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Algorithms in Discrete Mathematics

Code: M2007     Acronym: M2007     Level: 200

Keywords
Classification Keyword
OFICIAL Mathematics

Instance: 2016/2017 - 1S Ícone do Moodle

Active? Yes
Responsible unit: Department of Mathematics
Course/CS Responsible: Bachelor in Mathematics

Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
L:B 0 Official Study Plan 3 - 6 56 162
L:M 90 Official Study Plan 2 - 6 56 162
L:Q 0 study plan from 2016/17 3 - 6 56 162
Mais informaçõesLast updated on 2016-12-15.

Fields changed: Calculation formula of final grade, Componentes de Avaliação e Ocupação, Fórmula de cálculo da classificação final, Componentes de Avaliação e Ocupação, Fórmula de cálculo da classificação final, Componentes de Avaliação e Ocupação

Teaching language

Suitable for English-speaking students

Objectives





The student should know and be able to apply the concepts and basic results covered in the course. It is intended that this unit contribute to the development of skills in the fields of discrete mathematics and algorithms.





Learning outcomes and competences

It is intended that by the end of this course the student can:
• Complete and give structure to some previously acquired basic knowledge;

• Solve problems through structured elementary methods;
• Understand and apply basic and universal concepts, that are basic for several tools of various sciences, in a context close to the applications;
• Use (and create, whenever possible) algorithmic solutions to various problems.

Working method

Presencial

Program





1. Revision of some basic principles of combinatorics: counting, listing, ordering, sets and multisets, counting functions of certain types (one-to-one, onto, increasing, decreasing), partitions, etc.; the combinatorics of permutations.

2. Decision trees and recursion: basic definitions, order, rank, depth-first and breadth first; recursive algorithms, sorting, Gray codes; recurrence relations, characteristic equation, Fibonacci and Catalan sequences, derrangements.

3. Introduction to graph theory: definitions and examples, isomorphism, random graphs; digraphs and flows; Euler circuits and hamiltonian cycles; trees, Prim and Kruskal algorithms, depth-first and breadth first.

4. Introduction to the analysis of algorithms. [Time permitting.]





Mandatory literature

Bender Edward A. 1942-; Mathematics for algorithm and systems analysis

Complementary Bibliography

Bondy J. A.; Graph theory with applications. ISBN: 0-333-17791-6
Cormen Thomas H.; Introduction to algorithms. ISBN: 9780262031417 hbk
Sedgewick Robert 1946-; An introduction to the analysis of algorithms. ISBN: 978-0-201-40009-0

Teaching methods and learning activities





Lectures and classes: The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts. There are also practical lessons, where exercises and related problems are solved. All resources are available for students at the unit’s web page.





keywords

Physical sciences > Mathematics > Algorithms
Physical sciences > Mathematics > Combinatorial analysis

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation Weight (%)
Exame 100,00
Total: 100,00

Calculation formula of final grade

There will be (between 2 and 4) optional tests during the semester, worth 15/20. The marks obtained on each test can be used on the final exam, as described below.

The final exam consists of N+1 parts, where N is the number of tests that took place during the semester, and each of these N parts corresponds to one of the tests. The mark on one of these parts is the maximum of the marks obtained on the corresponding test and on that part of the exam. On the second exam period, the maximum will also be over the mark on the corresponding part on the normal exam period. Together, these N parts are worth 15/20. The remaining part on the exam is worth 5/20 and does not correspond to any of the tests.

Special assessment (TE, DA, ...)

Any type of special student evaluation may take one of the following forms: exclusively an oral examination; an oral examination plus a written examination, the student being required to pass both of them; only a written examination. The option for one of them is the sole responsibility of the professors in charge of the course unit.

Observations

Article 13 of General Regulations for Student Evaluation at the levels of First Cycle, Integrated Masters, and Second Cycle at U.Porto, approved on May 19, 2010 (cf. http://www.fc.up.pt/fcup/documentos/documentos.php?ap=3&ano=2011): "Fraud committed during an exam, in any form, implies the annulment of the exam and the communication to the statutorily competent organ for possible disciplinary action."

Any student may be required to take an oral examination should there be any doubts concerning his/her performance on the assessment pieces.

Jury:
Samuel António de Sousa Dias Lopes
Pedro Ventura Alves da Silva
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