History of Mathematics
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2023/2024 - 2S
Cycles of Study/Courses
Teaching language
Suitable for English-speaking students
Objectives
Students are expected to become familiar with some of the major milestones in the history of Mathematics, and the evolution of some of the main seminal ideas and methods of this discipline. It is expected that the students acquire some critical perspective relative to some oversimplifications and historical distortions that are, unfourtunately, all too common in mathematical textbooks.
Learning outcomes and competences
To know some of the major milestones in the history of mathematics, and the evolution of some of the main seminal ideas and methods of this discipline.
To acquire some critical perspective relative to the historical development of mathematics, and also of some of its epistemological aspects.
Working method
Presencial
Program
The mathematics of ancient Egypt and ancient Mesopotamia. The Ionian school and the theorems attributed to Thales of Miletus, the Pythagorean school and the arithmetic of figurate numbers, the beginning of the theory of proportions, the reciprocal process of subtraction and the determination of greatest common divisor of two numbers, the discovery of incommensurable magnitudes, the areas of geometry and quadratures; the school of Elea and Zeno arguments against plurality and against motion; proofs by reductio ad absurdum, the axiomatic structure of mathematics, the attempts to trissect the angle, squaring the circle and duplicating the cube. Euclid's Elements. The work of Archimedes, the work of Apollonius of Perga, the Arithmetic of Diophantus. The beginnings of trigonometry. The algebra of the Arabs: the quadratic equations in the treaties of al-Khwarizmi and Abu Kamil, the cubic equations in the treaty of Omar Khayam. Mathematics in Medieval and Renaissance Europe. Forerunners of Infinitesimal CalculusMandatory literature
Maria Fernanda Estrada;
História da matemática. ISBN: 972-674-315-X
Victor J. Katz;
A history of mathematics. ISBN: 0-673-38039-4
Carl B. Boyer;
História da matemática
Complementary Bibliography
Euclid;
The thirteen books of the Elements. ISBN: 0-486-60088-2 (Vol. 1)
C. H. Edwards, Jr;
The historical development of the calculus. ISBN: 0-387-90436-0
John, ed. lit. Fauvel;
The history of mathematics. ISBN: 0-333-42791-2
Teaching methods and learning activities
Lectures and classes: The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts and to give the students an orientation to solve problems and exercises. There are also practical lessons, where exercises and problems related are solved. The students have access to exercises and other resources to support their study. Also, there are weekly periods of tutorials.Evaluation Type
Distributed evaluation with final exam
Assessment Components
designation |
Weight (%) |
Exame |
75,00 |
Apresentação/discussão de um trabalho científico |
10,00 |
Trabalho escrito |
15,00 |
Total: |
100,00 |
Amount of time allocated to each course unit
designation |
Time (hours) |
Estudo autónomo |
71,00 |
Frequência das aulas |
56,00 |
Trabalho escrito |
35,00 |
Total: |
162,00 |
Eligibility for exams
Not appliable.
Calculation formula of final grade
There will be two tests of o90 minutes and 7,5 points each. The final exam will be a 3-hour examination for 15 points, consisting of two parts, corresponding to the tests and where students will be able to choose to make anew or use the marks obtained in the tests.
The examination of the "appeal" period will be made in the same way as the one of "normal" period.
There will be a written group work for 3 points and an individual presentation of that work for 2 points.
Final Mark = Exam+Presentation+Written Work
Special assessment (TE, DA, ...)
Exam for 15 points and possibility to resubmit a written work.
Classification improvement
Exam for 15 points and possibility to resubmit a written work.