Symmetry in mathematics

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Crystallography Basics: Symmetry and Crystal Classes

Introduces crystallography basics, covering symmetry elements, crystal classes, and their representations.

Symmetry in Modern Space

Explores the classification and practical applications of symmetries in 3D space, emphasizing user-driven determination of object symmetries.

Symmetry in Architecture

Delves into the mathematical definition of a frieze motif and the concept of symmetry in architecture.

Invariance Representations: Atomistic Machine Learning

Delves into invariance representations for atomistic machine learning, including symmetry functions and higher-order angular correlations.

Asymptotic States and S-matrix: Operators

Explores asymptotic states, S-matrix, and operators in quantum field theory, emphasizing the role of discrete symmetries and complete sets of states.

Symmetry Operations in Quantum Mechanics

Explores symmetry operations in quantum mechanics, emphasizing the preservation of state properties.

Symmetry and Group Theory: Exercises 1&2

Covers the identification of symmetry elements in molecules and exercises on linear molecules and high-order axes.

Fourier Transform Properties

Covers the properties of the Fourier transform, including linearity, shifts, time reversal, differentiation, integration, convolution, and conjugate symmetry.

Isometries in Euclidean Spaces

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

Anisotropic Elasticity 2: Symmetry Operations, Multiphysics

Covers anisotropic elasticity, symmetry operations, and multiphysics in material science.