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Lecture
Equivalence Relations
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Related lectures (37)
Equivalence Relations: Classes, Partitions
Explains equivalence relations, classes, and partitions in sets.
Relations and Sequences
Covers relations, sequences, and posets, emphasizing properties like anti-symmetry and transitivity, and introduces arithmetic and geometric progressions.
Symmetry in the Plane
Explores the modern definition of symmetry and its practical applications.
Isometries and Orthonormal Bases
Discusses isometries and orthonormal bases in mathematics.
Symmetry: Noether Theorem
Explores the consequences of symmetry, focusing on the Noether Theorem and coordinated charges in Lie groups.
Global Conservation Laws
Explores the dynamical consequences of symmetry, emphasizing conservation laws and the role of Noether currents.
Equivalence Classes
MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers
MOOC: Analysis I
Introduces equivalence classes for decomposing a set into subsets of equivalent elements, defining the quotient set X/~.
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.
Wigner Theorem; Translation Symmetry
Explores the Wigner theorem, translation symmetry, eigenstates, and wave functions in quantum physics.
Symmetry & Group Theory
Covers the fundamental concepts of symmetry and group theory.
Turbulence and Symmetry
Introduces turbulence and symmetry in fluid dynamics, exploring the effects of Reynolds number on flow patterns.
Symmetry in Modern Topology
Explores the concept of symmetry in various geometric transformations.
Staggered Bosons: Symmetry and Gaplessness
Explores staggered bosons, lattice realizations of gapless field theories with symmetry protection, commutation relations, and criticality.
Center of Mass Calculation in Mechanics
Explores center of mass calculation in mechanics, emphasizing system symmetry and spherical coordinates for simplifying calculations.
Symmetry and Group Theory: Exercise 5
Covers the basis for irreducible representations and characters of direct product representations.
Homotopies & Equivalence Relations
Covers homotopies, fundamental group, and equivalence relations in applications.
Rotational Dynamics: Angular Momentum
Explains angular momentum for rotating solids and discusses symmetry in mass distribution.
Equivalence Relations and Partitions
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Discusses equivalence relations, partitions, reflexivity, symmetry, transitivity, and set cardinality.
Inertia Tensor: Main Axes and Principal Moments
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Explains the inertia tensor, main axes, principal moments, and balancing of rotating solids.
Symmetry in Modern Geometry
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Delves into modern geometry, covering transformations, isometries, and symmetries.
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