Qualification and title awarded – Licenciatura in Computer Science, Licenciado

Regime: S1

2 hours lectures/week; 3 hours example classes in computer laboratory/week.

Programa:

Algebraic computational systems: graphical, symbolic and numerical capabilities. Introduction to programming with a computational system.

Métodos de Avaliação:

Two tests in computer laboratory and a practical assignment, in group, shared with the course of Linear Algebra / final written exam.

Pré-requisitos:

None.

Be familiar with the basic rules of the system Mathematica. Search for information about built-in functions using existing help systems in Mathematica. Understand the notions of precision and accuracy of a number. Define functions/programmes to solve specific problems using functional and rule-based programming. Use rewriting rules as assignment and programming elements. Build 2- and 3-dimensional graphic objects. Manipulate and build graphic objects using graphics primitives and style directives. Solve problems in Real Analysis, Linear Algebra and Number Theory with built-in and user-defined functions. Import and export data.

To give to the student a powerfull tool that will allow a modern aproach to the study and  discovery of mathematics.

Bibliografia:

Heikki Ruskeepää, Mathematica Navigator: Graphics and Methods of Applied Mathematics (Academic Press,1999);

R.J. Gaylord, S.N. Kamin & P.R. Wellin, An Introduction to Programming with Mathematica (TELOS 1996);

Nancy Blachman, Mathematica: a practical approach (Prentice Hall, 1992)

Wolfram, S., Mathematica: A System for Doing Mathematics by Computer (Addison Wesley, 1991);

Regime: S1

2 hours/week - lectures; 1 hours/week - examples classes; 2 hours/week - examples classes in computer room work.

Programa:

The functional programming paradigm using Haskell. Expressions, values and reduction. Basic types, algebraic types, induction and recursion. Higher-order functions. Polymorphism, classes, principal types. Modularity. Monads.

Métodos de Avaliação:

Written exam, tutorial exercises and project evaluation.

Pré-requisitos:

None.

At the end of the course the student should be able t

Bibliografia:

Introduction to Functional Programming, Richard Bird and Philip Wadler, Prentice-Hall, 1988 - Introduction to Functional Programming using Haskell, Richard Bird, Prentice-Hall, 1998 - The Craft of Functional Programming, Simon Thompson, Addison-Wesley, 1996.

Docentes:

Olga Pacheco

José Carlos Ramalho

Regime: S1

Theoretical and practical classes.

Programa:

Matrices, Linear systems, Vector spaces, Linear transformations, Determinants, Eingenvalues and Eingenvectors.

Métodos de Avaliação:

Two written tests and a practical assignment, in group, shared with the course of Computational Mathematics / final written exam.

Pré-requisitos:

Elementary set theory.

Resultados de Aprendizagem:

By the end of the course the students should be able to

Bibliografia:

António Monteiro, Álgebra Linear e Geometria Analítica (McGraw Hill, 2001)

Maria Paula Marques Smith, Emília Giraldes & Victor Hugo Fernandes, Curso de Álgebra Linear e Geometria Analítica (McGraw Hill, 1995).

Docentes:

Maria Isabel Caiado

Regime: S1

2 hours/week - lectures. 3 hours/week - examples classes.

Programa:

Introduction to the propositional calculus: connectives, formulas, truth-values, valuations, tautologies, logic equivalences.  Representation of sets, binary relations, functions, families of sets, equivalence relations, quotient sets. Finite and infinite sets, numerable and non-numerable, Cantor's theorem.  Induction and complete induction over natural numbers. Partially ordered sets: special elements, well-ordered sets, Zorn's lemma.

Métodos de Avaliação:

Written final exam (worth 70%) and two written exercises (worth 15% each).

Periodic assessment (two written tests) / Written final exam.

Pré-requisitos:

None.

Resultados de Aprendizagem:

Bibliografia:

Foundations of abstract mathematics, Kurtz, D.C., McGraw-Hill, 1992.

Introduction to set theory, K. Hrbacek and T. Jech, Marcel Dekker, Inc.2^nd edition.

Curso de Análise Matemática, J. Santos Guerreiro, Escolar Editora, 1989.

Bloch, E., Proofs and Fundamentals (Birkhauser, 2000).

Docentes:
José Carlos Cruz da Costa

Maria Joana Costa Cruz Oliveira Torres Ramos

Maria Paula Beirão Oliveira Marques Smith
Maria Suzana Freitas Sousa Mendes Gonçalves

Regime: S2

3 hours/week - lectures; 3 hours/week - examples classes.

Lectures (3 hours/week) and problem solving sessions (3 hours/week). The problems to be solved are proposed to the students with 1 or 2 weeks in advance.

Programa:

Sets and Functions: basic topics; Real numbers; Functions: limit and continuity; Integrals; Sequences of real numbers; Series of real numbers.

