Lecture notes | Czech | English |
---|---|---|

Algebra 1 | alg1_cz | alg1_en |

Algebra 2 | alg1_cz | alg2_en |

To get ''Zápočet'' (i.e. to pass the exercise classes) you need to score at least 45 out of 70 points. Points can be obtained from 2 homework assigments (2*30 points), and in-class presentation (10 points). For more details see Filippo Spaggiari' website.

The final grade will be determined by an oral exam, admission to the exam requires passing the exercise class.

- Homomorphisms (group homomorphism, quotient groups, ring homomorphisms, ideals, classification of finite fields)
- Number fields (ring and field extensions, algebraic elements, and finite degree extensions)
- Algorithms in polynomial arithmetic (fast polynomial multiplication and division, decomposition)
- Other algebraic structures (lattices and Boolean algebras)

Date | Topics | Lecture notes | Homework |
---|---|---|---|

13/02 | Group homomorphisms and isomorphisms, invariants, classificationsEx: Examples | Section 1 | |

20/02 | Normal subgroups, quotient groups, homomophism theorem, 1st isomorphism theorem | Section 2 | |

27/02 | Ideals and divisibility, PIDs, ideals in fields Ex: quotient groups, intersection and sum of ideals | Section 3 | |

06/03 | Quotient rings, homomorphism theorem, 1st and 2nd isomorphism theorem for rings | Section 4.1,4.2 | |

13/03 | prime and maximal ideals; Ring and field extensions, degree Ex:quotient rings, ring and field extensions | Sections 4.3, 5 | 1st HW due 27.3 |

20/03 | Algebraic and transcendental numbers Minimal polynomials of algebraic numbers | Section 6 | |

27/03 | Extensions by more than one element, constructability, ruler-and-circle constructionsEx: minimal polynomials and algebraic numbers | Section 6.3, 7 | |

03/04 | Uniqueness of splitting fields (up to isomorphism), Classification of finite fields | Sections 8, 9 | |

Easter Monday | |||

17/04 | Modular representations of rings, Fast Fourier Transformation | Section 10 | |

24/04 | Fast polynomial multiplication and division, formal power seriesEx: general field extensions and their degree | Section 11 | |

International Workers' Day | |||

V-Day | 2nd HW due 24.5 |
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15/05 | Square-free factorizations of polynomials Berlekamp's algorithm for decomposition into irreducibles | Section 12 | |

22/05 | Berlekamp's algorithm; algebraic structures, substructures, homomorphismsEx: ordered sets, lattices and Boolean algebras | Sections 12, 13 |

If you have questions, do not hesitate to ask (either in person or via e-mail)! I have no official office hours, but if required, a personal meeting can be arranged. Please make also use of the exercise classes to discuss your questions.