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Last version 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.
  Optional: Exercises 2 and 7.
• 27/01 (2pm-4pm) - Lesson 2 - Homeomorphisms
  Slides, video.
  Homework: Exercises 8 and 11.
  Optional: Exercise 10.
• 28/01 (2pm-4pm) - Lesson 3 - Homotopies
  Slides, video.
  Homework: Exercises 12 and 16.
  Optional: 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.
  Optional: 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.
  Optional: Exercise 27 and 28.
• 02/02 (2pm-4pm) - Lesson 6 - Incremental algorithm
  Slides, video.
  Homework: Exercises 31 and 34.
  Optional: Exercise 33.
• 03/02 (2pm-4pm) - Lesson 7 - Topological inference
  Slides, video.
  Homework: Exercise 37.
  Optional: Exercise 39, 40 and 41.
• 04/02 (2pm-4pm) - Lesson 8 - Datasets have topology + Tutorial
  Slides, video, notebook (html), notebook correction (html).
  Optional homework: Exercise 43.

Third week: Persistent homology

• 08/02 (2pm-4pm) - Lesson 9 - Persistence modules - Decomposition
  Slides, video.
  Homework: Exercise 52.
  Optional: 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 a Čech a filtration.