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数学

Discovery

Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
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Lietuvių kalba

Introduction E9F5FC

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software

Book.MathConcepts istorija

Paslėpti nežymius pakeitimus - Rodyti galutinio teksto pakeitimus

2019 vasario 13 d., 14:34 atliko AndriusKulikauskas -
Pridėta 5 eilutė:
[++++数学概念++++]
2019 sausio 20 d., 10:29 atliko AndriusKulikauskas -
Ištrinta 8 eilutė:
---------------------
2018 lapkričio 11 d., 17:17 atliko AndriusKulikauskas -
Pridėtos 28-29 eilutės:

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.
2018 lapkričio 11 d., 17:16 atliko AndriusKulikauskas -
Pridėtos 30-31 eilutės:

[[Variables]]
2018 lapkričio 11 d., 17:15 atliko AndriusKulikauskas -
Pridėta 106 eilutė:
* Intrinsic ambiguity of propositions - every proposition is a general rule, which can be questioned or applied.
2018 lapkričio 11 d., 17:13 atliko AndriusKulikauskas -
Pridėta 25 eilutė:
--------------
Pakeistos 27-28 eilutės iš
į:
--------------
Pridėtos 102-105 eilutės:

[+Notes on concepts+]

* Function can be partial, whereas a permutation maps completely.
2018 lapkričio 11 d., 16:51 atliko AndriusKulikauskas -
Pakeista 11 eilutė iš:
* What are the roles of abstraction-generalization and concrete examples?
į:
* What are the roles of [[abstraction | abstraction-generalization]] and concrete examples?
2018 lapkričio 11 d., 16:20 atliko AndriusKulikauskas -
Pakeistos 29-35 eilutės iš
Abstract concepts
* dualities
* Definite / deterministic (the) vs. Indefinite / Nondeterministic (a) - P vs. NP - compare with the Axiom of Choice

* mathematical examples
į:
[[Duality]]
Pridėtos 41-42 eilutės:
* Definite / deterministic (the) vs. Indefinite / Nondeterministic (a) - P vs. NP
* Axiom of Choice
2018 lapkričio 11 d., 16:19 atliko AndriusKulikauskas -
Pakeistos 21-22 eilutės iš
I think the most central concept in Math is [[duality]], which is the basis for logic.
į:
Basic ideas
* The
most central concept in Math is [[duality]], which is the basis for logic.
* The most fundamental symmetry is that of choice, as given by the ways we may interpret the binomial theorem, for it underlies the symmetry of algebraic expansions
.
Pakeista 45 eilutė iš:
Probability, [[Entropy]]
į:
Binomial, Choice, Probability, [[Entropy]]
2018 lapkričio 11 d., 16:17 atliko AndriusKulikauskas -
Pridėtos 42-43 eilutės:

Probability, [[Entropy]]
2018 lapkričio 11 d., 15:45 atliko AndriusKulikauskas -
Pakeista 9 eilutė iš:
į:
---------------------
Pakeista 14 eilutė iš:
į:
---------------------
2018 lapkričio 11 d., 15:45 atliko AndriusKulikauskas -
Pridėtos 8-14 eilutės:
>>bgcolor=#FFFFC0<<

* What is mathematical knowledge? How does it arise, develop and take the form of objects, concepts, theorems and endeavors?
* What are the roles of abstraction-generalization and concrete examples?
* Define the most basic concepts, especially the categories below.
* Organize the basic concepts. Show how they arise from the way we relate several [[variables]] and interpret [[duality]].
Ištrintos 22-25 eilutės:
I want to think about:
* how mathematical knowledge arises and develops to yield objects, concepts, theorems, endeavors
* the role of concrete examples and abstraction - generalization
Pakeista 34 eilutė iš:
[[Objects]]
į:
[[Objects]] and their [[Symmetry]]
Ištrintos 98-99 eilutės:

