# EMAp Summer Course

## Topological Data Analysis with Persistent Homology

Last release of the notes here. Video recordings of the lessons here.

#### First week: General topology

**26/01 (2pm-2:30pm) - Lesson 0 - Introduction**

Slides, notebook (html).*Homework: Exercise 0.***26/01 (2:30pm-4pm) - Lesson 1 - Topological spaces**

Slides, video.*Homework: Exercises 4 and 5.*

Facultative: Exercises 2 and 7.**27/01 (2pm-4pm) - Lesson 2 - Homeomorphisms**

Slides, video.*Homework: Exercises 8 and 11.*

Facultative: Exercise 10.**28/01 (2pm-4pm) - Lesson 3 - Homotopies**

Slides, video.*Homework: Exercises 12 and 16.*

Facultative: Exercises 13 and 14.**29/01 (2pm-4pm) - Lesson 4 - Simplicial complexes + Tutorial**

Slides, video, notebook (html), notebook correction (html).*Homework: Exercises 20 and 25.*

Facultative: Exercises 21 and 26.

**Comments:**

Correction of Exercises 4 and 5 by Lucas.

Correction of Exercises 8 and 11 by Tiago.

Correction of Exercises 12 and 16 by Manoel.

Learning the basics of Python on w3schools.

#### Second week: Simplicial homology

**01/02 (2pm-4pm) - Lesson 5 - Homological algebra**

Slides, video.*Homework: Exercises 29 and 30.*

Facultative: Exercise 27 and 28.**02/02 (2pm-4pm) - Lesson 6 - Incremental algorithm**

Slides, video.*Homework: Exercises 31 and 34.*

Facultative: Exercise 33.**03/02 (2pm-4pm) - Lesson 7 - Topological inference**

Slides, video.*Homework: Exercise 37.*

Facultative: Exercise 39, 40 and 41.**04/02 (2pm-4pm) - Lesson 8 - Datasets have topology + Tutorial**

Slides, video, notebook (html), notebook correction (html).

Facultative homework: Exercise 43.

#### Third week: Persistent homology

**08/02 (2pm-4pm) - Lesson 9 - Persistence modules - Decomposition**

Slides, video.*Homework: Exercise 52.*

Facultative: Exercises 48, 49 and 51.**09/02 (2pm-4pm) - Lesson 10 - Persistence modules - Stability**

Slides, video.*Homework: Exercise 53.***10/02 (2pm-4pm) - Lesson 11 - Persistent homology in practice + Tutorial**

Slides, video, notebook (html), notebook correction (html).

**Comments:**

Video of a barcode of Čech a filtration.