Sequences and series of real numbers. Power series. Real functions of a single variable. Limits and continuity. Derivatives. Taylor series. Integrals and applications.

Métodos de Avaliação:

Written examination.

Written tests (problem solving).

There are no prerequisites.

Basic knowledge of sequences and real functions of a single variable.

Resultados de Aprendizagem:

Dealing with real functions of one variable, to practise the rational thought, the immagination and the spirit of searching, to develop the student's ability for intuitive and rigorous presentations.

1. To solve problems on sequences and series. – 2. To use basic results about functions (continuity, derivatives, integrals) to solve problems. – 3. To calculate limits, derivatives and integrals. – 4. To develop functions in power series. – 5. To use the Taylor’s formula to compute approximations for values of functions and to bound the error.

Bibliografia:

T. Apostol, Cálculo - Vol 1 (Ed. Reverté, 1991); J. Campos Ferreira, Introdução à Análise Matemática (Fundação Calouste Gulbenkian, 1987); E. L. Lima, Curso de Análise - Vol 1 (Projecto Euclides, 1995).

1. Calculus (8th ed.), R. Larson, R. P. Hostetler, B. H. Edwards, McGraw-Hill (2006); 2- Calculus (3^rd ed.) Howard Anton, John Wiley & Sons (1988)

Docentes:

Rui Ralha

Regime: S2

Presentation classes, problem solving classes/tutorials, lab classes.

Programa:

Foundations of computers technology and computing: structure and

Métodos de Avaliação:

Tests, Practical assignments e Exam.

Pré-requisitos: None.

1. To describe and analyse data in a computer (text, images, integers, FP reals and CPU instructions) coded in different number systems

Bibliografia:

Computer Organization and Architecture - Designing for Performance, William Stallings, Prentice Hall, 6th Ed., 2002
Computer Systems: A Programmer's Perspective (CS:APP), Randal Bryant and David O'Hallaron,  Prentice Hall, 2003

Docentes:

Regime: S2

2 hours/week - lectures; 3 hours/week - example classes.

Programa:

Elements of Graph Theory: basic concepts; eulerian graphs; hamiltonian graphs; planar graphs; Euler formula. Introduction to Number Theory: divisibility; prime numbers; diophantine equations; modular adition; congruences modulo an integer; linear congruences and systems of linear congruences; Fermat's Little Theorem and Euler's generalisation; Wilson's Theorem; application to criptography.

Métodos de Avaliação:

Periodic evaluation and final written exam.

Pré-requisitos:

None.

On successfully completing this course, students should be able t

Bibliografia:

Burton, D. M., Elementary Number Theory (Wm. C. Brown Publishers, 1990)
Wiitala, S. A. , Discrete Mathematics - A unified approach (McGraw-Hill 1987)
Fejer, P.A., Simovici, D.A., Mathematical Foundations of Computer Science (Springer Verlag, New York, 1991).

Docentes:

Regime: S2

Theorical and practical classes.

Programa:

Procedural (Imperative) programming The C language. Searching & Sorting. Recursion and Try-and-error algorithms. Linear Data Structures, static and dynamic (arrays and linked-lists): concepts and algorithms.

Imperative Programming Introduction: The Programming concept (aims, difficulties and stages); The other programming paradigms; Imperative Languages History; Descendent Analysis of Problems; The Algorithm Concept:. C Programming Language: History and Philosophy; Information representation: data types; Simple instructions and C control structures; Information Access and storage: file management. Dynamic Data Structures: pointers, lists and trees;. Search and Sort Algothms. Recursion: problems; mathmatical case studies; "try-and-error" problem resolution. Structured Data Types: List --- Stacks e Queues; Associative Arrays; Tree-like structures --- binary trees, decision trees, expression trees, etc.

Métodos de Avaliação:

Theoric mark (x 0.60) and practica mark (x 0.40).

Pré-requisitos:

None.

Resultados de Aprendizagem:

Bibliografia:

Kernighan & Ritchie, The C Programming Language (ANSI C), 2nd edition, Prentice Hall Software series, 1988 P. Guerreiro, Elementos de Programação com C, FCA - Editora de Informática, 2001; L. Damas, Linguagem C, FCA - Editora de Informática, 1999; Leendert and Ammeraal, Programas e Estruturas de dados em C, Editora Presença, 1994; A.N. Ribeiro e J. Pina Miranda, Notas Práticas de Algorimtos e Estrruturas de Dados, Notas peda-gógicas, Univ. do Minho, 1995; J. A. Saraiva & A. N. Ribeiro, Estruturas de Dados: Listas ligadas dinâmicas. Notas peda-gógicas, Univ. do Minho, 1995.

Docentes:

Alberto Simões

Regime: S2

Lectures and tutorials.

Programa:

Regular languages, Finite Automata, Context-free Grammars, Push-down automata

Métodos de Avaliação:

Two tests during the semester; final exam.