[[Symmetry]]
2018 lapkričio 11 d., 15:27 atliko AndriusKulikauskas -
Pakeista 97 eilutė iš:
į:
[[Symmetry]]
2018 lapkričio 11 d., 15:13 atliko AndriusKulikauskas -
Pridėtos 52-53 eilutės:

[[Infinity]]
2018 lapkričio 11 d., 15:11 atliko AndriusKulikauskas -
Ištrintos 18-19 eilutės:

Attach:mathematicalmethodsofproof.png
2018 lapkričio 11 d., 14:52 atliko AndriusKulikauskas -
2018 lapkričio 11 d., 14:41 atliko AndriusKulikauskas -
Ištrintos 14-23 eilutės:

I am investigating from the following directions:
* the ways of figuring things out
* [[Duality]]
* the areas of math
* the methods of mathematical proof (natural objects, axioms)
* the objects in math
* the ways that variables are used
* geometries and transformations (for moods)
* visualizations (sequences, hierarchies, networks)
2018 lapkričio 11 d., 14:14 atliko AndriusKulikauskas -
Pakeistos 10-11 eilutės iš
I'm studying the lists of pages in Wikipedia about mathematics.
į:
On this page I am organizing a list of mathematical concepts that I wish to be able to account for. Sources of concepts include:
* [[https://en.wikipedia.org/wiki/Lists_of_mathematics_topics | List of mathematics topics]]
* [[https://en.wikipedia.org/wiki/List_of_mathematical_examples | List of mathematical examples]]
Ištrintos 34-36 eilutės:

* [[https://en.wikipedia.org/wiki/Lists_of_mathematics_topics | List of mathematics topics]]
* [[https://en.wikipedia.org/wiki/List_of_mathematical_examples | List of mathematical examples]]
2018 lapkričio 11 d., 14:07 atliko AndriusKulikauskas -
Pakeistos 1-3 eilutės iš
[[Math Big Picture]]

I'm trying to understand how to overview all of math. I'm studying the lists of pages in Wikipedia about mathematics.
į:
>>bgcolor=#E9F5FC<<
---------------------
See:
[[Math Big Picture]]


'''Overview all of the concepts in math and how they arise.'''
----------------------
>><<

I'm studying the lists of pages in Wikipedia about mathematics.
2018 sausio 21 d., 14:21 atliko AndriusKulikauskas -
Pakeista 11 eilutė iš:
* the methods of mathematical proof
į:
* the methods of mathematical proof (natural objects, axioms)
Pridėtos 14-19 eilutės:
* geometries and transformations (for moods)
* visualizations (sequences, hierarchies, networks)

I want to think about:
* how mathematical knowledge arises and develops to yield objects, concepts, theorems, endeavors
* the role of concrete examples and abstraction - generalization
2018 sausio 10 d., 12:37 atliko AndriusKulikauskas -
Pridėtos 16-17 eilutės:

Attach:mathconcepts.png
2018 sausio 10 d., 12:30 atliko AndriusKulikauskas -
Pridėtos 14-15 eilutės:

Attach:mathematicalmethodsofproof.png
2018 sausio 10 d., 12:29 atliko AndriusKulikauskas -
Pridėtos 6-13 eilutės:

I am investigating from the following directions:
* the ways of figuring things out
* [[Duality]]
* the areas of math
* the methods of mathematical proof
* the objects in math
* the ways that variables are used
2018 sausio 07 d., 19:11 atliko AndriusKulikauskas -
Pridėta 32 eilutė:
* [[http://math.ucr.edu/home/baez/octonions/node16.html | Magic Square of Lie algebras]]
2018 sausio 07 d., 18:20 atliko AndriusKulikauskas -
Pakeista 29 eilutė iš:
* Bott periodicity - Clifford Algebra shift clock
į:
* [[Bott periodicity]] - Clifford Algebra shift clock - and [[http://math.ucr.edu/home/baez/octonions/node10.html | Octonions]]
2018 sausio 07 d., 18:18 atliko AndriusKulikauskas -
Ištrinta 13 eilutė:
Ištrinta 14 eilutė:
Pakeistos 24-27 eilutės iš
į:
* partition topics
* factorial and binomial topics
* convexity topics
Pakeistos 33-40 eilutės iš
į:
* continuum
* order topics
* numeral system topics
* properties of sets of reals
* exceptional set concepts
* fractal topics

