앨지브라,algebra

Difference between r1.41 and the current

@@ -142,6 +142,7 @@

== De Morgan algebra ( + Ockham algebra + Kleene algebra ) ==
[[De_Morgan_algebra]] =,De_Morgan_algebra . De_Morgan_algebra
[[드모르간_대수,De_Morgan_algebra]] ?
{
De Morgan algebra
[[WtEn:De_Morgan_algebra]]
@@ -154,26 +155,17 @@
Hyper: (up)
[[Ockham_algebra]] =,Ockham_algebra . Ockham_algebra
{
Ockham algebra
'''Ockham algebra'''
오컴 대수 ?
오컴_대수 ??
[[WtEn:Ockham_algebra]] = https://en.wiktionary.org/wiki/Ockham_algebra
https://en.wikipedia.org/wiki/Ockham_algebra
"Ockham algebra" 
Ggl:"Ockham algebra" 
}
}// "Ockham algebra" .... Ggl:"Ockham algebra" Naver:"Ockham algebra" Bing:"Ockham algebra"

Hypo (sub)
[[Kleene_algebra]] =,Kleene_algebra . Kleene_algebra
{
[[WtEn:Kleene_algebra]] = https://en.wiktionary.org/wiki/Kleene_algebra
Kleene algebra

https://en.wikipedia.org/wiki/De_Morgan_algebra#Kleene_algebra 
"Kleene algebra"
Ggl:"Kleene algebra"
Kleene+algebra
}
Hypo (sub): 
[[클레이니_대수,Kleene_algebra]]

}

== Stone algebra ==
[[Stone_algebra]] =,Stone_algebra . Stone_algebra
@@ -377,6 +369,39 @@

WpEn:Commutative_algebra ?

== action algebra ==
WtEn:action_algebra
WpEn:Action_algebra
 
... Ggl:"action algebra" Bing:"action algebra"
 
== information * / valuation * ==
information algebra / valuation algebra
정보대수
값매김대수
 
[[정보,information]]
[[값매김,valuation]] .... Srch:valuation Srch:값매김
 
https://en.wikipedia.org/wiki/Information_algebra
 
https://en.wikipedia.org/wiki/Information_algebra#Connections
보면 정보대수에서 idempotency axiom ([[멱등성,idempotence]] [[공리,axiom]])을 빼면 valuation algebra.
 
Ggl:"information algebra / valuation algebra" Bing:"information algebra / valuation algebra"
 
== term algebra ==
'''term algebra'''
WtEn:term_algebra x 2024-08
WpEn:Term_algebra
 
// term algebra ... Naver:"term algebra" Bing:"term algebra" Ggl:"term algebra"
 
[[텀,term]] [[항,term]] [[대수,algebra]]?
 
== ADDHERE ==
 
== ADDHERE ==
== ADDHERE ==
== ADDHERE ==
== ADDHERE ==





Sub:

1. Sub

1.2. Boolean algebra

1.2.1. + complete Boolean algebra

Boolean_algebra =,Boolean_algebra . Boolean_algebra
{
See VG 불_대수,Boolean_algebra / MK 불_대수,Boolean_algebra


Boolean_algebra_expression = 불_식,Boolean_expression ? chk
WtEn:boolean_expression
complete_Boolean_algebra

1.2.2. free Boolean algebra

1.4. algebra of sets

algebra_of_sets =,algebra_of_sets . algebra_of_sets

1.6. sigma-algebra / σ-algebra


}

sigma에 대해: curr see VG:시그마대수,sigma-algebra#s-3 #"이름의 sigma에 대한 설명"

비슷한 느낌의 이름(?)인
F대수,F-algebra {

bmks en
Understanding F-Algebras - School of Haskell | School of Haskell
https://www.schoolofhaskell.com/user/bartosz/understanding-algebras


WpEn:F-algebra (여기선 F-algebra) ........대문자 slanted ??
https://encyclopediaofmath.org/wiki/F-algebra ....(여기선 f-algebra) ...... 소문자 italic ??
(임시, 검색:) https://ncatlab.org/nlab/search?query=f-algebra
....
Ggl:f-algebra
}
l대수,l-algebra {

