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## ALGEBRA 1

CODE 25897 2021/2022 9 cfu during the 1st year of 8766 STATISTICA MATEM. E TRATTAM. INFORMATICO DEI DATI (L-35) - GENOVA 9 cfu during the 1st year of 8760 MATEMATICA (L-35) - GENOVA MAT/02 Italian GENOVA 1° Semester 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.

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

ALDO CONCA (President)

MARIA EVELINA ROSSI

ALESSANDRO DE STEFANI (President Substitute)

## LESSONS

### 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
18/01/2022 09:00 GENOVA Scritto
20/01/2022 09:00 GENOVA Orale
15/02/2022 09:00 GENOVA Scritto
17/02/2022 09:00 GENOVA Orale
07/06/2022 09:00 GENOVA Scritto
08/06/2022 09:00 GENOVA Orale
04/07/2022 09:00 GENOVA Scritto
05/07/2022 09:00 GENOVA Orale
14/09/2022 09:00 GENOVA Scritto
15/09/2022 09:00 GENOVA Orale