Functions
Pakeistos 45-49 eilutės iš
į:
* polynomial topics
* exponential topics
* logarithm topics

Equations
Pridėta 55 eilutė:
Subspaces
Ištrinta 60 eilutė:
Pridėta 63 eilutė:
Operations
Pakeistos 69-71 eilutės iš
į:
* permutation topics

Algorithms
Pridėta 75 eilutė:
Proofs
Pakeistos 80-97 eilutės iš
Topics
* Combinatorics
** partition topics
** factorial and binomial topics
** convexity topics
* Numbers and sets
** order topics
** numeral system topics
** properties of sets of reals
** exceptional set concepts
** fractal topics
* Functions
** polynomial topics
** exponential topics
** logarithm topics
Operations
* permutation topics
į:
* theorems
2018 sausio 07 d., 18:15 atliko AndriusKulikauskas -
Pridėta 21 eilutė:
[[Objects]]
2018 sausio 07 d., 18:13 atliko AndriusKulikauskas -
Pridėta 29 eilutė:
* [[http://math.ucr.edu/home/baez/octonions/node7.html | Trialities]] and spinors
2018 sausio 07 d., 17:58 atliko AndriusKulikauskas -
Pakeistos 26-28 eilutės iš
[[Numbers]]
į:
[[Numbers]] Real, Complex, Quaternion
* Bott periodicity - Clifford Algebra shift clock
* Octonions
2018 sausio 07 d., 17:34 atliko AndriusKulikauskas -
Pakeista 26 eilutė iš:
* numbers
į:
[[Numbers]]
2018 sausio 07 d., 16:56 atliko AndriusKulikauskas -
Ištrintos 12-16 eilutės:



Pridėta 21 eilutė:
* combinatorial principles
Pridėtos 34-38 eilutės:
* equations
* inequalities
* mathematical identities
* formulae involving pi
Pakeista 53 eilutė iš:
į:
* algorithms
Pakeistos 61-70 eilutės iš
* algorithms

* combinatorial principles

* equations
* inequalities
* mathematical identities
* formulae involving pi

Topoics
į:
Topics
* Combinatorics
** partition topics
** factorial and binomial topics
** convexity topics
* Numbers and sets
** order topics
** numeral system topics
** properties of sets of reals
** exceptional set concepts
** fractal topics
* Functions
** polynomial topics
** exponential topics
** logarithm topics
Operations
Ištrintos 77-89 eilutės:
* convexity topics
* exceptional set concepts
* exponential topics
* factorial and binomial topics
* fractal topics
* logarithm topics
* numeral system topics
* order topics
* partition topics
* polynomial topics
* properties of sets of reals
2018 sausio 07 d., 16:49 atliko AndriusKulikauskas -
Pridėtos 4-5 eilutės:

I think the most central concept in Math is [[duality]], which is the basis for logic.
2018 sausio 07 d., 16:47 atliko AndriusKulikauskas -
Pakeistos 1-3 eilutės iš
I'm studying the lists of pages in Wikipedia about mathematics.
į:
[[Math Big Picture]]