Pré-requisitos:

Elementary set theory and induction.

Resultados de Aprendizagem:

- describe basic concepts about formal languages, automata, and grammars;

- identify regular languages;

- relate the notions of finite automata, recognizable languages, and regular languages;

- verify whether a word is accepted by a push-down automaton;

- determine the language generated by a context-free language and a push-down automaton recognizing it;

- understand automata as an abstract model of computation.

Bibliografia:

J. Hopcroft, J. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 1979; J. Costa, Autómatos e Máquinas de Turing, publicação do Departamento de Matemática da Universidade do Minho, 2004; J. Martin, Introduction to languages and the theory of computation, McGraw-Hill, 1996. T. Sudkamp, Languages and Machines, Addison-Wesley, 1997.

Docentes:

Regime: S1

Lectures (3 hours/week); example classes (3 hours/week).

Programa:

Introduction to group theory. Introduction to ring theory. Lattices and Boolean algebras. Introduction to universal algebra.

Métodos de Avaliação:

Periodic assessment / Final written examination.

Pré-requisitos:

Basic set theory and elementary number theory.

Resultados de Aprendizagem:

The student should be able to:

Bibliografia:

B.A. Davey and H.A. Priestley. Introduction to lattices and order, Cambridge Univ. Press, 1990.
J.B. Fraleigh. A First Course in Abstract Algebra, Addison-Wesley, 1982.
T.W. Hungerford, Algebra, Springer, 1996.

S. Burris e H. P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, 1981.

Docentes:

Carla Albertina Carvalhinho da Silva Mendes

Regime: S1

Lectures, Tutorials and Lab Classes.

Programa:

Algorithms vs Programming Languages: what is an algorithm? Algebraic algorithmic languages. Decisions in deterministic, non-deterministic and probabilistic machines.

Introduction to “Domain Theory”. Introduction to “Probability Theory”. Random variables and probabilistic model of algorithms.

Asymptotic notation. P and NP problems. Reduction. NP-complete problems.

Fundamental algorithms: the 2SAT and 3SAT problems. Davis-Putnam algorithm.

Causality nets. Integer Linear Programming.

Métodos de Avaliação:

Written examination and practical assignment.

Pré-requisitos:

Elementary knowledge of imperative programming and data-structures.

Resultados de Aprendizagem:

To be able to design algorithms for solving problems of different kinds, using an appropriate strategy and adequate (including non-linear) data-structures.

Bibliografia:

José Manuel Valença. Algoritmos e Complexidade.Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms. MIT Press, Cambridge,Mass., second edition, 2001.
Donald E. Knuth. The Art of Computer Programming: (1) Fundamental Algorithms, (2) Seminumerical Algorithms, (3) Sorting and Searching. Addison/Wesley, third edition, 1997/98. 3 volumes.

Docentes:

José Manuel Valença e Manuel Bernardo Barbosa

Regime: S1

 Theoretical and practical classes.

Programa:

Topological structure of Rn. Sucessions in Rn. Real functions of several variables. Multiple Integration.

Métodos de Avaliação:

Individual resolution of exercises  and  written examination.

Pré-requisitos:

One variable basic calculus.

Resultados de Aprendizagem:

By the end of the course the student should be able to:

- recognise topological notions of Rn;

- formulate simple arguments and conclusions about continuity and differenciability of several variables functions;

- apply, in simple cases, the theorems of inverse function and implicit function;

- identify and classify critical points;

- solve problems about multiple integration.

Bibliografia:

- “Introdução ao análise em Rm” J. Campos Ferreira, Dep. Mat. IST

- “Curso de análise, Vol II” E.L. Lima, Projecto Euclides

- “Cálculo diferencial e Integral”, N. Piskounov, Editorial Lopes da Silva

Docentes: Lucia Fernandez Suarez

Regime: S1

2 hours/week of theorectical lectures; 2 hours/week of practical work.

Programa:

Introduction to data communications. Elements of protocols.

Data link control. The HDLC protocol.

Local area networks. The TCP/IP Protocol Stack. Internetworking of TCP/IP networks.

Métodos de Avaliação:

Written examination (70%); Experimental component (25%); Development project (15%).

Pré-requisitos:

None.

The students should be able t

Bibliografia:

MSL, Comunicações por Computador, Notas de apoio às aulas teóricas, Grupo de

Comunicações por Computador, DI/UM, 2007.

J. Kurose and K. Rose, Computer Networking: A Top Down Approach Featuring The

Internet, Addison-Wesley, ISBN: 0-321-49770-8, 4th Edition 2008;

W.Stallings, Data and Computer Communications, 8ª Edição, Prentice Hall, ISBN: 0-

13-2433109, 2007.

A.S.Tanenbaum, Computer Networks, 4ª Edição, Prentice Hall, ISBN: 0130661023,

2003.