Complements of Mathematics 1
A.Y. 2021/2022
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.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
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.
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
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
Professors:
Barbieri Viale Luca, Bianchi Mariagrazia
Professor(s)
Reception:
Email contact (usually for Tuesday h. 2-4 p.m.)
Office - Math Department