## TATA34 Lectures

Schedule for 2023. (Intended plan, may be changed.)

*N.B. The course will be given*

**on campus**(as long as this isn't strictly forbidden).Lecture |
Date
| Subject | Course book |

1 | 28/8 13-15 | The real numbers | 1.1-1.4 |

2 | 1/9 13-15 | Infinite sets, Limits of sequences | 1.4-1.6, 2.2-2.3 + Kardinalitet |

3 | 4/9 15-17 | Limits of sequences | 2.4-2.6 |

4 | 11/9 15-17 | Series, The Cantor set | 2.7, 3.1 |

14/9 |
Hand-in round 1 ^{*}
| ||

5 | 18/9 13-15 | The Cantor function, topology | 3.2 |

22/9 13-15 | Discussion on exercises round 1 | ||

6 | 25/9 15-17 | Topology | 3.3-3.4 |

28/9 |
Hand-in round 2 ^{*}
| ||

7 | 2/10 13-15 | Limits and continuity | 4.2-4.5 |

6/10 13-15 | Discussion on exercises round 2 | ||

15/10 |
Hand-in round 3 ^{**}
| ||

8 | 16/10 15-17 | Fixed point theorems | Exercise 4.3.9 |

9 | 30/10 13-15 | Derivatives | 5.2-5.4 |

3/11 13-15 | Discussion on exercises round 3 | ||

10 | 6/11 15-17 | Uniform convergence | 6.2-6.4 |

7/11 |
Hand-in round 4 ^{*}
| ||

11 | 13/11 13-15 | Power series | 6.5 |

12 | 20/11 13-15 | The Riemann integral | 7.2-7.6 |

26/11 |
Hand-in round 5 ^{***}
| ||

13 | 27/11 15-17 | The Riemann integral | 7.2-7.6+ En konstig kurva |

4/12 15-17 | Discussion on exercises round 4 (and 5) | ||

10/12 |
Hand-in round 6 ^{*}
| ||

15/12 13-15 | Discussion on exercises round 5 (and 6) |

^{*}It is ok to hand in your solutions in the course's mailbox no later than 10.15 the day after the deadline listed above.

^{**}For round 3 it is ok to hand in your solutions in the course's mailbox no later than 15.00 the day after the deadline listed above, or at the

**very beginning**of the lecture starting at 15.15.

^{***}For round 5 it is ok to hand in your solutions in the course's mailbox no later than 15.00 the day after the deadline listed above, or at the

**very beginning**of the lecture starting at 15.15.

The book (Abbott) is mainly considering

**R**while I, during the lectures, will discuss many results more generally on metric spaces, in particular

**R**

^{n}, (when it doesn't cost too much). See the notes An introduction to metric spaces, by Andersson-Björn-Wiman for the metric space theory included in this course.

Page responsible: anders.bjorn@liu.se

Last updated: 2023-11-10