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History of Mathematics

Class at Faculty of Education |


Introduction to the study of history of mathematics. The available literature.

Prehistory. Phylogeny and ontogeny. Expression of quantity in aboriginal languages.

First mathematical manuscripts. Egypt, Mesopotamia.

Mathematics in ancient Greece. The main centres and main figures. The main contributions of Eudoxus, Euclid, Archimedes, Apollonius, Diophantos.

Mathematics of oriental countries (China, India, Islamic countries). The main contributions of Arabic mathematicians. The transmission of oriental mathematics to Europe.

Development of algebra, the solution of cubic equations - Tartaglia, Cardano. Cassus irreducibilis and the invention of complex numbers. The proof of the insolubility of the quintic equations Galois, Ruffini, Abel. The use of algebra in geometry - the birth of analytic geometry.

First steps of non-Euclidean geometry. Lobachevski, Bolyai and Gauss. Riemann and the generalisation of geometry. The birth of topology.

The development of the calculus. Newton, Leibniz, Euler, Cauchy. The birth of the theory of real numbers. From calculus to set theory - Cantor.


Ancient Mathematics, in particular Greek. Medieval Maths (European, Arabic).

Mathematics of 16th-19th century