Discrete Mathematics

Code:

L.EIC005

Acronym:

MD

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2023/2024 - 1S

Active?	Yes
Responsible unit:	Department of Informatics Engineering
Course/CS Responsible:	Bachelor 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
L.EIC	426	Syllabus	1	-	6	52	162

Teaching language

Suitable for English-speaking students

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 propositional and 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; (4) solving modular arithmetic equations; (5) performing inductive proofs; (6) formulating and solving problems through recurrence relations. (7) solve simple problems of graph theory.

Working method

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. Introduction to number theory. Congruences and modular arithmetic equations. Induction and recursion. Recurrent relations. Sets, relations, and partial orders. Functions. Graph theory.

Mandatory literature

Michael Huth; Logic in Computer Science. ISBN: 0-521-54310-X
Edgar G. Goodaire, Michael M. Parmenter; Discrete mathematics with graph theory. ISBN: 0-13-167995-3

Complementary Bibliography

John O.Donnell; Discrete mathematics using a computer, Springer. ISBN: 1-84628-241-1
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

Lectures: exposition of the elements in the syllabus.
Lab classes: resolution of exercises proposed each week.

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	92,00
Frequência das aulas	70,00
Total:	162,00

Eligibility for exams

To get attendance certificate, the student must attend the legal number of lectures. Students who obtained attendance in the previous year are exempted from attending practical classes.

Calculation formula of final grade

First test (50% of the final mark).
Second test (50% of the final mark).
If FT is the mark obtained in the first test and ST the mark obtained in second test, then the final mark is given by:
F = FT*(0.5) + ST*(0.5)  
FT,ST >= 6 and F >= 9.5
To get approval in the distributed evaluation, students must obtain a minimum of 6 points (in a total of 20) in each test and a minimum of 9.5 as final mark.

The students not obtaining approval, can take a resit exam, with a weight of 100% of the final mark.
Students that obtain a mark of at least 9.5 in one of the tests (FT >= 9.5 or ST >= 9.5) but have a final mark F < 9.5 may choose to take only the part (for a mark of 10) of the resit exam corresponding to the failing test < 6.

Special assessment (TE, DA, ...)

Students whose enrollment type do not require lecture attendance must perform the two tests. Special exams cover all the subjects.

Classification improvement

The second chance exam scope is on the whole course contents.
This exam can be used for classification improvement.