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Mathematical Applications

Code:

LTE21118

Sigla:

AM

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2022/2023 - 1S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2223/course/view.php?id=1717
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	36	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.

Some practical classes to use appropriate software for solving Mathematical Programming problems.

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

Leveraging the curricular unit can be obtained through two evaluation processes: Continuous Assessment and Evaluation for Exam.

Fórmula de cálculo da classificação final

CF=(T1+T2)/2