Discrete Mathematics

Code:

EIC0011

Acronym:

MDIS

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2011/2012 - 1S

Active?	Yes
E-learning page:	http://moodle.fe.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	162	Syllabus since 2009/2010	1	-	5	56	135

Teaching language

Portuguese

Objectives

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.
The skills to be acquired include:
- the ability to represent situations using first order logic and to analyze them both in the models and the proof perspectives;
- mastering the basic concepts of sets, relations and functions;
- the ability to solve simple problems of number theory, in particular in its application to cryptography;
- the ability to perform inductive proofs and to formulate and solve problems through recurrence relations;
- the ability to solve problems using counting techniques.

Program

Propositional logic. Proof methods in propositional logic.
Quantifiers and knowledge representation. Proof methods in first order logic.
Sets and relations.
Functions.
Introduction to number theory.
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, Prentice-Hall International, 1998. ISBN: 0-13-602079-8

Complementary Bibliography

Richard Johnsonbaugh; Discrete mathematics. ISBN: 0-13-127767-7

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.

Software

LPL

keywords

Physical sciences > Mathematics > Discrete mathematics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	52,00
Test 1	Exame	2,00		2011-11-15
Test 2	Exame	2,00		2011-12-16
Test 3	Exame	2,00		2012-01-17
Test 4	Exame	2,00		2012-02-03
Personal study	Exame	75,00
	Total:	-	0,00

Eligibility for exams

To get attendance certificate, the student must obtain a global assessment of 7,5 and attend the legal number of lectures.

Calculation formula of final grade

Classification = [sum(Ti)-min(Ti)]/3
Ti (i=1,..,4) - test i classification

Examinations or Special Assignments

N/A.

Special assessment (TE, DA, ...)

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

Classification improvement

Classification improvement is possible in the next year.