Lectures related to The Discriminant: Symmetry and Orbits

Normed Spaces

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

Symmetry in Modern Geometry

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

Symmetry in Modern Topology

Explores the concept of symmetry in various geometric transformations.

Mechanics: Symmetric Haltere and Center of Mass

Covers the mechanics of a symmetric haltere and the importance of center of mass calculation.

Multipole Expansion in Electrostatics and Magnetostatics

Explores multipole expansion in electrostatics and magnetostatics, focusing on monopole, dipole, and higher-order moments, and their mathematical representations.

Symmetry in Finite Element Models

Explores using symmetries in Finite Element models to simplify boundary conditions and reduce rigid-body motions.

Geometry: Modern Interpretation of Symmetry

Introduces a new online format for the geometry course, emphasizing the study of isometries and the modern interpretation of symmetry.

Hyperbolic Functions: sinh(x) and cosh(x)

Explores the properties of sinh(x) and cosh(x) functions and their symmetry.

Wigner Theorem; Translation Symmetry

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

Global Conservation Laws

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

Symmetry in the Plane

Explores the modern definition of symmetry and its practical applications.

Circle Orthogonal & Poincaré Disk

Covers circle orthogonal and Poincaré disk concepts in geometry.

Orthogonal Projections: Symmetry and Matrices

Explores orthogonal projections, symmetry of matrices, and their applications.

Isometries & Orientation: Modern Symmetry

Explores isometries, reflections, rotations, and translations in space, as well as the structure theorem and configurations of planes and lines.

Inertia Tensor: Main Axes and Principal Moments

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

Real Functions: Definitions and Properties

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

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Christoffel Symbols and Gravity Before Einstein

Introduces Christoffel symbols and gravity concepts before Einstein, discussing mathematical tensors and the Nobel Prize in Physics.

Symmetry in Modern Topology

Explores fundamental theorems and practical applications of modern symmetry theory, including decorative motifs and linear pattern extensions.

Equilibrium in Tension: Verification and Compatibility

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