Mathematics Connections

Code: MAT13961M

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Mathematics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese

Presentation

The UC Mathematical Connections promotes the learning of mathematics simultaneously with the learning of themes from other disciplines. Lectures are combined with the use of the experimental method, as well as the exploration of applications in various areas of knowledge.

Sustainable Development Goals

Educação de qualidade - Assegurar a educação inclusiva, e equitativa e de qualidade, e promover oportunidades de aprendizagem ao longo da vida para todos.

Inovação infraestrutura - Construir infraestrutura resiliente, promover a industrialização inclusiva e sustentável, e fomentar a inovação.

Cidades e comunidades sustentáveis - Tornar as cidades e os assentamentos humanos inclusivos, seguros, resilientes e sustentáveis.

Vida na água - Conservação e uso sustentável dos oceanos, dos mares, e dos recursos marinhos para o desenvolvimento sustentável.

Vida terrestre - Proteger, recuperar e promover o uso sustentável dos ecossistemas terrestres, gerir de forma sustentável as florestas, combater a desertificação, deter e reverter a degradação da Terra e deter a perda da biodiversidade.

Learning Goals

Recognize the contribution that mathematics offers to explain and model phenomena.
Master and understand the concepts, reasoning and mathematical techniques introduced.
Deepen mathematical themes, enhancing the use of mathematical concepts with ideas, techniques and practices from different disciplines such as the study of language, history, architecture, music, painting, biology, geography, among others.
Develop abstraction skills that allow the identification of mathematical notions and relationships in different phenomena.
Improve the ability to formalize reasoning, its articulation, the ability to communicate results and achieve them in an appropriate way.

1.Natural languages: Grammars. Historical approach. Structures in the literature. Combinatory. Demonstration and induction. Codes. Decryption.

2,Music: Scales and instruments. Musical writing. Harmony. Timbre. Resonance. Xylophones. Drums.

3.Architecture. Construction and geometry. Proportions, measures, vectors, stability. Parable, catenary. Models.

4. Painting: Physiology of vision and perception. Color systems. Perspective. The digital image. Natural pigments. Light and shadow by color.

5. Geography: Orography and geology. Landscape grammars. Logistics problems. Fractals. Models of geological accidents. Simulation of erosion processes.

6.Ecology: Trophic networks. Epidemics. Graphs. Simulation in board games.

7. Dance and performance: Movement. Choreographies. Symmetries and shapes. Kinematics. Representation.

8. Programming: Computers. Artificial intelligence, machine learning. Data base. Algorithms. Cellular automata. Natural computing

Teaching Methods

Each will be self-contained, although the sequence of topics is not casual. In each class:
(1) The context theme, the connection, is introduced, the mathematical contents involved are exposed, how they are articulated and examples of relationships and properties are presented.
(2) A list of exercises, to be carried out in and at home, which focuses on the mathematical techniques taught, is provided.
(3) Complementary experimental activities are illustrated and proposed.
The possibility of study visits and the invitation of expert speakers in some of the connections is foreseen.
Evaluation:
A final written test that focuses on formal and technical mathematical aspects (50%).
A written essay with experimental component, in group, on a theme of choice, with a final presentation (50%). The writing, the synthesis capacity, the adequacy of the complementary theme, the experimental design, the communication capacity and the argumentation capacity are evaluated
Final exame 100%