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##
ALGEBRA 1

## AIMS AND CONTENT

### LEARNING OUTCOMES

### TEACHING METHODS

### SYLLABUS/CONTENT

## TEACHERS AND EXAM BOARD

### Exam Board

## LESSONS

### TEACHING METHODS

### LESSONS START

### Class schedule

## EXAMS

### EXAM DESCRIPTION

### Exam schedule

CODE | 25897 |
---|---|

ACADEMIC YEAR | 2017/2018 |

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 |

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

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.

**Office hours:** To be decided later on when the general timetable will be fixed.

MARIA EVELINA ROSSI (President)

ALDO CONCA

MATTEO VARBARO

In presence

The class will start according to the academic calendar.

All class schedules are posted on the EasyAcademy portal.

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

Date | Time | Location | Type | Notes |
---|---|---|---|---|

22/01/2018 | 09:00 | GENOVA | Scritto | |

23/01/2018 | 14:00 | GENOVA | Orale | |

07/02/2018 | 14:00 | GENOVA | Scritto | |

12/02/2018 | 09:00 | GENOVA | Orale | |

07/06/2018 | 09:00 | GENOVA | Scritto | |

08/06/2018 | 09:00 | GENOVA | Orale | |

11/07/2018 | 09:00 | GENOVA | Scritto | |

13/07/2018 | 09:00 | GENOVA | Orale | |

13/09/2018 | 09:00 | GENOVA | Scritto | |

14/09/2018 | 09:00 | GENOVA | Orale |