Complements of Mathematics 1

A.Y. 2021/2022
6
Max ECTS
42
Overall hours
SSD
MAT/04
Language
Italian
Learning objectives
Present a wide range of classical algebra issues by building basic knowledge in elementary algebra from a higher point of view.
Expected learning outcomes
Application of knowledge and methods for the solution of classical algebra problems.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
More specific information on the delivery modes of training activities for academic year 2021/22 will be provided over the coming months, based on the evolution of the public health situation.
Course syllabus
The course will focus on the concept of number. We will deal with explicit equations and their solutions with radicals, the solvability of equations and some geometric constructions.
Natural numbers, prime numbers and zero.
Algebraic numbers, equations and roots. Fields and splitting fields.
Real and complex numbers. Archimedean and non-Archimedean fields. Transcendent numbers.
Cubic and biquadratic. Diophantine equations. Elements of Galois theory.
Quaternions. Integers of Hurwitz. Group of quaternions.
Prerequisites for admission
Knowledge of the common basic notions (mainly of algebra) covered in the programs of the first and second year courses of mathematics is required.
Teaching methods
Lectures
Teaching Resources
M. Artin: Algebra, Bollati Boringhieri, 1997. Ultima edizione (in inglese): Algebra (2nd Edition) Addison Wesley, 2010
R. Bombelli: L'Algebra, Biblioteca della Scuola Normale Superiore, 1550 (sulla teoria geometrico sintetica delle equazioni algebriche)
B. Mazur: Imagining Numbers: (particularly the Square Root of Minus Fifteen), Farrar, Straus, and Giroux, 2003
Assessment methods and Criteria
Oral exam on the topics of the course. Students are invited to agree on a topic for conducting a seminar.
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 6
Lessons: 42 hours
Professor(s)
Reception:
Wednesday h. 2-4 p.m. or email contact
Zoom Meeting