Department of Computer Science  Institute of Theoretical Computer Science  CADMO
Prof. Emo Welzl and Prof. Bernd Gärtner
Lecturers: 
Patrick Schnider (OAT Z 13.1) 

Assistants: 
Simon Weber (OAT Z 18), contact assistant Shengzhe Wang 
Lectures: 
Thu 1314, CAB G 51, Fri 1214, CAB G 61 
Exercise:  Wed 1012, CHN F 46 
Language:  English 
Contents: 
Fundamental concepts, techniques and results in Topological Data Analysis.
Preliminary list of topics:

Literature: 
The complete lecture notes can be found here: [L] Lecture Notes.

Prerequisites:  The course assumes knowledge of discrete mathematics, algorithms and data structures and linear algebra, as supplied in the first semesters of Bachelor Studies at ETH. 
Special Assignment 1:  21.3.  11.4. 12:15  Exercise Sheet 1 

Special Assignment 2:  2.5.  17.5. 12:15  Exercise Sheet 2 
Absence. If there are compelling reasons why you cannot hand in a special assignment on the due date foreseen, please contact us posthaste and we can look for a solution. Note, however, that we will grant requests of this type only in very exceptional cases (doctor's note, military service, funeral, etc.). Private events (vacation, sports, career fairs, etc.) are never sufficient grounds. As far as special assignments are concerned, you can hand them in to the contact assistant by email at any time before the due date, so there is no need to be present in person. Regarding the final exam, ETH regulations apply.
Exchange students. Exchange students enrolled for TDA in spring might want to return to their home university prior to the date of the final exam. If this applies to you and you nonetheless wish to be evaluated and given credits for TDA, then please take a look at the following website for current regulations.
In the table below you can find the lecture dates and the preliminary topics. The exercises and their solutions will be published here.
Date  Content  Exercises and links  Relevant chapters  
#1 22.02.2024  Information about the course, Intro to Topological Spaces  Slides, Colab  [L] 1  
#2 23.02.2024  Mathematical Background  Exercises 1 (Video for Exercise 6)  [L] 2.1, 2.2, 2.3  
#3 29.02.2024  Algebra  [L] 2.4  
#4 01.03.2024  Simplicial Complexes, Intro to Homology  Slides, Exercises 2  [L] 3.1, 3.2.1, 3.2.2  
#5 07.03.2024  Homology  [L] 3.2.13.2.3  
#6 08.03.2024  Homology  Exercises 3 Colab  [L] 3.2.43.2.6  
#7 14.03.2024  Homology of spheres  [L] 3.2.7  
#8 15.03.2024  Induced Homology, Brouwer fixedpoint theorem  Exercises 4  [L] 3.2.8, 3.2.9  
#9 21.03.2024  Persistent Homology  Slides  [L] 4.1, 4.2  
#10 22.03.2024  Persistent Homology, Algorithms  Slides Exercises 5 
[L] 4.3  
#11 28.03.2024  Complexes on Point Clouds  Slides  [L] 5.1, 5.2  
#12 11.04.2024  Complexes on Point Clouds (cont'd)  Exercises 6 SPA 1  [L] 5.2, 5.3  
#13 12.04.2024  Bottleneck distance, Stability  [L] 6.1.1  
#14 18.04.2024  Wasserstein distance  Exercises 7 Colab  [L] 6.1.2  
#15 19.04.2024  Guest Lecture: Bastian Rieck (Helmholtz München)  Slides  
#16 25.04.2024  Guest Lecture: Bernadette Stolz (EPFL)  Exercises 8  
#17 26.04.2024  Interleaving Distance  [L] 6.2  
#18 02.05.2024  Stability for Cech Complexes  Exercises 9 Colab  [L] 6.2.3  
#19 03.05.2024  Guest Lecture: Marius Huber (UZH)  
#20 10.05.2024  Interval Decompositions, Reeb graphs  Exercises 10 Slides  [L] 6.3, 7.1, 7.3  
#21 16.05.2024  Homology of Reeb graphs  [L] 7.1.1  
#22 17.05.2024  Interleaving Distance for Reeb graphs  Exercises 11 Colab SPA 2  [L] 7.2.1  
#23 23.05.2024  Multiscale Mapper  [L] 7.4  
#24 24.05.2024  Optimal Generators  Exercises 12 Slides  [L] 8.1, 8.2  
#25 30.05.2024  Applications  Slides  [L] 9  
#26 31.05.2024  Applications  TDA Challenge  
Every week we provide you with exercises. The students are split into small groups, and the members of each group work together. At the end of the session, for each exercise, a student from a group presents their solution to the rest of the students. In addition to the exercise sessions, we encourage you to solve the exercises in written form and to hand in your solutions to the teaching assistant. Your solutions are thoroughly commented, but they do not count towards your final grade. The motivation to work on the exercises stems from your interest in the topic (and possibly also the desire to succeed in the exam).
In addition, you receive two special assignments during the semester. The special assignment is to be solved in written form and you have two weeks of time to return your solutions/reports, typeset in LaTeX. In contrast to the exercises, these special assignments do count towards the final grade: Your two grades will account for 20% of your final grade each. Solving the special assignments in teams is not allowed. Besides one or two exercises, the special assignments may include a small research project, or you are asked to give a short talk about your last small research project. The format of this talk will be determined by the number of students who register for the course.
There is an oral exam of 30 minutes during the examination period. Your final grade consists to 60% of the grade for the exam and to 40% of the grade for the homework assignments.
You are expected to learn proofs discussed in the lecture, should be able to explain their basic ideas and reproduce more details on demand. You should also be able to give a short presentation on any topic treated throughout the course. One of the questions given to you during the exam is to solve one of the exercises posed throughout the semester. Roughly half an hour before the exam you get to know the exercise to be solved and one topic that you will be questioned about in particular, that is, you have 30 minutes preparation time. For this preparation, paper and pens will be provided. You may not use any other material, like books or notes.
For PhD students, the same rules apply for obtaining credit points as for all other participants. Taking the exam and achieving an overall grade of at least 4.0 (computed as a weighted average of grades for homework and the oral final exam as detailed above) qualifies for receiving credits. In order to comply with new regulations recently issued by the department, merely attending the course and/or handing in exercises is no longer sufficient.
This course is complemented by a special type of seminar Projects in Topological Data Analysis in the following fall semester. In this seminar, students from four different universities will collaborate on projects in Topological Data Analysis in an international setting. After having completed the course, it is possible to do a semester, master or diploma thesis in the area.