2024
History of Mathematics
Name: History of Mathematics
Code: MAT14235L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese, English
Regime de Frequência: Presencial
Presentation
This curricular unit allows students to acquire knowledge on the most important points in the history of mathematics, from ancient times to the present day.
Sustainable Development Goals
Learning Goals
O1 - Knowledge: experiencing the most important marks in the history of mathematics, from ancient history until today.
O2 - Skills and Competences: developing abstract reasoning, proof making, and the capacity of finding strategies to solve new problems, and relating different approaches to mathematics through time.
O2 - Skills and Competences: developing abstract reasoning, proof making, and the capacity of finding strategies to solve new problems, and relating different approaches to mathematics through time.
Contents
1. Aspects of Babylonian, Egiptian, and Greek mathematics in ancient history. Conceptions of infinity of ancient philosophers. Pitagorians, Exodus and the question of incommensurability. Euclid and the axiomatic method. The "method" of Archimedes. Zeno and the motion paradoxes. Plato and Platonism. Aristotle and logic.
2. Medieval mathematics and Renaissance. Fibonacci. Italian algebrists. Pedro Nunes. Cavalieri, Torricelli, Pascal, Kepler, and Galileu's indivisibles.
3. Descartes, Fermat, Newton, and Leibnitz. Birth of analytic geometry and infinitesimal calculus. The importance of series.
4. Important aspects of mathematics from 17th to 20th century: conceptions of mathematical infinity, analysis' rigour, algebraic resolubility, non-Eucledean geometries, impossibility theorems, set theory and other questions of foundations of mathematics.
5. Most important philosophical trends and their representants: Platonism, logicism, formalism, intutionicism, empiricism, nominalism.
2. Medieval mathematics and Renaissance. Fibonacci. Italian algebrists. Pedro Nunes. Cavalieri, Torricelli, Pascal, Kepler, and Galileu's indivisibles.
3. Descartes, Fermat, Newton, and Leibnitz. Birth of analytic geometry and infinitesimal calculus. The importance of series.
4. Important aspects of mathematics from 17th to 20th century: conceptions of mathematical infinity, analysis' rigour, algebraic resolubility, non-Eucledean geometries, impossibility theorems, set theory and other questions of foundations of mathematics.
5. Most important philosophical trends and their representants: Platonism, logicism, formalism, intutionicism, empiricism, nominalism.
Teaching Methods
Problem-solving sessions, where students are invited to work on their own or in small groups, with some moments of exposition or discussion involving the whole class.
The evaluation may be either continuous, done through between two and six partial tests and quizzes, done preferably during the classes, weighting 100% of the classification, the number of which is to be defined by the professor who is responsible for the course unit in each academic year, or by a final exam. Students who achieve a grade of 18 or above may have to do an extra oral exam. For these students the final grade is the maximum between 17 and the simple average of the previous grade and the oral exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process; the elements of formative evaluation will have no weight on the final mark
The evaluation may be either continuous, done through between two and six partial tests and quizzes, done preferably during the classes, weighting 100% of the classification, the number of which is to be defined by the professor who is responsible for the course unit in each academic year, or by a final exam. Students who achieve a grade of 18 or above may have to do an extra oral exam. For these students the final grade is the maximum between 17 and the simple average of the previous grade and the oral exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process; the elements of formative evaluation will have no weight on the final mark
Teaching Staff
- Bruno Miguel Antunes Dinis [responsible]
Certificações
