Lectures related to Isometry in Space Synthesis

Geometry: Reflections and Transformations

Explores geometry transformations, emphasizing isometries, point reflections, rotations, and translations to illustrate fundamental geometric principles.

Geometry: Transformations and Isometries

Explores transformations and isometries in geometry, preserving properties through translations, rotations, and reflections.

Rotations and Symmetries

Covers the preservation of isometry by rotations and symmetries.

Mixing Properties of Infinite Measure Preserving Systems

Explores mixing properties of infinite measure preserving systems, focusing on suspensions, Govers transformations, and Lorentz gas.

Rotations: Isometries and Axes

Explores rotations as isometries composed of reflections with common axes and the flexibility in choosing rotation axes.

Isometries in Space: Synthesis

Covers the synthesis of isometries in space and the complexities of determining symmetries in 3D objects.

Surfaces in Space

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.