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

Algebra 1 | alg1_cz | alg1_en |

Algebra 2 | alg1_cz | alg2_en |

To obtain the credit (

- 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 |
---|---|---|---|

22/02 | Repetition groups, group homomorphisms and isomorphisms, invariantsEx: Examples | Section 1.1-1.3 | |

29/02 | Group classifications; Normal subgroups, quotient groups | Section 1.4, 2 | |

06/03 | The homomomorphism theorem and isomorphism theorems for groups; Ideals, PIDsEx: determining quotient groups, sums and intersections of ideas in Z |
Section 2, 3 | HW1 due 21/03 |

13/03 | Ring homomorphisms, quotient rings | Section 4 | |

20/03 | Isomorphism theorems for rings, prime/maximal ideals, ring and field extensions Ex:computing quotient rings, ring extensions |
Section 4,5.1 | |

28/03 | Algebraic and transcendental elements, the degree of a field extension, minimal polynomials | Section 5.2,6.1,6.2 | |

04/04 | minimal polynomials, degrees of general extensions, algebraic numbers are a fieldEx: computing minimal polynomials, degrees of extensions, splitting fields |
Section 6.2, 6.3 | HW2 due 18/04 |

11/04 | Problems solvable by ruler and compass Uniqueness of rupture fields and splitting fields | Section 7, 8 | |

18/04 | The classification of finite fieldsEx: Constructability of regular n-gons | Section 9 | |

25/04 | Modular representations, Fast Fourier Transform | Section 10 | |

02/05 | (self study) fast polynomial multiplication and division using FFTEx: primitive roots, FFT |
Section 11 | HW3 due 16/05 |

09/05 | fast polynomial multiplication and division using FFT square-free decomposition | Section 11, 12.1 | |

16/05 | Berlekamp's algorithmEx: formal power series, discussion of 3rd homework | Section 12 | |

23/05 |

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.