Mathematics of Machine Learning 2025

This is the main website for the Mathematics of Machine Learning course in the spring of 2025, as part of the bachelor of mathematics at the University of Amsterdam. Visit this page regularly for changes and updates.

Instructor: Tim van Erven (tim@ No spam, please timvanerven. No really, no spam nl)  
Teaching Assistants: TBA    

General Information

Machine learning is one of the fastest growing areas of science, with far-reaching applications. This course gives an overview of the main techniques and algorithms. The lectures introduce the definitions and main characteristics of machine learning algorithms from a coherent mathematical perspective. In the workgroups, students will both solve mathematical exercises to deepen their understanding, and apply algorithms from the course to a selection of data sets using Python Jupyter notebooks.

We will use Canvas for announcements, grades and submitting homework. I will also post my handwritten lecture notes there.

Required Prior Knowledge

  • Linear algebra, gradients, convexity
  • Ability to write mathematical proofs
  • Programming in Python with Jupyter notebooks
  • Writing in LaTeX

Although mainly targeting mathematics students, the course is accessible to other science students (AI, CS, physics, …) with an interest in mathematical foundations of machine learning.

Lectures and Exercise Sessions

  • Weekly lectures:

  • Weekly exercise classes

Examination Form

The course grade consists of the following components:

  • Homework assignments. H = Average of homework grades,
    excluding the lowest homework grade.
  • Two exams: midterm (M) and final (F).

The final grade is computed as 0.3H + 0.3M + 0.4F. If between 5 and 6, it is rounded to a whole point: 5 or 6. Otherwise it is rounded to half points.

Exams (closed book):

The midterm will be about the first half of the course. The final exam will only be about the second half of the course. The resit exam (R) will cover both halves; it will replace both the midterm and the final exam, with final grade 0.3H + 0.7R. Both exams will be closed book, meaning that it is not allowed to use external resources during the exam.

Course Materials

The main book for the course is The Elements of Statistical Learning (ESL), 2nd edition, by Hastie, Tibshirani and Friedman, Springer-Verlag 2009. In addition, we will use selected parts from Ch. 18 of Computer Age Statistical Inference: Algorithms, Evidence and Data Science (CASI) by Efron and Hastie, Cambridge University Press, 2016. Some supplementary material will also be provided, as listed in the Course Schedule.

Both books are freely available online, but you may consider buying a paper copy of the ESL book, because you will need to study many of its chapters. The standard edition of ESL is hard cover, but there also exists a cheaper soft-cover edition for €39.99. To get the cheaper offer, open this link from inside the university network.

Course Schedule

This schedule is subject to change during the course. Literature marked ‘optional’ is recommended for background, but will not be tested on the exam. TBA=To Be Announced.

Homework Assignments

The homework assignments will be made available here. It is allowed to work together in pairs of two students, which can change per assignment. It is not allowed to collaborate with other people. In case you miss a deadline because of illness or other special circumstances, contact Tim to discuss possible solutions.

Submit via Canvas. Write your answers in LaTeX.

Homework Extra Files Available Deadline

Further Reading

Here is a list of references for advanced further reading. These are all optional, and will not be tested on the exam.