Group Theory: Basics

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Related lectures (54)

Group Theory: Definition and Examples Log in to Mediaspace to watch this video

Covers the definition of a group, properties of symmetries, and group operations.

Symmetries in Mechanics and Wave Equations Log in to Mediaspace to watch this video

Explores symmetries in Newtonian mechanics and wave equations, highlighting their significance in understanding physical laws.

Isometries & Orientation in Modern Geometry Log in to Mediaspace to watch this video

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Elliptic Curves: Group Structure and Isomorphism Log in to Mediaspace to watch this video

Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.

Equilibrium in 3D: System Isolation and Constraints Log in to Mediaspace to watch this video

Covers the equilibrium conditions in 3D, system isolation, free-body diagrams, and constraints.

Symmetry in Modern Geometry Log in to Mediaspace to watch this video

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

Symmetry in Materials Science Log in to Mediaspace to watch this video

Explores symmetry in materials science, covering crystal elements, symmetry groups, crystal classes, and Bravais lattice system.

The classical Lie algebras Log in to Mediaspace to watch this video

Covers the classical Lie algebras, focusing on calculations and dimensions.

Symplectic Geometry Log in to Mediaspace to watch this video

Covers the background on symplectic geometry, focusing on symplectic manifolds and canonical structures.

Orthogonality and Least Squares Log in to Mediaspace to watch this video

Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.

Untitled Log in to Mediaspace to watch this video

CloudCompare: Rotations and Functions Log in to Mediaspace to watch this video

Introduces tools for manipulating and analyzing 3D point clouds using CloudCompare software.

Group Actions: Examples and Applications Log in to Mediaspace to watch this video

Explores examples of group actions on sets, emphasizing the utility of group actions to understand groups.

Numerical Flow Simulation: Boundary Conditions Log in to Mediaspace to watch this video

Covers the numerical simulation workflow for fluid dynamics, focusing on boundary conditions and their importance for solution convergence.

Introduction to Physics: Understanding Natural Phenomena Log in to Mediaspace to watch this video

Covers the basics of physics, emphasizing understanding natural phenomena and the role of mathematics in representing physical laws.

Calculus of Variations and Euler's Elastica Log in to Mediaspace to watch this video

Explores the calculus of variations and Euler's Elastica in the context of beam equilibrium and inextensible elastic curves under large rotations.

Algebraic Cycles and Etale Cohomology Log in to Mediaspace to watch this video

Explores algebraic cycles, etale cohomology, and counterexamples to the Hodge conjecture.

Functions Composition: Continuity & Elements Log in to Mediaspace to watch this video

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Game Theory: Decision Making in Interdependent Environments Log in to Mediaspace to watch this video

Explores game theory, decision-making in interdependent environments, equilibrium concepts, and economic applications in management.

Linear Applications: Matrices and Transformations Log in to Mediaspace to watch this video

Covers linear applications, matrices, transformations, and the principle of superposition.

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