History of Mathematics

Code:

M385

Acronym:

M385

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2015/2016 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	17	Plano de estudos a partir de 2009	3	-	7,5	-

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. The symbolic algebra Viète. The creation of analytic geometry. At least one of the following three topics: the origins of the infinitesimal calculus, the genesis of non-Euclidean geometries, the genesis of the theory of groups. The foundational crisis in the late nineteenth and early twentieth century.

Mandatory literature

Katz Victor J.; A history of mathematics. ISBN: 0-673-38039-4
Estrada Maria Fernanda; História da matemática. ISBN: 972-674-315-X

Complementary Bibliography

Kline Morris; Mathematical thought from ancient to modern times. ISBN: 0-19-501496-0
Euclid; The thirteen books of the Elements. ISBN: 0-486-60088-2 (Vol. 1)
Waerden Barten L. van der; Science awakening
Gillings Richard J.; Mathematics in the time of the pharaohs. ISBN: 0-486-24315-X

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	100,00
Total:	100,00

Calculation formula of final grade

The final classification may result from the sum of the marks obtained in the two tests or the classification in the final exam.