• Problem sheet 1: Thursday, 16 October 2025, 14:00 (via e-mail or in person)
• Problem sheet 2: Thursday, 30 October 2025, 14:00 (via e-mail or in person)
• Problem sheet 3: Thursday, 13 November 2025, (via e-mail or in person)
• Problem sheet 4: Thursday, 27 November 2025, (via e-mail or in person)

1. Thursday, 18 September 2025, 14:00–15:30: Organisation and overview
2. Thursday, 25 September 2025, 14:00–15:30: Graph Theory
3. Thursday, 02 October 2025, 14:00–15:30: Network Theory, Problem sheet 1
4. Thursday, 09 October 2025, 14:00–15:30: Information Theory – Entropy
5. Thursday, 16 October 2025, 14:00–15:30: Information Theory – Applications, Problem sheet 2
6. Thursday, 23 October 2025, 14:00–15:30: Game Theory – Shapley Values
7. Thursday, 30 October 2025, 14:00–15:30: Problem sheet 3
8. Thursday, 06 November 2025, 14:00–15:30:
9. Thursday, 13 November 2025, 14:00–15:30: Problem sheet 4
10. Thursday, 20 November 2025, 14:00–15:30:
11. Thursday, 27 November 2025, 14:00–15:30:
12. Thursday, 04 December 2025, 14:00–15:30: Repetition and questions
13. Thursday, 11 December 2025, 14:00–15:30: Written Exam
14. Thursday, 18 December 2025, 14:00–15:30: Exam review

• network and graph theory
• combinatorics and probability theory
• game theory
• information theory
• recursion and complexity theory
• formal language theory
• additional topic: formalisations of hierarchies in language and action (order theory)
• additional topic: statistical learning within machine learning
• additional topics: set theory and measure theory
• additional topics: derivation of Zipf's Law
• further additional topics: depending on students' research focus

• A. Kornai, Mathematical Linguistics (Springer, London, 2008). [General resource]
• R. J. Wilson, Introduction to Graph Theory, 5th edn (Pearson, Harlow, 2010). [Graph Theory]
• S. Müller, Grammatical theory, 5th edn (Language Science Press, Berlin, 2023). [Graph Theory]
• T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd edn (Wiley, Hoboken, 2006). [Information Theory]
• further sources to follow

Evolutionary Language Science: Introduction and Primer

• Bickel: 21 October 2025, 10:15–11:45 (AND 2.06)
• Krapp: 22 October 2025, 12:15–13:45 (AFL E-22)
• Townsend (Howard-Spink): 24 October 2025, 12:15–13:45 (AFL E-22)

1. Hierarchical systems for sequence production (lecture by PD Dr Lothar Sebastian Krapp, Wednesday, 22 October 2025, 12:15–13:45, AFL E-22)
   • General topic: Mathematical foundations from set and graph theory, formal language theory (Chomsky hierarchy, automata), "recursion"; complexity.
   • Learning objectives, keywords, or key concepts: automata for sequence production and their relation to formal grammars; formalisations and visualisations of hierarchy
   • Short summary / take-home messages: There are different formal systems that can produce strings of symbols (i.e. formal expressions). Although the expressions themselves appear in a linearised order, they witness different degrees of hierarchical structure within the generating systems they originate from. 
2. Mathematical foundations of hierarchies (practical session by Jannik Kochert, Thursday, 23 October 2025, 08:00–09:45, AFL E-22)
   • General topic: Practical exercises on different notions of “hierarchy” and translations between them.
   • Learning objectives, keywords, or key concepts: 
     • You know and understand the definitions of partially ordered sets, sets ordered by inclusion, and directed acyclic graphs
     • You can translate from any one of the three above into any of the other.
     • You can find minimal counterexamples to false mathematical statements concerning any of the three.
   • Short summary / take-home messages: While the general concept of hierarchies is intuitively relatively clear, formalizing the concept in mathematics still requires some thought. In particular, there are three different mathematical structures, partially ordered sets, sets ordered by inclusion, and directed acyclic graphs, which are all used in literature to mean "hierarchy". One can (more or less easily) translate between each of the structures, but sometimes one can lose information.