History of Mathematics
- Professors:
- Rosso Riccardo
- Year:
- 2016/2017
- Course code:
- 500668
- ECTS:
- 6
- SSD:
- MAT/04
- DM:
- 270/04
- Lessons:
- 48
- Period:
- I semester
- Language:
- Italian
Objectives
The course is aimed at presenting the historical development of the theory of algebraic equations
Teaching methods
Lessons in a class
Examination
Oral exam
Prerequisites
A knowledge of algebra of an undergraduate student
Syllabus
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. The quintic and elliptic functions
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. The quintic and elliptic functions
Bibliography
S. Maracchia: "Storia dell'Algebra". Liguori, Naples (2005)
J.P. Tignol: "Galois Theory of Equations". World Scientific, Singapore (2001).
J.V. Armitage, W.F. Eberlein: "Elliptic functions". Cambridge University Press (2006).
Notes available on the website of the course
J.P. Tignol: "Galois Theory of Equations". World Scientific, Singapore (2001).
J.V. Armitage, W.F. Eberlein: "Elliptic functions". Cambridge University Press (2006).
Notes available on the website of the course
Dipartimento di Matematica ''F. Casorati''
Università degli Studi di Pavia -
Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602