Students should be comfortable with abstract mathematical reasoning and have completed a proof-oriented undergraduate course in discrete mathematics, combinatorics, or graph theory.

The n-dimensional hypercube is a central object in discrete mathematics and theoretical computer science. It can be viewed as a graph, a partially ordered set, a polytope, or a Cayley graph, and these perspectives lead to rich structural and algorithmic questions. This is a theoretical and proof-oriented mathematics course. Its primary focus is the combinatorial structure of the hypercubes.

Course dates at TUW: Monday 16/11 to Friday 20/11.

Course content:

- Definitions, characterisation, basic properties

- Symmetries and automorphisms of the hypercube

- Gray codes, paths, and cycles in the hypercubes

- Matchings and selected decomposition results

Welcome Session: Saturday 14 November, 5 pm at TU Wien.

EDA (European Dimension Programme) takes place on 14-15 November & on 2 evenings during the week. Planned activities: Welcome Dinner (Coffee Hour format) 14/11, City Rally, Visit to a Viennese museum, bonding/activities to get to know each other. Participation fee: EUR 35,-.

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The tentative schedule of every day is as follows: 9:00 - 12:00: Lecture and Exercises (including breaks)13:30 - 16:30:  Lecture and Exercises (including breaks)

Graded exercises throughout the course and a final exam on the last day.

 Final exam on the last day

Welcome Dinner (Saturday = first day of ATHENS week),

City Rally (Sunday = 2nd day of ATHENS week),

Visit to a Viennese museum - date tbd (after your class during the week),

bonding/activities to get to know each other - date tbd (after your class during the week).