History of Mathematics

Code:

M2021

Acronym:

M2021

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2019/2020 - 2S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:CC	6	Plano de estudos a partir de 2014	2	-	6	56	162
			3
L:F	0	Official Study Plan	3	-	6	56	162
L:G	0	study plan from 2017/18	3	-	6	56	162
L:M	68	Official Study Plan	2	-	6	56	162
L:Q	0	study plan from 2016/17	3	-	6	56	162

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

Katz Victor J.; A history of mathematics. ISBN: 0-673-38039-4
Estrada Maria Fernanda; História da matemática. ISBN: 972-674-315-X
Waerden Barten L. van der; Science awakening

Complementary Bibliography

Edwards, Jr C. H.; The historical development of the calculus. ISBN: 0-387-90436-0
Euclid; The thirteen books of the Elements. ISBN: 0-486-60088-2 (Vol. 1)
Gillings Richard J.; Mathematics in the time of the pharaohs. ISBN: 0-486-24315-X
Katz Victor J.; Taming the unknown. ISBN: 978-0-691-14905-9
Neugebauer O.; The exact sciences in antiquity. ISBN: 486-22332-9

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.

keywords

Physical sciences > Mathematics > Geometry
Physical sciences > Mathematics > Algorithms
Physical sciences > Mathematics > Number theory

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	100,00
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

Two written tests, the first for 8 points and the second for 12. The final classification results from the sum of the marks obtained in the two tests.

On the calendar day of the exam, the student can do an exam that consists of 2 parts, each corresponding to one test that can replace that part of the exam.

The jury can summon a student to an extra test to clarify any aspect of the student's test or exam.

Observations

Júri: Rosário Pinto e José Carlos Santos

New evaluation method for the unit History of Mathematics:

Weekly submission of exercise resolutions, counting the percentage of submissions in the student's classification; this item accounts for 4 points distributed as follows: 1 point for the submission in March and 1.5 points for those during April and during May;

A short written work, submitted via Moodle until the end of May, with different themes that students can choose from a list at Moodle; this item accounts for 4 points

A synchronous open-book test via Moodle, with open answers and different questions, although equivalent, for each student, drawn by themes by Moodle from a base of questions, covering the material presented in the slides provided; this item accounts for 12 points.

A short individual session by videoconference, intended to validate the test and the work of the student.