Coxeter Groups: Reflections and Fundamental Regions

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Explores the McKay correspondence, Coxeter groups, and finite subgroups of SU(2) and SO(3, emphasizing odd order properties and root system constructions.

Matrices and Orthogonal Transformations

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Symmetry in Modern Geometry

Delves into modern geometry, covering transformations, isometries, and symmetries.

Representation Theory: Finite Subgroups of SU(2)

Explores representation theory and character theory of finite groups, including scalar product and McKay graph.

Coxeter Groups: Spectral Theorem and Sylvester's Criterion

Explores the spectral theorem, Coxeter graphs, eigenvalues, and determinants of positive definite matrices.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Isometries in Euclidean Spaces

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Geometric Transformations in R2 and R3

Explores geometric transformations in R2 and R3, including reflections, rotations, and practical applications like billiards.

2D Transformations: Linear Maps & Matrices

Covers 2D transformations, linear maps, matrices, affine transformations, and orthogonal transformations.

Composition of Plane Reflections & Isometries in Space

Explores the composition of plane reflections and isometries in space, showcasing how reflections can lead to rotations and different isometries.