### SET2020SPRING Course

#### Budapest Semester in Mathematics

*Instructor:*Dr Lajos Soukup

*E-mail:*lsoukup@gmail.com

*Text*: The course is based on printed handouts distributed in class

Link to the Handout

*Learning Outcomes*

we learn how to use set theory as a powerful tool in algebra, analysis, combinatorics, and even in geometry; we study how to build up a rich mathematical theory from simple axioms; we get an insight how set theory can serve as the foundation of mathematics

Course outline |
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Introduction. Logic in nutshell |

Set theory as the study of infinity. |

Countable sets and their combinatorics. |

Cardinalities. Cardinal arithmetic. |

Axiom of Choice. Ordered and well-ordered sets. Zorn lemma and its applications. |

Well-ordering Theorem. Transfinite induction and recursion. |

Applications in algebra, analysis, combinatorics and geometry |

Ordinals, ordinals arithmetic and its applications. |

Cardinalities revisited. Cofinalities. |

Infinite combinatorics. Continuum hypothesis. |

Axiomatic Set Theory |

*Homeworks:*

Link to file | Availability | Deadline |
---|---|---|

HW1 | available since Feb. 4, 2020, 10 a.m. | Feb. 11, 2020, 8:15 a.m. |

HW2 | available since Feb. 11, 2020, 10 a.m. | Feb. 25, 2020, 8:15 a.m. |

HW3 | available since Feb. 25, 2020, 10 a.m. | March 3, 2020, 8:15 a.m. |

HW4 | available since March 3, 2020, 10 a.m. | March 10, 2020, 8:15 a.m. |

2020s-HW5 | available since March 10, 2020, 10 a.m. | March 17, 2020, 8:15 a.m. |

*Grading*

- Homework assignments: 40%, midterm exam: 20%, final exam: 40%
- 12 homework assigments, the best 10 count
- Extra hw problems for extra credits
- A: 80-100%, B: 60-79%, C: 50-59%, D: 40-49% take-home midterm, in class, open book, comprehensive final.