Linear Algebra: DiagonalizationExplores the diagonalization of matrices and the conditions for exact diagonalization, with examples demonstrating the process.
Counting labeled treesExplores counting labeled trees using Prüfer codes and algorithms, providing maps between trees and sequences.
Geometry: Eulerian CircuitsExplores Eulerian circuits through the Königsberg bridges problem, leading to the development of graph theory and topology.
Stochastic Block ModelCovers the Stochastic Block Model and its application in community detection, exploring its mathematical formulation and challenges.
Polynomial Identity TestingCovers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.
