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# Discrete Mathematics

 Code: EIC0011 Acronym: MDIS

Keywords
Classification Keyword
OFICIAL Mathematics

## Instance: 2013/2014 - 1S (of 09-09-2013 to 20-12-2013)

 Active? Yes E-learning page: http://moodle.up.pt/ Responsible unit: Department of Informatics Engineering Course/CS Responsible: Master in Informatics and Computing Engineering

### Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
MIEIC 178 Syllabus since 2009/2010 1 - 6 70 148,5

### Teaching - Hours

 Lectures: 2,00 Recitations: 2,00
Type Teacher Classes Hour
Lectures Totals 1 2,00
Gabriel de Sousa Torcato David 2,00
Recitations Totals 6 12,00
Gabriel de Sousa Torcato David 4,00
Carla Alexandra Teixeira Lopes 8,00
Last updated on 2013-09-14.

Fields changed: Objectives, Resultados de aprendizagem e competências, Pre_requisitos, Métodos de ensino e atividades de aprendizagem, Fórmula de cálculo da classificação final, Componentes de Avaliação e Ocupação, Avaliação especial, Melhoria de classificação, Obtenção de frequência, Programa, Provas e trabalhos especiais

Portuguese

### Objectives

Background

Logic is the fondament of any scientific reasoning and that is the main reason for its inclusion in the first year of the program. Furthermore, in the case of a Computer Science program, Logic has direct operational relevance in multiple professional aspects.

Specific aims

The goals are the development of skills of rigorous reasoning and in the techniques of discrete mathematics required in several areas of computer science like problem solving, algorithm design and analysis, theory of computing, knowledge representation and security.

Percentual distribution

Scientific component: 100%

Technological component: 0%.

### Learning outcomes and competences

The skills to be acquired include: (1) representing situations using first order logic and to analyze them both in the models and the proof perspectives; (2) mastering the basic concepts of sets, relations, partial orders, and functions; (3) solving simple problems of number theory, in particular in its application to cryptography; (4) solving modular arithmetic equations; (5) performing inductive proofs; (6) formulating and solving problems through recurrence relations; (7) solving problems using counting techniques.

Presencial

### Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Knowledge of elementary mathematics.

### Program

Propositional logic. Proof methods in propositional logic. Quantifiers and knowledge representation. Proof methods in first order logic. Sets, relations, and partial orders. Functions. Introduction to number theory. Congruences and modular arithmetic equations. Induction and recursion. Recurrent relations. Counting principles. Permutations and combinations.

### Mandatory literature

Jon Barwise, John Etchemendy; Language proof and logic. ISBN: 1889119083
Edgar G. Goodaire, Michael M. Parmenter; Discrete mathematics with graph theory. ISBN: 0-13-167995-3

### Complementary Bibliography

Richard Johnsonbaugh; Discrete mathematics. ISBN: 0-13-127767-7
Edward R. Scheinerman; Mathematics: A Discrete Introduction, 3rd ed., Brooks/Cole Cengage Learning, 2013. ISBN: 978-0-8400-6528-5

### Teaching methods and learning activities

In theoretical lectures the syllabus topics are presented and application examples are discussed. Practical lectures are devoted to analyzing and solving problems aiming at developing and testing the above mentioned skills, resorting to support software in the logic topics.

LPL

### keywords

Physical sciences > Mathematics > Discrete mathematics

### Evaluation Type

Distributed evaluation without final exam

### Assessment Components

Designation Weight (%)
Participação presencial 0,00
Teste 100,00
Total: 100,00

### Amount of time allocated to each course unit

Designation Time (hours)
Estudo autónomo 106,00
Frequência das aulas 56,00
Total: 162,00

### Eligibility for exams

To get attendance certificate, the student must obtain a global assessment of 7,5 and attend the legal number of lectures. The attendance certificate may, in case of failure, release the student from attending classes on the next year.

### Calculation formula of final grade

Classification = [sum(Ti)-0.8*min(Ti)]/3.2 , Ti (i=1,..,4) - test i classification

### Examinations or Special Assignments

Test 1: 2013-10-14

Test 2: 2013-11-18

Test 3: 2013-12-16

Test 4: 2014-01-27

### Special assessment (TE, DA, ...)

Students whose enrollment type do not require lecture attendance must perform the four tests. Special exams are 2H30 long.

### Classification improvement

Classification improvement is possible in the next year.