手册

数学

Discovery

Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

Lietuvių kalba

Introduction E9F5FC

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software


See: Math notebook, Category theory glossary

Investigation: Relate my concepts with persistent homology, topological data analysis and homotopy type theory.


  • Understand these domains.
    • Make a map of key concepts in these domains.
    • Relate the univalence axiom (A=B) \simeq (A\simeq B) and the Yoneda lemma.
    • Relate persistent homology to the kissing number.
  • Relate to my philosophical concepts.
    • Study the kinds of equivalences. Associate them to the relationship between level and metalevel.
    • Relate spectral sequences, exact sequences and divisions of everything.
  • Do calculations with practical examples.
    • Make a map of mathematics by studying sets of tags at Math Stack exchange and Math Overflow. Use it to predict (using duality) the location of new theorems and concepts.
    • Study ways of identifying new concepts in chess.
    • Make a map of deepest values.

Readings: Topological data analysis

Readings: Homotopy type theory

Ideas

  • What about a reverse approach... where we divide up the space into regions where there are points and where there are not. Consider the largest circles that you can create with no points in it. You can do this by considering the bisecting points on the segments between each pair of points - use these as the centers of your circles. So this will give you a break down into regions. Now do this again allowing a circle to contain one point. (This is perhaps the current case? - for we can use each point as the center of a circle.) Then continue by allowing it to contain 2 points. And so on.

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Puslapis paskutinį kartą pakeistas 2019 vasario 15 d., 17:58
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