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Discrete Mathematics 2017/2018

  • 6 ECTS
  • Taught in Portuguese
  • Both continuous and final Assessment

Objectives

- Identify and apply the basic concepts of set
- Identify binary relations
- know and apply logic knowledge
- know and apply graphs theory
- know the counting techniques and applying combinatorial calculation
- Interpret, analyze and apply probability theory to different practical problems

Recommended Prerequisites

Knowledge acquired in Mathematics of Elementary and Secondary Education.

Teaching Metodology

Through the presentation of concrete problems, new concepts and mathematical methods, will be introduced.
Handouts for the lectured contents will be provided.
Exercises and problems will be proposed and for being explore by the students.

Body of Work

1. Basic Structures
1.1 Sets: representation and set operations
1.2 Sequences, summations and Products
2. Binary Relations
3. Logical operations and properties of these operations
4. Graph theory
4.1 Graphs and their representation
4.2 Matrix adjacencies
4.3 Euler Paths
4.4 Weighted graphs
4.5 Trees and Kruskal´s algorithm
4.6 Graphs and maps coloring
5. Combinatorial calculation
6. Probability theory

Recommended Bibliography

Murteira, B., Ribeiro, C., Andrade e Silva, J., Pimenta, C. Pimenta, F. (2015). Introdução à Estatística (3ª edição). Escolar Editora.
Rosen, K. H. (2007). Discrete Mathematics and Its Applications (6th edition). McGraw-Hill. ISBN-13: 978-007-124474-9.
Lipschutz, S. (2004). Matemática Discreta (2.ª edição). Bookman. ISBN. 0-07-038045-7.

Complementary Bibliography

Gersting, J. L. (2006). Mathematical Structures for Computer Science: A Modern Approach to Discrete Mathematics (6th edition). W.H. Freeman & Company. ISBN 071676864X.

Weekly Planning

WEEK 0- Week host
WEEK 1 - Information regarding the operation of the course (UC): teacher, summarized the program, learning outcomes, bibliography, evaluation method. Sets;
WEEK 2- Sets: representation and set operations
WEEK 3 - Sequences and Summations;
WEEK 4 - arithmetic and geometric progressions
WEEK 5 - Binary Relations
WEEK 6 - Logical operations
WEEK 7 - Logical operations and properties of these operations
WEEK 8 - First test; Graphs theory: representation
WEEK 9 - Matrix adjacencies; Euler paths
WEEK 10 -Weighted graphs; Trees
WEEK 11- Kruskal´s algorithm
WEEK 12- Graphs and Maps coloring
WEEK 13 - Combinatorial calculation. Probability theory
WEEK 14- Probability theory

Demonstration of the syllabus coherence with the curricular unit's objectives

Topics 1, 2 and 3 contribute to the objectives, allowing the student to understand and apply a variety of mathematical tools that will be required not only in the
remaining Curricular Units of the course but also in problematic situations that may arise in their professional future.
In a general way all topics contribute in an integrated way to the development of the intended skills.

Demonstration of the teaching methodologies coherence with the curricular unit's objectives

Combining lecturing, demonstration and questioning will not only allow the transmission of new knowledge and skills, but also enables student participation in the learning
process, encouraging group dynamics and individual work. Problem solving, individually or in group, will provide that, in an active way, the student develops oral, writing and
criticism skills as well as the ability to adapt to new situations. The use of mathematical software to solve specific problems gives the students the opportunity to explore
computationally the contents of this Course. Moreover will also contribute to the development of skills acquired in the area of Curriculum Units for Mathematics and relate
them to the computational skills learned under other Curricular Units of the course. The two mini-tests are a methodology across all objectives of the course since these are all covered syllabus.

relevant generic skillimproved?assessed?
Achieving practical application of theoretical knowledgeYesYes
Adapting to new situationsYesYes
Analytical and synthetic skillsYesYes
Balanced decision makingYesYes
Commitment to effectivenessYesYes
Commitment to qualityYesYes
Creativity  
Ethical and responsible behaviourYes 
Event organization, planning and managementYesYes
Information and learning management  
Problem Analysis and AssessmentYes 
Problem-solvingYesYes
Relating to others  
Research skillsYes 
Self-assessmentYes 
TeamworkYes 
Written and verbal communications skillsYesYes
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