliography:
1. S. Lipschutz e M. Lipson, Matemática Discreta, 2ed, Bookman, 2004
2. K. Rosen, Discrete Mathematics and Its Applications, 7ed, McGraw-Hill, 2011
3. S. Lipschutz and M. Lipson, Schaum's Outline of Discrete Mathematics, 3ed, McGraw-Hill, 2009
4. S. Pemmaraju and S. Skiena, Computational Discrete Mathematics, Cambridge, 2009
5. Vagner Morais e Cláudio Vieira, Matlab 7 & 6 : curso completo, 2ed, FCA-Editora de Informática, 2006
6. J. Sousa Pinto, Tópicos de Matemática Discreta, Universidade de Aveiro, 2003
Additional Bibliography:
1. Balakrishnan, V.K., Introductory Discrete Mathematics, Dover Publications, Inc. New York, 1996.
2. Deborah S. Franzblau, Joseph G. Rosenstein, Fred S. Roberts, Discrete Mathematics in the Schools, AMS Bookstore, 2000.
3. Garnier, R. and Taylor, J., Discrete Mathematics for New Technology, IoP (Institute of Physics) (UK).
4. Simões Pereira, J.M.S. , Matemática Discreta: Grafos, Redes e aplicações, Editora Luz da Vida, 2009.