I'm trying to understand how to overview all of math.
I'm studying the lists of pages in Wikipedia about mathematics.
2018 sausio 01 d., 10:13 atliko AndriusKulikauskas -
Pakeista 18 eilutė iš:
* Definite / deterministic (the) vs. Indefinite / Nondeterministic (a) - P vs. NP
į:
* Definite / deterministic (the) vs. Indefinite / Nondeterministic (a) - P vs. NP - compare with the Axiom of Choice
2018 sausio 01 d., 10:10 atliko AndriusKulikauskas -
Pakeista 24 eilutė iš:
* regular polytopes
į:
* regular polytopes - points on a circle or sphere, etc.
2018 sausio 01 d., 09:56 atliko AndriusKulikauskas -
Pridėtos 16-17 eilutės:
* dualities
Ištrinta 19 eilutė:
Ištrintos 21-22 eilutės:
* mathematical knots and links
Ištrintos 22-24 eilutės:

* matrices
Pakeistos 27-28 eilutės iš
į:
* matrices
Pridėta 31 eilutė:
* transforms
Pridėta 35 eilutė:
* mathematical knots and links
Pridėta 48 eilutė:
Pakeistos 51-66 eilutės iš
į:
* axioms
* conjectures
* lemmas
* mathematical proofs

* algorithms

* combinatorial principles

* equations
* inequalities
* mathematical identities
* formulae involving pi

Topoics
* permutation topics
Ištrinta 67 eilutė:
* dualities
Ištrintos 77-92 eilutės:
* transforms
* permutation topics


* algorithms
* axioms
* conjectures

* Combinatorial principles
* equations
* formulae involving pi
* mathematical identities
* inequalities
* lemmas
* mathematical proofs
2018 sausio 01 d., 09:52 atliko AndriusKulikauskas -
Pakeistos 52-78 eilutės iš
į:
* convexity topics
* dualities
* exceptional set concepts
* exponential topics
* factorial and binomial topics
* fractal topics
* logarithm topics
* numeral system topics
* order topics
* partition topics
* polynomial topics
* properties of sets of reals
* transforms
* permutation topics


* algorithms
* axioms
* conjectures

* Combinatorial principles
* equations
* formulae involving pi
* mathematical identities
* inequalities
* lemmas
* mathematical proofs
2018 sausio 01 d., 09:42 atliko AndriusKulikauskas -
Pakeistos 16-55 eilutės iš
* Definite / deterministic (the) vs. Indefinite / Nondeterministic (a) - P vs. NP
į:
* Definite / deterministic (the) vs. Indefinite / Nondeterministic (a) - P vs. NP


* mathematical examples

* mathematical knots and links

* mathematical shapes

* matrices

* polygons, polyhedra and polytopes
* regular polytopes

* numbers

* mathematical functions
* special functions and eponyms
* Fourier-related transforms

* curves
* surfaces
* algebraic surfaces
* manifolds

* examples in general topology

* small groups
* finite simple groups
* simple Lie groups
* Table of Lie groups
* complex reflection groups

* complexity classes




2018 sausio 01 d., 08:58 atliko AndriusKulikauskas -
Pakeista 16 eilutė iš:
* Definite / deterministic (the) vs. Indefinite / Nondeterministic (a)
į:
* Definite / deterministic (the) vs. Indefinite / Nondeterministic (a) - P vs. NP
2018 sausio 01 d., 08:57 atliko AndriusKulikauskas -
Pakeistos 6-16 eilutės iš
* [[https://en.wikipedia.org/wiki/List_of_mathematical_examples | List of mathematical examples]]
į:
* [[https://en.wikipedia.org/wiki/List_of_mathematical_examples | List of mathematical examples]]







Abstract concepts

* Definite / deterministic (the) vs. Indefinite / Nondeterministic (a)
2018 sausio 01 d., 08:50 atliko AndriusKulikauskas -
Pridėtos 1-6 eilutės:
I'm studying the lists of pages in Wikipedia about mathematics.

[++Mathematical concepts++]

* [[https://en.wikipedia.org/wiki/Lists_of_mathematics_topics | List of mathematics topics]]
* [[https://en.wikipedia.org/wiki/List_of_mathematical_examples | List of mathematical examples]]

MathConcepts


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Puslapis paskutinį kartą pakeistas 2019 vasario 13 d., 14:34
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