Erstsemestereinführungswoche (ESE) Lehramt 2026

Time: 

Lecture: Wednesdays  9.45-11.15 PRÜ 1103, public holiday at Nov 19th

Example class: to be moved.

Algorithmic_Topology.pdf

Part 1: Point set topology (until Nov 26th).

You should be familiar with:

• Definition of a topological space and related notation such as: open, closed, compact, connected, path-connected, continuous)
• Basic examples of topological spaces: discrete Topology, subspaces of Rn
• Subspace and Quotient topology, Product topology
• Hausdorff separation property

Further topics:

knot theory

embedding problems for simplicial complexes

classification of compact 2-manifolds

Topics of lectures:

29.10. -- Introduction to Topology

05.11. -- Definition Topological Space, Basis of Topology, Subspace Topology (explicitly and via universal property), Quotient Topology (explicitly and via universal property), continuous, connected, plus lots of examples

12.11. -- Product Topology and statement of Tychnov's theorem plus examples, compactness principle and proof that an infinite graph is k-colourable if and only if all finite subgraphs are k-colourable

19.11. (public holiday)

26.11. -- Proof of Tychonov's theorem

03.11. -- Introduction to topological graph theory

10.12. -- Kuratowski's theorem

17.12. -- Embedding 2-complexes in 3-space

7.1. -- Introduction to knot theory (definition of knots, equivalence of knots, how knots are displayed by knot diagrammes, we proved used FOX tri-colourability that the trefoil knot is nontrivial. This is a prime example of a nonexistence proof by invariant)

14.1. -- Introduction to Fundamental groups (definition homotopy equivalent, fundamental group, basic examples)

21.1. -- Fundamental groups of knot complement

28.1. -- Introduction to Homology theory

4.2. -- classification of 2-manifolds

11.2. Wrap up and "Prüfungsvorgespräche"

The examination will be a 30 minutes oral exam. Dates will be discussed towards the end of the semester. 

Literature for the course:

For Topology, I recommend the book of Armstrong.

For Grapg Theory, I recommend the book of Diestel

For advanced topics later in the course, I will provide notes here.