| Kurzbeschreibung | Applied Category Theory is an exciting multidisciplinary field of research which harnesses the mathematical language of category theory for applications across a broad range of disciplines. This course is a gentle introduction to the theory, emphasizing applications in engineering and the “compositional approach” to systems analysis, co-design, and computation. |
| Lernziel | 1) Learn basic concepts from algebra and category theory, together with ways to make use of these concepts for engineering applications.
2) Become familiar with case studies of applied category theory, for instance involving dynamical systems, databases, and complex system co-design (e.g. in the context of autonomous vehicles).
3) Be able to recognize compositional structures in concrete scenarios at different levels of abstraction.
4) Understand the “compositional way of thinking” as an approach to systems analysis, co-design, and computation. |
| Inhalt | Review of basic algebraic structures [sets, relations, (semi)groups, monoids, actions, order theory]
Gentle introduction to category theory [series and parallel composition, feedback, actions, functors, universal properties]
Many simple applied examples illustrating concepts along the way. Extended examples from dynamical systems, databases, and systems co-design in engineering.
Homework will consist of weekly homework exercises to check one’s understanding of core mathematical concepts and practice working with the theory (writing mathematical computations and proofs).
Homework will constitute 100% of the grade (no exam). |
| Skript | Slides and a (work-in-progress) textbook for the course will be provided (A. Censi, J. Lorand, G. Zardini, "Applied Compositional Thinking for Engineers"). |
| Literatur | Censi, Lorand, Zardini, "Applied Compositional Thinking for Engineers" (https://tinyurl.com/579kw5bh).
See also https://applied-compositional-thinking.engineering for many further resources. |
| Voraussetzungen / Besonderes | A knowledge of algebra at the level of a bachelor’s degree in engineering/computer science. |
Kompetenzen | | Fachspezifische Kompetenzen | Konzepte und Theorien | geprüft | | Methodenspezifische Kompetenzen | Analytische Kompetenzen | geprüft | | Problemlösung | geprüft | | Soziale Kompetenzen | Kommunikation | gefördert | | Persönliche Kompetenzen | Kreatives Denken | geprüft | | Kritisches Denken | gefördert | | Integrität und Arbeitsethik | gefördert | | Selbststeuerung und Selbstmanagement | gefördert |
|
Leistungskontrolle als Semesterkurs