# Subject description - XP33CHM

Summary of Study |
Summary of Branches |
All Subject Groups |
All Subjects |
List of Roles |
Explanatory Notes
Instructions

XP33CHM | Chapters in higher mathematics | ||
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Roles: | S | Extent of teaching: | 2P |

Department: | 13133 | Language of teaching: | EN |

Guarantors: | Pták P. | Completion: | ZK |

Lecturers: | Pták P. | Credits: | 4 |

Tutors: | Semester: |

**Anotation:**

**Content:**

**Course outlines:**

1. | Introduction. Metric spaces | |

2. | Connectedness and the curve connectedness in metric spaces | |

3. | Compact metric spaces | |

4. | Complete metric spaces and the Banach fixed-point theorem | |

5. | Elementary proof of the Fundamental theorem of algebra | |

6. | Lattices and Boolean algebras | |

7. | The Stone representation for Boolean algebras | |

8. | Extension of states on a Boolean algebra (the Tychonoff theorem) | |

9. | Categories and morphisms | |

10. | Normal and Hilbert spaces | |

11. | The Riesz representation theorem for linear forms | |

12. | The Sperner lemma | |

13. | The Brower theorem on the fixed-points on the continuous mappings on ball in Rn | |

14. | An application on Brower theorem: The Perron theorem on eigenvalues |

**Exercises outline:**

**Literature:**

**Requirements:**

**Webpage:**

**Subject is included into these academic programs:**

Program | Branch | Role | Recommended semester |

DOKP | Common courses | S | – |

DOKK | Common courses | S | – |

Page updated 1.3.2021 17:52:22, semester: Z/2020-1, L/2021-2, L/2020-1, Z/2021-2, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |