Introduce the basic notions and techniques of abstract algebra through the study of the first properties of fundamental algebraic structures: groups, rings and fields.
Curriculum
teacher profile teaching materials
I. Herstein, Algebra - Editori Riuniti (2010)
D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.
Programme
Groups: symmetri, dihedral, cyclic groups. Subgroups. Cosets and Lagrange theorem. Homomorphisms. Normal subgroups and quotient groups. Homomorphism theorems. Actions of a group on a set. Orbits and stabilizers theorems. Sylow theorems and their applications. Rings: Rings, domains and fields. Sub-rings, subfields and ideals. Homomorphisms. Quotient rings. Homomorphism theorems. Prime and maximum ideals. The quotient field of a domain. Divisibility in a domain. Fields: Field extensions (simple, algebraic and transcendental). Splitting field of a polynomial. Finite fields.Core Documentation
G.M. Piacentini Cattaneo, Algebra,un approccio algoritmico, Decibel -Zanichelli.I. Herstein, Algebra - Editori Riuniti (2010)
D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.
Type of delivery of the course
The course will take place with lectures, exercises and tutoring. In the event of an extension of the health emergency from COVID-19, the methods of carrying out the teaching activities and student assessment will be implemented. If necessary, the Microsoft Teams platform will be used for distance learning.Type of evaluation
The exam will consist of a written and an oral test at the end of the course. During the course there will be two partial written tests that will be evaluated as a written exam. To those who pass both tests during the course with a vote higher than 18/30 (for each test) the teacher will propose a vote to verbalize the exam without the need to take an oral test. This proposal may also be refused by students if they wish to take an oral test to try to improve the final result. The oral is however necessary for those who want to aspire to praise. The written test (including the partial tests) consists of 5/6 practical / theoretical exercises to be carried out in 2.30 / 3 hours. teacher profile teaching materials
I. Herstein, Algebra - Editori Riuniti (2010)
D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.
Programme
Groups: symmetri, dihedral, cyclic groups. Subgroups. Cosets and Lagrange theorem. Homomorphisms. Normal subgroups and quotient groups. Homomorphism theorems. Actions of a group on a set. Orbits and stabilizers theorems. Sylow theorems and their applications. Rings: Rings, domains and fields. Sub-rings, subfields and ideals. Homomorphisms. Quotient rings. Homomorphism theorems. Prime and maximum ideals. The quotient field of a domain. Divisibility in a domain. Fields: Field extensions (simple, algebraic and transcendental). Splitting field of a polynomial. Finite fields.Core Documentation
G.M. Piacentini Cattaneo, Algebra,un approccio algoritmico, Decibel -Zanichelli.I. Herstein, Algebra - Editori Riuniti (2010)
D. Dikranjan - M.S. Lucido, Aritmetica e algebra, Liguori.
Type of delivery of the course
The course will take place with lectures, exercises and tutoring. In the event of an extension of the health emergency from COVID-19, the methods of carrying out the teaching activities and student assessment will be implemented. If necessary, the Microsoft Teams platform will be used for distance learning.Type of evaluation
The exam will consist of a written and an oral test at the end of the course. During the course there will be two partial written tests that will be evaluated as a written exam. To those who pass both tests during the course with a vote higher than 18/30 (for each test) the teacher will propose a vote to verbalize the exam without the need to take an oral test. This proposal may also be refused by students if they wish to take an oral test to try to improve the final result. The oral is however necessary for those who want to aspire to praise. The written test (including the partial tests) consists of 5/6 practical / theoretical exercises to be carried out in 2.30 / 3 hours.