The History and Issues of Mathematics

Objectives

1. To explain the historical evolution of ideas and mathematical theories.

2. To develop mathematical thinking based on its development over time, throughout civilizations and by way of the progress underlying different areas of mathematical knowledge.

3. To work on solutions for problems typical of different periods and civilizations, using relevant knowledge.

4. To explore different mathematical topics, deemed relevant for a better understanding of inherent curricular content.

5. To reflect on the historical dimension of mathematics in order to obtain motivational content and facilitate usefull kwnoledge for educational practice.

Program

1. Connection between men and mathematics, throughout history;

2. General aspects of the history of mathematics in Ancient Ages: Mathematics in Egypt, in Babylon, Greece, Rome, Arabia, China, India, Central America and Africa;

3. History of geometry: famous Problems and history of trigonometry – astronomy;

4. History of algebra: Mathematical Writings;

5. History of arithmetic: numeric system – numbering types;

6. History of probabilities and statistics;

7. Medieval mathematics and mathematics in the Renaissance – Europe;

8. History of Modern Mathematics;

9. Biography of some mathematicians;

10. Current topics of mathematics;

11. The importance of mathematics in the development of new technologies: some historical facts.

Teaching Methodologies

The student has theoretic-practical lessons and tutorial sessions in which the syllabus is explored in detail through problem solving and worksheets with practical exercises. The course will benefit from the use of Moodle, the learning management platform available at the University of the Azores, thus enhancing the performance of asynchronous activities.

Bibliography

Fernando Vasconcelos, História da Matemática na Antiguidade, 1927 e Ludus, 2009.

António C. Canas e M.E. Ferrão, A Matemática no Tempo do Mestre José Vizinho. Gradiva, 2009.

Edward B. Burger e Michael Starbird, O Matemático Disfarçado. Academia do Livro, 2009.

Nuno Crato, A Matemática das coisas: Do Papel A4 aos Atacadores de Sapatos, do GPS às Rodas Dentadas. Temas de Matemática, Gradiva, 2008.

B. J. Caraça, Conceitos Fundamentais da Matemática. Gradiva, 1998.

Philip J. Davis e Reuben Hersh, A experiência Matemática, Gradiva, 1995.

H. Eves, An Introduction to the History of Mathematics. Saunders College Publ.,1990.

S. Dirk, História Concisa da Matemática. Gradiva, 1989.

Carl B. Boyer, History of Mathematics. Princeton University Press, New Jersey, 1968.

Helena Melo, Breves notas sobre as normas programáticas nas escolas açorianas no século XIX que abarcam a disciplina de matemática, Supl. Boletim SPM, nº 65, pp 46-48, 2011.