History of Mathematics

Code:

M3028

Acronym:

M3028

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2021/2022 - 2S

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	33	Official Study Plan	2	-	6	56	162
			3

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 Calculus

Mandatory 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 (%)
Teste	60,00
Exame	40,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

Not appliable.

Calculation formula of final grade

Approval of the course unit is obtained in the final exam.

There will be two tests of one hour each (on dates to be determined). Each test will have a weight of 30% of the final mark.

The final exam will be a 3-hour examination with a weight of 100%, consisting of three parts, the first two 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.

Special assessment (TE, DA, ...)

Examinations required under special statutes shall consist of a written test that may be preceded by an oral test, to assess if the student satisfies minimum conditions to attempt to obtain approval at the discipline in the written test.