Albert-Ludwigs-Universität Freiburg AG Pfaffelhuber
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Basics in Applied Mathematics (WS 2026/27)

Part I – Numerics: JProf. Dr. Diyora Salimova

Part II – Stochastics: Prof. Dr. Peter Pfaffelhuber

Part III – Optimization: Dr. Simon Buchwald

Assistant: Samuel Ayomide Adeosun

Tutor: Anas Achmit

Lecture: Tuesday and Thursday, 10–12, HS II, Albertstr. 23b.

Tutorials: Friday, 12–14 and 14–16, HS II, Albertstr. 23b. Every student is assigned to one of the two groups.

The course consists of three parts of five weeks each, taught by three different lecturers:

Lecturer Weeks Dates

Part I: Numerics

 Salimova 1–5 20.10.2026 – 19.11.2026

Part II: Stochastics

 Pfaffelhuber 6–10 24.11.2026 – 22.12.2026

Part III: Optimization

 Buchwald 11–15 12.1.2027 – 11.2.2027

Studienleistung for the three parts: there are two written tests per part (30 minutes each), and you need to pass one of the two for every part. There is no obligation to be present at the sessions. In class, you discuss the exercise sheets — which are optional — look critically at AI output, and engage with the course material. On every exercise sheet, about one exercise is practical, i.e. it asks you to write a program.

Studienleistung for the practical exercise (Praktische Übung): see the separate section below.

Oral examination: every student has to prepare all three parts, but will be examined on two of them only. There will be two examination dates; students are assigned to a date according to their wishes.

If you do not know how to program, note the course Python for Data Analysis, Thursday 14–16.

Lecturer: JProf. Dr. Diyora Salimova, 20.10.2026 – 19.11.2026.

Material for this part will be announced here.

Lecturer: Prof. Dr. Peter Pfaffelhuber, 24.11.2026 – 22.12.2026.

Content: elementary probability without measure theory. We start with the basic models (coin tossing, dice, urns), random variables and combinatorial formulae, then treat independence, product spaces and conditional probability, discrete random variables with expectation and variance, and finally densities and the central limit theorem. A catalogue of the most important distributions is given in the appendix.

Manuscript: The current version is here.

Exercise sheets: The sheets are handed out on Tuesdays and are discussed in the tutorials in the same week. About one exercise per sheet is practical, i.e. it asks you to write a program.

Sections Handed out

Sheet 1: Combinatorics and the configuration model for random graphs

Section 1 24.11.2026

Sheet 2: Independence, product spaces, conditional probability; Bernoulli, binomial and hypergeometric distributions

Sections 2, 5 1.12.2026

Sheet 3: Expectation, variance and covariance; geometric, negative binomial, Poisson and multinomial distributions

Sections 3, 5 8.12.2026

Sheet 4: Continuous random variables: densities, expectation and variance, the central limit theorem; the gamma distribution

Sections 4, 5 15.12.2026

Lecturer: Dr. Simon Buchwald, 12.1.2027 – 11.2.2027.

Material for this part will be announced here.

The practical exercise (Praktische Übung) takes place one or two weeks after the end of the lecture period, i.e. after 13.2.2027. The exact dates will be announced here.

Every lecturer hands out a few topics. You work in groups of two: a group is assigned one topic from the topic list, has to hand in a report on it, and gives a presentation about it. This is what is required for the Studienleistung of the practical exercise.

The list of topics will be published here.