2025
Computational mathematics and algorithms
Name: Computational mathematics and algorithms
Code: MAT14992L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
1.Understand the concept of algorithms and develop the ability to use and design algorithms to solve various problems.
2. Consolidate learning from the curricular units of mathematics, arithmetic, algebra and combinatorics, elements of geometry, statistics and probability.
3. Ability to use computational methods and algorithms in non-mathematical application areas.
4. Ability to use online digital tools to solve mathematical problems or other areas.
2. Consolidate learning from the curricular units of mathematics, arithmetic, algebra and combinatorics, elements of geometry, statistics and probability.
3. Ability to use computational methods and algorithms in non-mathematical application areas.
4. Ability to use online digital tools to solve mathematical problems or other areas.
Contents
A1 Algorithm design. Algorithm performance.
A2 Diagrams, flowcharts and pseudocode
B1 Arithmetic algorithms: addition, subtraction, multiplication, division.
B2 Representation of numbers. Base-shifting algorithms.
B3 Greatest common divisor, least common multiple. Euclid algorithm, extended Euclid algorithm.
C Fast exponentiation algorithm in modular arithmetic.
D Sorting algorithms.
E Latin squares.
F Random number generators: random and pseudo-random.
G Substitution systems.
I Graph algorithms.
J Combinatorial games and strategies. Trickster game, Tower of Hanoi, other mathematical games.
A2 Diagrams, flowcharts and pseudocode
B1 Arithmetic algorithms: addition, subtraction, multiplication, division.
B2 Representation of numbers. Base-shifting algorithms.
B3 Greatest common divisor, least common multiple. Euclid algorithm, extended Euclid algorithm.
C Fast exponentiation algorithm in modular arithmetic.
D Sorting algorithms.
E Latin squares.
F Random number generators: random and pseudo-random.
G Substitution systems.
I Graph algorithms.
J Combinatorial games and strategies. Trickster game, Tower of Hanoi, other mathematical games.
Teaching Methods
Classes in theoretical-practical format, expository of content, articulated with the presentation of examples and exercises. The presentation moments alternate with the presentation of applications and discussion on solving associated problems. Applications can be proposed and presented by students and must be related to the algorithmization of a problem. Moments to perform exercises in groups and individually. Calls to the board for students to present concepts and solve problems to their colleagues. Some software will be used, possibly Python, R, Excel or another to be decided by the teacher. In this way, the recommendations and guidelines of the pedagogical model of the university of Évora are taken into account.
Assessment
Continuous assessment regime or a final exam assessment regime.
Continuous assessment will consist of several short moments - questions in class, these assessment moments being simultaneously assessment and practice/learning. They can be held every week or with a schedule to be agreed by the teacher at the beginning of the academic year. These moments must be more than 5 throughout the semester (1/3 of the total number of weeks).
In addition to the questions in class, a final written test and group work will be carried out, focusing on the implementation of an algorithm.
Each question in will have a fixed price (e.g. 2 points). The final grade for questions in is obtained by adding the partial grades for each question and normalized to 20 points. The weight of questions in will be 30% of the final grade. Group work will account for 30% of the final grade. The final test will weigh 40% of the final grade.
Continuous assessment will consist of several short moments - questions in class, these assessment moments being simultaneously assessment and practice/learning. They can be held every week or with a schedule to be agreed by the teacher at the beginning of the academic year. These moments must be more than 5 throughout the semester (1/3 of the total number of weeks).
In addition to the questions in class, a final written test and group work will be carried out, focusing on the implementation of an algorithm.
Each question in will have a fixed price (e.g. 2 points). The final grade for questions in is obtained by adding the partial grades for each question and normalized to 20 points. The weight of questions in will be 30% of the final grade. Group work will account for 30% of the final grade. The final test will weigh 40% of the final grade.
Teaching Staff
- Carlos Correia Ramos [responsible]
Certificações
