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Mathematical Applications

Code:

LTE21118

Sigla:

AM

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2023/2024 - 1S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2324/course/view.php?id=1836
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
LTE	25	Plano de Estudos	2	-	6	60	162

Língua de trabalho

Portuguese
Obs.: Portuguesa

Objetivos

This course aims to present a first reference to the modeling of real optimization problems, as well as to provide ample information about some of the techniques used to solve those problems. There will be an approach to the various themes according to the degree area, with a view to developing the ability to apply modeling and optimization techniques to real situations.

Resultados de aprendizagem e competências

• Understanding the origins, evolution, methodology and application areas of Operational Research.


• Modeling real problems in Mathematical Programming.


• Solving a Linear Programming (LP) problem by Simplex algorithms and geometrically.


• Formulating the dual problem of a LP problem and know the concepts associated with duality.


• Understanding the basics of modeling Integer Linear Programming (ILP) problems.


• Knowing methods of solving ILP problems – Cutting and Branch and Bound techniques.


• Solving the Transportation and Allocation problems through appropriate algorithms.


• Understanding the fundamental concepts of graphs.


• Solving the next problems through appropriate algorithms: Minimum Spanning Tree, Graph Coloring, Shortest-Path and Maximum Flow.


• Solving project management problems through appropriate techniques.


• Using specific software for solving Mathematical Programming problems and analyze the obtained solutions.

Modo de trabalho

Presencial

Pré-requisitos (conhecimentos prévios) e co-requisitos (conhecimentos simultâneos)

Knowledge of Mathematics acquired in secondary education and in the curricular units of Mathematics I and Mathematics II.

Programa

1. Origin and Nature of Operational Research
1.1. Components of an Operational Research (OR) study.
1.2. Mathematical modeling.
1.3. Brief reference to different OR models through illustrative examples.

2. Linear Programming
2.1. Introduction to Linear Programming (LP).
2.2. Methods of solving LP problems.
2.3. Duality.
2.4. Integer Linear Programming: solving methods.
2.5. Transportation and Allocation problems.

3. Graph Theory
3.1. Graphs: terminology, notation and basic concepts.
3.2. Minimum Spanning Tree problem, Graph Coloring problem, Shortest-Path problem and Maximum Flow problem.
3.3. Project management through PERT/CPM techniques.

Bibliografia Obrigatória

Departamento de Matemática; Aplicações de Matemática

Bibliografia Complementar

Biggs, N.L. ; Discrete Mathematics, Oxford University Press, 2ª edição, 2008
Hillier, F.S.; Lieberman, G.J., ; Introduction to Operations Research, McGraw-Hill, 2015
Oliveira, R.; Ferreira, J.; Investigação Operacional em ação: casos de aplicação, Imprensa da Universidade de Coimbra, 2014
Ramalhete, M.; Guerreiro, J.; Magalhães, A.; Programação Linear, vols 1 e 2, McGraw-Hill, 1985
Tavares, L.V.; Oliveira, R.C.; Themido, I.H.; Correia, F.N.; Investigação Operacional, McGraw-Hill, 1996

Métodos de ensino e atividades de aprendizagem

In the theoretical-practical classes are presented the basic concepts of the different subjects of the syllabus and the proofs of the main results, followed by problems solving. In this type of classes students will acquire an overview of the themes and their interconnections.

Tipo de avaliação

Distributed evaluation with final exam

Componentes de Avaliação

Designation	Peso (%)
Teste	100,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	102,00
Frequência das aulas	60,00
Total:	162,00

Obtenção de frequência

Fórmula de cálculo da classificação final

Let T1 and T2 be the test classifications rounded to tenths and CF=0.5T1x0.5T2 (rounded to units).

Avaliação especial (TE, DA, ...)

Students with special rights referred to in the Regulation of Academic Activities and Guidelines for Assessment and School Performance of IPS Students must, by the second week of the beginning of the semester, contact the person responsible for the curricular unit, to present their relevant specificities, under the terms provided for in the respective diplomas, otherwise they cannot be executed due to lack of objective conditions.

Melhoria de classificação

According to Article 11 of the Regulation of Academic Activities and Guidelines for the Assessment of Academic Performance of IPS Students, the improvement of classification may occur in the academic year of enrollment, at the time of appeal, or in the academic year following the of approval, in any period of assessment by examination, except for the special period.

Observações

Rules for conducting assessment tests/exams:

• During the assessment tests/exams, the presentation of an oficial identification document with a photograph will be mandatory.


• Students must take the tests/exams in their own IPS notebooks, for which they must first acquire a notebook from reprography (with 1 cover and 4 continuation sheets).


• The handling or display of mobile phones, or any other means of remote communication, during the test is not allowed, which is sufficient reason for the cancellation of the assessment test, regardless of whether they were used.


• The use of calculators is allowed.


• A form is allowed for consultation during the tests and will be made available in Moodle in advance.


• Leaving the room can only take place one hour after the start of the test/exam and will imply the final delivery of the test/exam.


• Exams or questions written in pencil are not accepted.


• It is not allowed to use a corrector pen in test/exam.

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Informations:

• Office hours will be published in Moodle.


• The CU will have all the information and specific materials in the Moodle platform. 


• Communication with students is made exclusively to the institutional address (@estudantes.ips.pt). It is up to the student to consult their area in the information system, on the course page in Moodle, as well as to manage and periodically consult their email account in the IPS domain, using it to communicate with the IPS services.