Department of Computer Science | Institute of Theoretical Computer Science | CADMO
Theory of Combinatorial Algorithms
Prof. Emo Welzl and Prof. Bernd Gärtner
Department of Computer Science | Institute of Theoretical Computer Science | CADMO
Prof. Emo Welzl and Prof. Bernd Gärtner
| Lecturers: |
Patrick Schnider (OAT Z 13.1) Lucas Slot (OAT Z 24) |
|---|---|
| Assistants: |
Julia Hütte Hannah Rotzoll Mats Bierwirth |
| Lectures: |
Tue 13-14, ML H 44, Fri 12-14, LFW C 5 |
| Exercise: | Wed 10-12, CHN F 46 |
| Language: | English |
| Contents: |
Fundamental concepts, techniques and results in Topological Data Analysis.
Preliminary list of topics:
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| Literature: |
The complete lecture notes from FS25 can be found here: [L] Lecture Notes.
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| 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. |
| Graded Homework 1: | Deadline April 11, 12:15 | Homework 1 |
|---|---|---|
| Graded Homework 2: | Deadline May 21, 23:59 | Homework 2 |
Absence. If there are compelling reasons why you cannot hand in a graded homework on the due date foreseen, please contact us post-haste 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 graded homeworks 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 18.02.2025 | Information about the course, Intro to Topological Spaces | Slides, Colab | [L] 1 | |
| #2 21.02.2024 | Mathematical Background | [L] 2.1, 2.2, 2.3 | ||
| #3 25.02.2025 | Algebra | Exercises 1 (Video for Exercise 6) | [L] 2.4 | |
| #4 28.02.2025 | Simplicial Complexes, Intro to Homology | Slides | [L] 3.1 | |
| #5 04.03.2025 | Homology | Exercises 2 | [L] 3.2.1-3.2.3 | |
| #6 07.03.2025 | Homology | [L] 3.2.4-3.2.6 | ||
| #7 11.03.2025 | Homology of spheres | Exercises 3, Colab | [L] 3.2.7 | |
| #8 14.03.2025 | Induced Homology, Brouwer fixed-point theorem | [L] 3.2.8, 3.2.9 | ||
| #9 18.03.2025 | Persistent Homology | Slides, Exercises 4 | [L] 4.1, 4.2 | |
| #10 21.03.2025 | Persistent Homology, Algorithms | Slides | [L] 4.3 | |
| #11 25.03.2025 | Complexes on Point Clouds | Slides, Exercises 5, Solution to Exercise 5.4 | [L] 5.1, 5.2 | |
| #12 28.03.2025 | Complexes on Point Clouds (cont'd) | Slides, Homework 1 | [L] 5.2, 5.3 | |
| #13 01.04.2025 | Bottleneck distance, Stability | Slides, Exercises 6 | [L] 6.1.1 | |
| #14 04.04.2025 | Guest Lecture: Bernadette Stolz (Max Planck Institute) | |||
| #15 08.04.2025 | Wasserstein Distance | Exercises 7, Colab | [L] 6.1.2 | |
| #16 11.04.2025 | Guest Lecture: Bastian Rieck (University of Fribourg) | |||
| #17 15.04.2025 | Interleaving Distance | Exercises 8 | [L] 6.2 | |
| #18 29.04.2025 | Stability for Cech Complexes | Exercises 9, Colab | [L] 6.2.3 | |
| #19 02.05.2025 | Stability for Cech Complexes, Interval decompositions | [L] 6.2, 6.3 | ||
| #20 06.05.2025 | Reeb graphs | Exercises 10, Slides, Homework 2 | [L] 7.1 | |
| #21 09.05.2025 | Guest Lecture: Pepijn Roos Hoefgeest | |||
| #22 13.05.2025 | Mapper | Exercises 11, Colab | [L] 7.3 | |
| #23 16.05.2025 | Homology and Interleaving Distance of Reeb graphs | [L] 7.1, 7.2 | ||
| #24 20.05.2025 | Multiparameter Persistence | Exercises 12, Slides | [L] 9 | |
| #25 23.05.2025 | Multiparameter Persistence | [L] 9 | ||
| #26 27.05.2025 | Applications | Slides | [L] 9 | |
| #27 30.05.2025 | Applications | TDA challenge | [L] 9 | |
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 graded homeworks during the semester. The graded homework 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 graded homeworks do count towards the final grade: Your two grades will account for 20% of your final grade each. Solving the graded homeworks in teams is not allowed. Besides one or two exercises, the graded homeworks 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 intro course is sometimes complemented by a special type of follow-up course called Projects in Topological Data Analysis in the following fall semester. In this course, students from four different universities will collaborate on projects in Topological Data Analysis in an international setting. After having completed the intro course, it is possible to do a semester, master or diploma thesis in the area.
