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ALGEBRA 1

CODE 25897
ACADEMIC YEAR 2020/2021
CREDITS 9 credits during the 1st year of 8760 Mathematics (L-35) GENOVA

9 credits during the 1st year of 8766 Mathematical Statistics and Data Management (L-35) GENOVA

SCIENTIFIC DISCIPLINARY SECTOR MAT/02
LANGUAGE Italian
TEACHING LOCATION GENOVA (Mathematics)
SEMESTER 1° Semester
TEACHING MATERIALS AULAWEB

AIMS AND CONTENT

LEARNING OUTCOMES

Provide basic mathematical language. Introduction to abstract algebraic notions by studying the algebra of integers, polynomials in a rational, real, complex or finite coefficient variable and their quotients. Theoretical notions of groups.

TEACHING METHODS

In presence

SYLLABUS/CONTENT

Introduction to the basic notions: sets, maps, surjectiive, , injective and bijective.

- Binary operation and their properties. Equivalence relations and induced quotients.

- Cardinality: countsble and uncountable sets. Permutations. Induction. Newton binomial formula.

- The integers: Euclidean algorithm and its applications. Prime numbers and unique factorization. The integers mod n. 

- Complex numbers.

- Polinomials: with rational, real or complex coefficients. Unique factorization property for polynomials. Irreducibility criteria.  Quotients and their properties: zero-divisors, nilpotents and invertible elements.

- Introduction to algebraic structures. Abelian groups. Subgroups, homomorphisms and quotients.

TEACHERS AND EXAM BOARD

Exam Board

MARIA EVELINA ROSSI (President)

MATTEO VARBARO

ALESSANDRO DE STEFANI (President Substitute)

LESSONS

TEACHING METHODS

In presence

LESSONS START

The class will start according to the academic calendar.

Class schedule

All class schedules are posted on the EasyAcademy portal.

EXAMS

EXAM DESCRIPTION

The exam consists of a written test and an oral exam.

Exam schedule

Date Time Location Type Notes
15/01/2021 09:00 GENOVA Scritto
18/01/2021 09:00 GENOVA Orale
12/02/2021 09:00 GENOVA Scritto
16/02/2021 09:00 GENOVA Orale
07/06/2021 09:00 GENOVA Scritto
08/06/2021 09:00 GENOVA Orale
08/07/2021 09:00 GENOVA Scritto
12/07/2021 09:00 GENOVA Orale
10/09/2021 09:00 GENOVA Scritto
13/09/2021 09:00 GENOVA Orale