The course consists of two mutually independent units. The outcome of Unit I is presenting the historical development of some basic concepts in mathematics The outcome of Unit II is presenting the historical development of the theory of algebraic equations

Lessons in a class

Oral exam

A knowledge of algebra of an undergraduate student

The contents of Unit I are the following:

Euclid and his ``Elements".
History of parallel straight lines and the birth of hyperbolic geometry.
Birth, development and acceptance of integer relative numbers.
History of numerical sets.

The contents of Unit II are the following:

Outline of the history of notations in algebra.
History of the rule of signs.
Algebra in Greek and arabic mathematics.
The solution of equations of the third and fourth degree: the Bologna school.
Birth of the modern formalism: Bombelli and Viète. The roots of unity.
History of Decartes' rule.
Rolle's theorem in the history of algebraic equations.
Prehistory and story of the fundamental theorem of algebra.
Lagrange and the algebraic solution of equations.
Abel-Ruffini's theorem.
The birth of group theory: Ruffini, Galois, Cauchy.

S. Maracchia: Storia dell'Algebra. Liguori, Naples (2005)
J.P. Tignol: Galois Theory of Equations. World Scientific, Singapore (2001)
Notes available on the website of the course