Unit ALGEBRA II
- Course
- Mathematics
- Study-unit Code
- GP006035
- Curriculum
- In all curricula
- Teacher
- Anna Lorenzini
- Teachers
-
- Anna Lorenzini
- Hours
- 73 ore - Anna Lorenzini
- CFU
- 9
- Course Regulation
- Coorte 2021
- Offered
- 2021/22
- Learning activities
- Caratterizzante
- Area
- Formazione teorica
- Academic discipline
- MAT/02
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Groups, rings, fields.
- Reference texts
- Dikranjan-Lucido, Aritmetica e algebra, Liguori (2007)
Herstein, Topics in Algebra, Wiley (1975) - Educational objectives
- Mathematical comprehension and capability to connect the various subject of the course and to solve the proposed exercises.
- Prerequisites
- Good knowledge of the subjects of Algebra I, independently of the passing of such exam. What is needed in particular is a good confidence with the properties of natural and integer numbers (including the Euclidean division) and of the residue classes, of the functions and their invertibility, of the relations and finite cardinalities (including basic notions of combinatorics) an infinite cardinalities.
- Teaching methods
- face to face lessons and tutoring by advanced students
"assisted teaching" (exercises done with the help of the teacher and/or a tutor) - Other information
- Upon request, both the written test and the oral examination are given in English
usage of platform "uni-studium" - Learning verification modality
- Oral examination, lasting 45-60 minutes, which tends to evaluate the level of understanding of the topics treated and of critic study and personal rethinking.
The topic of the first question is chosen by the student. - Extended program
- Algebraic structures. Permutations. Omomorphisms. Direct products. Normality and conjugates. Cuachy theorem and Sylow theory.
Fundamental theorem of omomorphisms for groups and rings. Prime and maximal ideals.
Euclidean, principal and factorial rings. Characteristic of rings and fields. Polynomial rings.
Ring and field extensions. - Obiettivi Agenda 2030 per lo sviluppo sostenibile