multilinear algebra 1, a synoptic view


what is math? let us discuss:

Baby Abstract Multilinear Algebra
Baby Multilinear Algebra  of Inner Product Spaces
Calculus in \mathbb{R}^n
Algebraic Differential Geometry
  • Parameterizations: curves and surfaces
  • Tangent vectors, tangent space, tangent bundle
  • Curves in \mathbb{R}^2 and \mathbb{R}^3 and on surfaces in \mathbb{R}^3
  • Surfaces in \mathbb{R}^3
    1. all classical surfaces rendered
    2. tangent space change of basis
    3. vector fields and tensor fields
    4. Christoffel’s symbols (connection coefficients)
    5. Curvatures (Gaussian, Mean, Principals, Normal and Geodesic)
  • Vector Fields, Covector Fields, Tensor Fields
  • Integration: Gauss-Bonnet, Stokes
Baby Manifolds (topological, differential, analytic, anti-analytic, aritmetic,…)
Examples: Lie groups and Fiber bundles

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Filed under algebra, calculus on manifolds, categoría, differential equations, differential geometry, fiber bundle, geometry, math analysis, maths, multilinear algebra, topology, what is math

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