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227-0434-10L 9 Credits DR , MSC , WBZ D-ITET , D-INFK , D-MATH , D-PHYS

Mathematics of Information

Lecturers & Examiners: Prof. Dr. Helmut Bölcskei

VVZ CR 4.0

Last Updated: 2026-06-03 00:14:09

Abstract

The class focuses on mathematical aspects of1. Information science: Sampling theorems, frame theory, compressed sensing, sparsity, super-resolution, spectrum-blind sampling, subspace algorithms, dimensionality reduction2. Learning theory: Approximation theory, greedy algorithms, uniform laws of large numbers, Rademacher complexity, Vapnik-Chervonenkis dimension

Objective

The aim of the class is to familiarize the students with the most commonly used mathematical theories in data science, high-dimensional data analysis, and learning theory. The class consists of the lecture and exercise sessions with homework problems.

Content

Mathematics of Information 1. Signal representations: Frame theory, wavelets, Gabor expansions, sampling theorems, density theorems 2. Sparsity and compressed sensing: Sparse linear models, uncertainty relations in sparse signal recovery, super-resolution, spectrum-blind sampling, subspace algorithms (ESPRIT), estimation in the high-dimensional noisy case, Lasso 3. Dimensionality reduction: Random projections, the Johnson-Lindenstrauss Lemma Mathematics of Learning 4. Approximation theory: Nonlinear approximation theory, best M-term approximation, greedy algorithms, fundamental limits on compressibility of signal classes, Kolmogorov-Tikhomirov epsilon-entropy of signal classes, optimal compression of signal classes 5. Uniform laws of large numbers: Rademacher complexity, Vapnik-Chervonenkis dimension, classes with polynomial discrimination

Resources

Lecture Notes

Detailed lecture notes will be provided at the beginning of the semester.

Learning Materials (Links)

Main link
Course Website

General Information

Language: English
Levels: DR , MSC , WBZ
Frequency: Yearly recurring

Examination

Type: session examination
Mode: written 180 minutes
Aids: 10 handwritten or printed A4 pages summary (or 5 A4 pages on both sides). Electronic devices (laptops, calculators, cellphones, etc...) are not allowed.

Course Components

Type	Title	Time & Place	Hours
lecture	Mathematics of Information	Thu 09:15-12:00 (ML F 36)	3 h weekly
exercise	Mathematics of Information	Mon 14:15-16:00 (ML E 12)	2 h weekly
independent project	Mathematics of Information	No time listed	2 h weekly

Offered In

Computational Science and Engineering Master
- Electives (In the ‘electives’ subcategory, at least two course units must be successfully completed. All courses listed as core courses (not electives) for one of the following ETH MSc programmes, MSc Statistics, MSc Physics, MSc Computer Science, MSc (Applied) Mathematics, MSc Neural Systems and Computation, MSc Robotics, Systems, and Control, MSc Data Science, MSc Electrical Engineering and Information Technology, can be taken as an elective course in the MSc CSE without prior permission.)
Computer Science Master
- Majors
  - Major in Machine Intelligence
    - Elective Courses
Mathematics Master
- Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
  - Electives: Applied Mathematics and Further Application-Oriented Fields (¬)
    - Selection: Further Realms and Some UZH Courses
Electrical Engineering and Information Technology Master
- 01 - Courses of specializations
  - Track: Communication (The core courses and specialization courses below are a selection for students who wish to specialize in the area of "Communication", see . The individual study plan is subject to the tutor's approval.)
    - Specialization Courses (These specialization courses are particularly recommended for the area of "Communication", but you are free to choose courses from any other field in agreement with your tutor. Semester / Research Projects are not allowed in this category. A minimum of 40 credits must be obtained from specialization courses during the Master's Programme.)
  - Track: Computers and Networks (The core courses and specialization courses below are a selection for students who wish to specialize in the area of "Computers and Networks", see . The individual study plan is subject to the tutor's approval.)
    - Specialization Courses (These specialization courses are particularly recommended for the area of "Computers and Networks", but you are free to choose courses from any other field in agreement with your tutor. Semester / Research Projects are not allowed in this category. A minimum of 40 credits must be obtained from specialization courses during the Master's Programme.)
  - Track: Signal Processing and Machine Learning (The core courses and specialization courses below are a selection for students who wish to specialize in the area of "Signal Processing and Machine Learning ", see . The individual study plan is subject to the tutor's approval.)
    - Core Courses (These core courses are particularly recommended for the field of "Signal Processing and Machine Learning". You may choose core courses form other fields in agreement with your tutor. A minimum of 24 credits must be obtained from core courses during the MSc EEIT.)
      - Advanced Core Courses
Statistics Master (The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible.)
- Subject Specific Electives
Physics Master
- Electives
  - General Electives (Students may choose General Electives from the entire course programme of ETH Zurich - with the following restrictions: courses that belong to the first or second year of a Bachelor curriculum at ETH Zurich as well as courses from GESS "Science in Perspective" are not eligible here. The following courses are explicitly recommended to physics students by their lecturers. (Courses in this list may be assigned to the category "General Electives" directly in myStudies. For the category assignment of other eligible courses keep the choice "no category" and take contact with the Study Administration ( ) after having received the credits.))
CAS in Computer Science
- Focus Courses and Electives
Doctorate Information Technology and Electrical Engineering (A minimum of 12 ECTS credit points must be obtained during doctoral studies (also see sub-categories for details) More Information at )
- Subject Specialisation (The courses on offer below are but a small selection out of a much larger available number of courses. Please discuss your course selection with your PhD supervisor.)
Data Science Master
- Master Studies (Programme Regulations 2017)
  - Core Courses
    - Data Analysis
      - Information and Learning
- Master Studies (Programme Regulations 2023)
  - Core Courses
    - Data Analysis
Cyber Security Master
- Minor
  - Machine Intelligence
    - Elective Courses
Quantum Engineering Master
- Electives (This is a selection of courses particularly suitable for the MSc QE. In agreement with the tutor, students may choose other courses from the ETH course catalogue.)