Lectures related to Equivalence Classes

Discusses equivalence relations, partitions, reflexivity, symmetry, transitivity, and set cardinality.

Equivalence Relations: Classes, Partitions

Explains equivalence relations, classes, and partitions in sets.

Covers relations, sequences, and posets, emphasizing properties like anti-symmetry and transitivity, and introduces arithmetic and geometric progressions.

Equivalence Relations

Covers the concept of equivalence relations and how to determine them.

Isometries and Orthonormal Bases

Discusses isometries and orthonormal bases in mathematics.

Equivalence Classes and Relations

Covers equivalence classes, relations, quotient sets, and functions properties.

Linear Transformations: Matrices and Applications

Explores linear transformations, matrices, and their properties, including surjectivity, injectivity, and symmetry operations.

Understanding Equivalence Relations and Integer Construction

Covers the construction of integers through equivalence relations and their properties in mathematics.

From embedded to general manifolds: Why?

Explores upgrading foundations from embedded to general manifolds in optimization, discussing smooth sets and tangent vectors.

Inertia Tensor: Main Axes and Principal Moments

Explains the inertia tensor, main axes, principal moments, and balancing of rotating solids.

Symmetry in the Plane

Explores the modern definition of symmetry and its practical applications.

Symmetry in Modern Geometry

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

Symmetry: Noether Theorem

Explores the consequences of symmetry, focusing on the Noether Theorem and coordinated charges in Lie groups.

Conformal Field Theory: Generators and Commutation Relations

Covers the definition of generators of the conformal group and the application of Wick's theorem.

Global Conservation Laws

Explores the dynamical consequences of symmetry, emphasizing conservation laws and the role of Noether currents.

Matrix Equivalence: Definitions and Properties

Explores matrix equivalence, including reflexivity, symmetry, transitivity, and change of basis.

Advanced Physics I

Covers velocity, acceleration, dynamics, moments of inertia, and kinetic energy storage systems.

Symmetry and Group Theory: Exercise Set 3

Covers Exercise Set 3 on Symmetry and Group Theory, focusing on chiral molecules, point groups, conjugacy, and group properties.

Equilibrium in Tension: Verification and Compatibility

Covers the verification of equilibrium equations and compatibility in tension scenarios, ensuring uniform stress distribution.

Wigner Theorem; Translation Symmetry

Explores the Wigner theorem, translation symmetry, eigenstates, and wave functions in quantum physics.