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Math

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Andrius Kulikauskas

  • ms@ms.lt
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Time: A moving point is a line, a moving line is a plane, a moving plane is a volume... Time is the addition of a scalar (from a field), thus the addition of choice. Time relates affine and projective space. Compare time with space. A moving "center" is a point: the center is what moves, thus what has time.

Function can be partial, whereas a permutation maps completely.

Derangements. Interpret? Not likely...

Symmetry group relates:

  • Algebraic structure, "group"
  • Analytic (recurring activity) transformations

Axiom of infinity - can be eliminated - it is unnecessary in "implicit math".

The factoring (number of simplexes n choose k - dependent simplex) x (number of flags on k - independent Euclidean) x (number of flags on n-k - independent Euclidean) = (number of flags on n)

What kind of conjugation is that?

Relate triangulated categories with representations of threesome

Kan extension - extending the domain - every concept is a Kan extension https://en.wikipedia.org/wiki/Kan_extension

Express the link between algebra wnd analysis in terms of exact sequences and Kan extensions. Explain why category theory not relevant for analysis.

What is Mathematical Music Theory?

Consider the connection between walks on trees and Dynkin diagrams, where the latter typically have a distinguished node (the root of the tree) from which we can imagine the tree being "perceived". There can also be double or triple perspectives.

The mind is augmented through the "symmetric group" which is the system that augments our imagination.

Matematikos įrodymo būdai

  • 6 matematikos irodymo budai skiriaisi nuo issiaiskinimo budu taciau kaip jie susiję

Apibrėžti "gebėjimus" ir kaip matematinis mąstymas suveda skirtingus gebėjimus suvokti kelis, keliolika, keliasdešimts, tūkstančius ir t.t. daiktų

Kodėl yra tiek daug būdų įrodyti Pitagoro teoremą?

Gramatika visada turi prasmę. Matematika yra tai, kas pavaldu logikai, bet nebūtinai turi prasmę.

Variables

  • A variable is an "atom" of meaning as in my paper, The Algebra of Copyright, which can be parsed on three different levels, yielding four levels and six pairs of levels.

Apibendrinimas

  • Protas apibendrina. Kaip nagrinėti apibendrinimą? Suvokti neurologiškai (arba tinklais). Jeigu keli pavyzdžiai (ar netgi vienas) turi tam tikras bendras savybes, tada tas apibendrintas savybes gali naujai priskirti naujoms jų apibudintoms sąvokoms.
  • Apibendrinimas yra "objekto" kūrimas.

Differentiability of a complex function means that it can be written as an infinite power series. So differentiation reduces complex functions to infinite power series. This is analogous to evolution abstracting the "real world" to a representation of it. And differentiation is relevant as a shift from the known to focus on the unknown - the change.

How do special rim hook tableaux (which depend on the behavior of their endpoints) relate to Dynkin diagrams (which also depend on their endpoints)?

Study the duality between 1^N and N in symmetric functions (Young tableaux) but also Catalan numbers, etc.

Montažas ir geometrinės permainos:

  • Shear: sideshot

Mandelbort

  • Mandelbrot aibė skiria vidines ir išorines veiklas, besilaikančias erdvės ir nesilaikančios jokios erdvės.
  • Įsivaizduoti, kaip Mandelbrot aibės transformacija veikia visą plokštumą arba vieną jos kampelį.
  • Catalan numbers foster a duality between horizontal concatenation ()()() and vertical embedding ((())). Šis dualizmas taip pat sieja visko savybes Visaką priima (Kaip) ir Be aplinkos (Kodėl). Palyginti ir su žaidimų gramatika, su medžiai ir sekomis.

Darij Grinberg http://www-users.math.umn.edu/~dgrinber/ http://www.cip.ifi.lmu.de/~grinberg/about/rs.pdf See: Combinatorics and the field with one element. Witt vectors - p-adic integers

Matematikos savokų pagrindas yra dvejybinis-trejybinis - operacijos jungia du narius trečiu nariu. Matricų elementai sieja du narius ir išgauna trečią. Kategorijų teorija panašiai. O geometrija lygiaverčiai sieja tris narius trikampiais, įvairiai suprastais. Tad tai paaiškintų geometrijos svarbą.

Jiri Raclavsky - Frege, Tichy - Two-dimensional conception of inference. Inference rules operate on derivations. Go from one truth to another truth, not from one assumption to another assumption.

Intrinsic ambiguity of propositions - every proposition is a general rule, which can be questioned or applied.

What is the connection between the universal grammar for games and the symmetric functions of the eigenvalues of a matrix?

An example of extending the domain: Lie algebra (infinitesimal) vs. Lie group (broader domain).

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Puslapis paskutinį kartą pakeistas 2018 sausio 31 d., 22:01
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