ALGEBRA 1

ALGEBRA 1

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iten
Code
25897
ACADEMIC YEAR
2019/2020
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

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

Ricevimento: By appointment

Exam Board

MARIA EVELINA ROSSI (President)

MATTEO VARBARO

ALESSANDRO DE STEFANI

LESSONS

Teaching methods

In presence

LESSONS START

The class will start according to the academic calendar.

EXAMS

Exam description

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

Exam schedule

Date Time Location Type Notes
11/02/2020 09:00 GENOVA Scritto
13/02/2020 09:00 GENOVA Orale
04/06/2020 09:00 GENOVA Scritto
05/06/2020 09:00 GENOVA Orale
06/07/2020 09:00 GENOVA Scritto
08/07/2020 09:00 GENOVA Orale
10/09/2020 09:00 GENOVA Scritto
11/09/2020 09:00 GENOVA Orale