Selected Topics in Combinatorics and Geometry

In this 6-weeks course we introduce selected mathematical topics in Combinatorics and Geometry through Math Puzzles and Problems.

There will be NO OVERLAP of topics with the course ‘The Maths of Puzzles‘ from the Spring semester 2026.

All lectures will be given by using computer presentation.

The topics we plan to cover and the schedule are as follows:

• Puzzles about Probability and the Probabilistic Method with applications.
• Puzzles about distances
• Monsky’s Theorem, Sperner’s Lemma with applications, and $p$-adic numbers
• Puzzles and Problems on Vectors
• Extremal problems on Graphs and their applications
• Projective Geometry: central projections and inversion – the classical theorems through useful tools with relations to complex numbers and functions
  
  

Only if time allows, we will also present the following two topics:

• The Polynomial Method
• Continued Fractions and Diophantine Approximation

The first week will be a bit different with two lectures.
Starting from the second week, the students will use the first class of the week to present their solutions in class for the HW puzzles of the topic of previous week. Then in the second class of the week there will be a lecture on a new topic followed by HW puzzles to be presented in the following week. Some open problems will be discussed as well – every week.