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Introduction E9F5FC

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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.

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 and six transformations
• 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
• Understand the divisions of everything
• express divisions of everything in terms of finite exact sequences
• understand and interpret Bott periodicity
• 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

• A theory of what "equivalence" variously means
• The g-conjecture about an h-vectors of a simplicial polytope and the triangulation of a sphere.
• P vs. NP-complete
• a unifying perspective on cohomology (or has Lurie already achieved this?)
• higher order homotopy groups for sphere

Overviews of Math and Its History

Math to Learn

Math Videos

General

Collections

Geometry

Foundations

Web courses

Areas of math that I want to learn more about.

Automata theory

I want to understand how the characteristic q can be identified with infinity. This may relate to automata theory.

Geometry

I am trying to describe the cognitive significance of 4 geometries (affine, projective, conformal, symplectic) and 6 transformations between them (reflection, shear, rotation, dilation, squeeze, translation).

• Study these different kinds of geometry. Collect the main theorems of geometry and organize them into these different kinds to illustrate them.
• I want to understand the basics of Geometric algebra, Clifford algebra and visual complex analysis. I think they are related to symplectic geometry.
• I want to understand Bott periodicity, which can be understood in terms of Clifford algebra and its clock shifts. I want to be able to relate Bott periodicity to the eight divisions of everything, if possible.
• I want to understand the theorem distinguishing the reals, complexes, quaternions, octonions and why there is nothing higher. I want to understand the basics of working with (noncommutative) quaternions and (nonassociative) octonions.
• I want to have a basic understanding of circle folding and origami and what their operations mean geometrically.
• I want to understand Grothedieck's six operations and how they might relate or not to my six transformations. I want to understand the related algebraic geometry (such as sheaves) and category theory.

Foundations of Mathematics

I want to understand some of the conceptual Foundations of Mathematics.

• I want to understand the basics of Homotopy type theory and Category theory. I want to understand how equivalences are considered in math. I want to relate that to my theory of variables.
• I want to show how the possible relationship between logic and metalogic is given by the four geometries

I am trying to make a map of how all of mathematics unfolds. I want to understand the basics of Lie groups and Lie algebras because I think they play a central role in linking analysis and geometry.

• In particular, I want to understand intuitively the 4 classical groups.
• I want to understand tensors and be able to calculate them. I think they define triviality.
• I want to understand how to prove the Fundamental Theorem of Algebra in various ways and understand its importance in organizing mathematics.
• I want to review Galois theory.

Other assorted concepts: Tetrahedron, Triality, Associativity, Unit

#### StudyMath

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 Puslapis paskutinį kartą pakeistas 2018 gruodžio 10 d., 12:59