Isometries: Transformations Preserving Distances in the Plane

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Explores the fundamental theorem of isometries in space and the modern definition of symmetry, emphasizing the complexities of determining symmetries in 3D objects.

Geometric Transformations: Symmetries and Inversion

Explores geometric transformations, symmetries, inversion, and isometries in plane geometry.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Symmetries of Navier-Stokes Equations

Explores the symmetries of Navier-Stokes equations in periodic boxes, including translations, transformations, rotations, and scaling.

Isometries: Final Panorama

Explores the synthesis of plane isometries and their composition through axial reflections, rotations, translations, and glided reflections.

Discrete Symmetries: Asymptotic States and S-matrix

Covers the concept of discrete symmetries, focusing on the introduction to asymptotic states and S-matrix.

Symmetry in Modern Space

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

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Symmetry in Lagrangian Mechanics

Explores symmetry in Lagrangian mechanics and its impact on physical systems.