吴军《数学之美》:数学模型帮您实现认知跨越

吴军《数学之美》:数学模型帮您实现认知跨越

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The ‘Useless’ Perspective That Transformed Mathematics | Quanta Magazine

https://www.quantamagazine.org/the-useless-perspective-that-transformed-mathematics-20200609/

“Representation” is the concretization / visualization of Abstract Math,
eg.
“Group Representation Theory” 群表示论 using Matrix (Linear Algebra).

Reference:

Artin’s Algebra book with matrix representation, lectured by Harvard Dean Prof Gross :

An “Introduction of Introduction” to Category Theory

Category : 范畴 has 3 things: (hence richer than a Set 集合 which is only a collection of objects)

  1. Objects 对象
  2. Arrow (Morphism 态射) between Objects, includes identity morphism.
  3. Associativity 结合性

Functor (函子) between 2 Categories (preserve structure)

Natural Transformation 自然变换

  • Example :
    Matrices -> Determinants

    ..

    Darcy Lecture 5 ~ 9: Applied Algebraic Topology

    [Revision – Lecture 1 ~4: Foundation of Applied Algebraic Topology

    Lecture 6: Creating Simplicial Complex]

    Lecture 5: 4/9/2013 (三)  Clustering Via Persistent Homology

    Lecture 7: 6/9/2013 (五) Calculating Homology using matrix

    Lecture 8: Column Space and Null Space of a matrix



    Lecture 9: 9/9/2013 (一)  Create your own Homology: (Important lecture in Applied Algebraic Topology)

    Ref:
    http://slideplayer.com/slide/9473277/