Mathematics for Machine Learning (Winter term 2026/27)
Page is still under construction ...Lecture
What: Mathematics for Machine Learning, 9 CPLecturer: Prof. Ulrike von Luxburg
When and where: Tuesdays 10:15 - 11:45, lecture hall XX , Maria von Lindenstrasse 1; Thusdays 10:15 - 11:45, lecture hall XX , Maria von Lindenstrasse 1; First lecture is on Oct XX.
Background information
This course is intended for the students of the master
program in machine learning. Depending on your background,
some of the material might be a recap - or not. Contents of
the course are Linear algebra, Mulitvariate analysis,
Probability Theory, Statistics, Optimization. Note that the
course requires a solid basis in mathematics,
similar to what students would have attended in our Bachelor
program in computer science. The course is not recommended
for students without this background.
Info sheet about the setup of the lecture, coming soon
Registration
You need to register for this course in Ilias, link coming soon. Registration will be possible until the first week of term.Tutorials
We have weekly tutorial sessions in small groups of about 30 students, where you can ask questions and interact with other students, and work on assignments. The teaching assistants are: tbaLecture notes
The latex version (converted in hindsight, not yet perfectly proof-read)The handwritten slides from 2024
Assignments
... coming soon ...Exams
To be admitted to the exam, .... tba ...The exam is written. There will be two exams, one at the beginning of the semester break and one at the end. The dates are not known yet, they are determined by a central process. You can choose which exam to take, both will have the same difficulty. But note that there won't be a third exam nor oral exams: if you skip the first exam and fail the second one, you would need to wait for next winter term to take the exam again.
To see how the exam might look like, you can have a look at the following Mock exam.
Literature:
General:- Deisenroth, Faisal, Ong: Mathematics for Machine Learning, 2019. Not as deep as what we do in this class, but a good start.
- For linear algebra, I recommend: Sheldon Axler: Linear Algebra Done Right. Third edition, 2015. There are also online videos by the author if you want to get longer explanations than the ones I will provide.
- Calculus (Integration, Measures, Metric spaces and their topology): Sheldon Axler: Measure, Integration & Real Analysis. 2019
- Calculus (Differential calculus in R^n): Here I haven't found
my one favorite textbook for this course yet (some are too
recipe-like, the others a bit too abstract)
- My current favorite textbook, mathematically rigorous (but not
easy to read):
Terence Tao, Analysis 1 and 2.
- Books with many figures, but partly informal or recipe-like (might be good as a start if you need to get the intuition before diving deeper):
Stanley Miklavcic: An Illustrative Guide to Multivariable and Vector Calculus.
Charles Pugh: Real Mathematical Analysis - A classic: Rudin: Principles of Mathematical Analysis.
- If you are looking for a german book, I like: Walter: Analysis 1 and Analysis 2. The second one covers everything that we have been discussing.
- My current favorite textbook, mathematically rigorous (but not
easy to read):
- Probability theory: Jacod, Protter: Probability essentials. Short and to the point, tries to avoid measure theory whereever possible, yet is rigorous. Good compromise.
- Statistics:
- For a very short overview over all the topics we cover: Wasserman: All of statistics, a concise course in statisticial inferece.
- A bit more details: Casella/Berger, Statistical Inference.
- Testing, rigorously: Lehmann/Romano: Testing statistical hypotheses.
- Optimization
- For convex optimization: Boyd/Vandenberghe: Optimization
- Non-convex optimization basics, in the new book by Francis Bach, Learning Theory from first principles, pdf
- For high-dimensional probability and statistics there are several good books, but they go
much deeper than our lecture:
- Wainwritght: High-dimensional statistics
- Vershynin: High-dimensional probability
- Bühlmann, van de Geer: Statistics for High-dimensional data (this is from the more traditional statitics point of view)
