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Code: | M3015 | Acronym: | M3015 | Level: | 300 |

Keywords | |
---|---|

Classification | Keyword |

OFICIAL | Mathematics |

Active? | Yes |

Web Page: | https://moodle.up.pt/course/view.php?id=372 |

Responsible unit: | Department of Mathematics |

Course/CS Responsible: | First Degree in Mathematics |

Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|

L:B | 2 | study plan from 2016/17 | 3 | - | 6 | 56 | 162 |

L:CC | 9 | Plano de estudos a partir de 2014 | 2 | - | 6 | 56 | 162 |

3 | |||||||

L:F | 1 | study plan from 2017/18 | 2 | - | 6 | 56 | 162 |

3 | |||||||

L:G | 1 | study plan from 2017/18 | 3 | - | 6 | 56 | 162 |

L:M | 47 | Plano estudos a partir do ano letivo 2016/17 | 2 | - | 6 | 56 | 162 |

3 | |||||||

L:Q | 0 | study plan from 2016/17 | 3 | - | 6 | 56 | 162 |

MI:ERS | 3 | Plano Oficial desde ano letivo 2014 | 2 | - | 6 | 56 | 162 |

Teacher | Responsibility |
---|---|

Christian Edgar Lomp |

Theoretical and practical : | 4,00 |

Type | Teacher | Classes | Hour |
---|---|---|---|

Theoretical and practical | Totals | 1 | 4,00 |

Christian Edgar Lomp | 4,00 |

Last updated on 2018-09-18.

Fields changed: Components of Evaluation and Contact Hours

Fields changed: Components of Evaluation and Contact Hours

To introduce the basic concepts and results of Number Theory, together with some of its computational aspects. To give some of its cryptographical applications.

To know the basic concepts and results of Number Theory, as well as some of its computational aspects and some of its cryptographical applications.

M141 Álgebra Linear I

M142 Álgebra Linear II

CC101 Introdução à Programação

2. Unique factorization in Z

3. Unique factorization in k[x]

4. Gauss integers and applications to unique factorization

5. Arithmetic functions

6. Congruences

7. Primitive roots and the group of units U(Z/nZ)

8. Artin conjecture and nth power residues

9. Quadratic residuies

10. The Law of quadratic reciprocity

11. Legendre symbol and proof of the law of quadratic reciprocity

12. Algebraic numbers and algebraic integers

13. Quadratic Gauss sum

14. Introduction to algebraic number theory

15. Unique factorization in field of algebraic numbers

16. Cryptography: classical ciphers

19. Public Key Cryptography: Deffie-Hellman RSA

20. Fast algorithm to calculate powers mod n. Cryptographic system ElGamal

21. Finite fields

22. Proof of the Theorem that the multiplicative group of a finite field is cyclic.

24. Elliptic curves

Shoup Victor; A computational introduction to number theory and algebra. ISBN: 0-521-85154-8

Menezes Alfred J.; Handbook of applied cryptography. ISBN: 0-8493-8523-7

Endler O.; Teoria dos Números Algébricos

Lectures on the concepts and results of the subject matter, with many examples, and exercise solving classes.

designation | Weight (%) |
---|---|

Teste | 100,00 |

Total: |
100,00 |

designation | Time (hours) |
---|---|

Estudo autónomo | 106,00 |

Frequência das aulas | 56,00 |

Total: |
162,00 |

Quiz 1: in the first quiz, which will take place during class time and which is still to be scheduled, students can obtain up to 10 points. A student who does not obtain 2 points will automatically obtain a "failed" in the first exam period.

Teste 2: in the second quiz, which will take place in January, students can obtain up to 10 points. A student who does not obtain 2 points will automatically obtain a "failed" in the first exam period.

The final grade is the sum of the scores obtained in both quizzes or "failed" in case one of the scores is below 2 points.

2. The make-up exam consists of only one exam which contains two parts corresponding to Quiz 1 + 2. Students have to have at least 2 points in each of the parts.

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Page created on: 2019-03-18 at 16:41:33

Page created on: 2019-03-18 at 16:41:33