Mathematics of Information

Prof. Dr. Helmut Bölcskei

Offered in:

Basic information:

Lecture:Thursday, 9:15-12:00, live broadcast on the ETH video portal. The first lecture takes place on Thursday 03 March 2022, 9:15-12:00.
Exercise session:   Monday, 14:15-16:00, live broadcast on the ETH video portal. The first exercise session takes place on Monday 28 Feb. 2022, 14:15-16:00.
Instructor: Prof. Dr. Helmut Bölcskei
Teaching assistants: Thomas Allard, Clemens Hutter
Office hours: Monday, 16:15-17:15, via Zoom. Please contact the TAs for their Zoom IDs.
Lecture notes:Detailed lecture notes can be found below in the section 'Lecture notes and prerequisite material'. Exercise problem sets along with detailed solutions will be made availble as we go along, see the section 'Exercise sessions'. The access information for the notes will be sent by email to all students registered for the class.
Credits: 8 ECTS credits

Lecture Recordings:

The recordings of the lectures will be available the next day on the ETH video portal.

Course structure


We will post important announcements, links, and other information here in the course of the semester, so please check back often!

There will be no lecture and no exercise session in the first week of the semester. The class will start with the exercise session on Feb. 28th, 2022. During the first week of the semester, the students are kindly asked to watch the videos from last year's lecture starting from 25.2.2021 at 30:00 until 11.03.2021 at 00:39. The videos can be found under the following link or in the table below.

Course Info

The class focuses on mathematical aspects of information science and learning theory.

We encourage students who are interested in mathematical data science to take both this course and "401-4944-20L Mathematics of Data Science" by Prof. A. Bandeira. The two courses are designed to be complementary.

H. Bölcskei and A. Bandeira


This course is aimed at students with a background in linear algebra, probability, and basic functional analysis. In particular, familiarity with Hilbert spaces is expected on the level of the "Hilbert spaces" chapter posted below (excluding the appendices).

Lecture notes and prerequisite material

Recordings and handwritten notes

DateRecording LecturesHandwritten NotesRecording Exercises
03.03.2022 Lecture 1 iPad notes Exercise 1
10.03.2022 Lecture 2 iPad notes Exercise 2
17.03.2022 Lecture 3 iPad notes Exercise 3
24.03.2022 Lecture 4 iPad notes V2 Exercise 4
31.03.2022 Lecture 5 iPad notes Exercise 5
07.04.2022 Lecture 6 iPad notes Exercise 6
14.04.2022 Lecture 7 iPad notes Exercise 7
28.04.2022 Lecture 8 iPad notes no exercise
05.05.2022 Part 1, from 24:41
Part 2, until 44:30
iPad notes Exercise 9
12.05.2022 Lecture 10 iPad notes Exercise 10

Recordings from 2021

DateRecording LecturesHandwritten NotesRecording Exercises
25.02.2021 Lecture 1 (Notes) iPad notes Exercise 1 (Camera) Exercise 1 (Notes)
04.03.2021 Lecture 2 (Camera) Lecture 2 (Notes) iPad notes Exercise 2 (Camera) Exercise 2 (Notes)
11.03.2021 Lecture 3 (Camera) Lecture 3 (Notes) iPad notes Exercise 3 (Camera) Exercise 3 (Notes)
18.03.2021 Lecture 4 (Camera) Lecture 4 (Notes) iPad notes Exercise 4 (Camera) Exercise 4 (Notes)
25.03.2021 Lecture 5 (Camera) Lecture 5 (Notes) iPad notes Exercise 5 (Camera) Exercise 5 (Notes)
01.04.2021 Lecture 6 (Camera) Lecture 6 (Notes) iPad notes Exercise 6 (Camera) Exercise 6 (Notes)
15.04.2021 Lecture 7 (Camera) Lecture 7 (Notes) iPad notes
22.04.2021 Lecture 8 (Camera) Lecture 8 (Notes) iPad notes Exercise 8 (Camera) Exercise 8 (Notes)
29.04.2021 Lecture 9 (Camera) Lecture 9 (Notes) iPad notes Exercise 9 (Camera) Exercise 9 (Notes)
06.05.2021 Lecture 10 (Camera) Lecture 10 (Notes) iPad notes Exercise 10 (Camera) Exercise 10 (Notes)
13.05.2021 Exercise 11 (Camera) Exercise 11 (Notes)
20.05.2021 Lecture 12 (Camera) Lecture 12 (Notes) iPad notes
27.05.2021 Lecture 13 (Camera) Lecture 13 (Notes) iPad notes Exercise 13 (Camera) Exercise 13 (Notes)
03.06.2021 Lecture 14 (Camera) Lecture 14 (Notes) iPad notes

Homework Assignments

There will be exercise session notes posted every Thursday after the lecture. The TAs will inform you by email which of the problems in these notes will be solved in the exercise session the following Monday. The expectation is that you prepare these problems before the exercise session.

Exercise sessions

28.02.2022 Set 1 Solutions 1 Complements on the Fourier Transform
07.03.2022 Set 2 Solutions 2
14.03.2022 Set 3 Solutions 3 Complements on Wavelets
21.03.2022 Set 4 Solutions 4
28.03.2022 Set 5 Solutions 5
04.04.2022 Set 6 Solutions 6
11.04.2022 Set 7 Solutions 7
02.05.2022 Set 8 Solutions 8
09.05.2022 Set 9 Solutions 9 Notes on compact sets
16.05.2022 Set 10 Solutions 10

Previous years' exams and solutions

Recommended reading

If you want to go into more depth or if you need additional background material, please check out these books: