Notes

Book

Math 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


  • Make a diagram of concrete mathematical structures that I want to learn about, and related branches of mathematics.
  • Survey combinatorics, especially Stanley's book and Wikipedia, for the various kinds of combinatorial constructions.

学习数学

Math Notebook: Investigations

  • Map of math How do math's branches, concepts and results unfold?
  • Binomial theorem The heart of mathematics. In particular, the reason why there are 4 infinite families of classical Lie groups/algebras.

Challenges in Math to take on

  • Understand the ways of figuring things out
    • understand the binomial theorem
    • explain the four classical Lie groups
    • express and apply four geometries (affine, projective, conformal, symplectic) and six transformations (reflection, shear, rotation, dilation, squeeze, translation).
    • relate level and metalevel in four ways to provide the basis for logic and geometry
    • understand the use of variables
  • Understand how math results unfold
    • the relationship between the concious and the unconscious, duality, logic
      • Langlands program, Poincare/Serre duality
    • the association of (conscious) questions and (unconscious) answers
    • theorems, and in particular, geometry theorems, Galois theory, the Fundamental Theorem of Algebra, its proofs and its centrality
  • Understand the divisions of everything
  • Model how God goes beyond himself
  • Understand entropy as the basis for prayer
  • Completely characterize an area of math such as plane geometry or chess

Open math challenges to consider

Overviews of Math and Its History

Math to Learn

Math Videos

General

Collections

Geometry

Foundations

Web courses

StudyMath


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Puslapis paskutinį kartą pakeistas 2019 kovo 13 d., 10:49
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