1.7. Weyl algebra

Weyl_algebra =,Weyl_algebra . Weyl_algebra
{
https://en.wikipedia.org/wiki/Weyl_algebra
https://ko.wikipedia.org/wiki/바일_대수
Weyl+algebra
}

1.8. *-algebra / involutive algebra

*-algebra // star-algebra ?? .... cf. https://mathworld.wolfram.com/C-Star-Algebra.html = WpEn:C*-algebra
involutive_algebra
=,*-algebra =,star-algebra =,involutive_algebra .
involutive algebra
https://en.wikipedia.org/wiki/*-algebra
WpKo:대합_대수 = https://ko.wikipedia.org/wiki/대합_대수
MKL involution =,involution . involution { 인볼루션 대합 (??) (wk) 매우 간단한 개념. 연산,operation 연산자,operator 주기,period 둘,two ... https://mathworld.wolfram.com/Involution.html WpKo:대합_(수학) = https://ko.wikipedia.org/wiki/대합_(수학) involution }

1.9. symmetric algebra

1.11. Witt algebra

Witt_algebra =,Witt_algebra =,Witt_algebra . Witt_algebra
{
Witt algebra
// named after Ernst Witt

KmsE:witt - 위트 - 같은사람? https://en.wikipedia.org/wiki/Ernst_Witt -> https://en.wikipedia.org/wiki/Witt's_theorem 같은사람임. 근데 위트? "was a German mathematician" 비트가 맞지 않을까? https://ko.wikipedia.org/wiki/에른스트_비트


1.13. De Morgan algebra ( + Ockham algebra + Kleene algebra )

1.14. Stone algebra

Stone_algebra =,Stone_algebra . Stone_algebra
Stone algebra


"Stone algebra"
Ggl:Stone algebra

1.15. Hurwitz algebra

Hurwitz_algebra =,Hurwitz_algebra . Hurwitz_algebra
{
Hurwitz algebra


rel
Hurwitz_problem

"Hurwitz algebra"
}

1.16. composition algebra

composition_algebra =,composition_algebra . composition_algebra
{
composition algebra
합성대수 ?




"composition algebra"
Ggl:composition algebra

}



#divalg

1.17. division algebra

나눗셈대수,division_algebra
=나눗셈대수,division_algebra =,division_algebra . 나눗셈대수 division_algebra
{
division algebra



WtEn:division_algebra
= https://en.wiktionary.org/wiki/division_algebra
  1. A linear algebra such that its non-zero vectors form a multiplicative_group.
  2. An algebra over a field such that every non-zero element of it has a multiplicative inverse. (It is not required to have a unity element( Ggl:unity element ).)

WpEn:Division_algebra
= https://en.wikipedia.org/wiki/Division_algebra




Ndict:division algebra
at 2023-08-19 - 사원수,quaternion { WtEn:quaternion KmsE:quaternion VG: 사원수,quaternion } 팔원수,octonion =팔원수,octonion =,octonion { octonion KmsE:octonion WtEn:octonion Ndict:팔원수 https://ko.wikipedia.org/wiki/팔원수 https://en.wikipedia.org/wiki/Octonion Ggl:octonion } 에 대한 수학백과 항목 두 곳에서만 언급중.


} // "division algebra" .... Ggl:division algebra


#assoc_alg

1.19. non-associative algebra

non-associative_algebra (w)
=,non-associative_algebra . non-associative_algebra

AKA distributive algebra = distributive_algebra =,distributive_algebra .
"or distributive algebra"



1.20. power-associative algebra

power-associative_algebra =,power-associative_algebra . power-associative_algebra

power-associative algebra




1.28. cofree coalgebra

cofree_coalgebra =,cofree_coalgebra . cofree_coalgebra
WtEn:cofree_coalgebra
cofree coalgebra
https://en.wikipedia.org/wiki/Cofree_coalgebra

1.29. measuring coalgebra

1.33. commutative *

commutative algebra = commutative_algebra =,commutative_algebra . commutative_algebra |=,commalg .




1.35. information * / valuation *

1.36. term algebra

1.37. ADDHERE


1.38. ADDHERE

1.39. ADDHERE

1.40. ADDHERE

1.41. ADDHERE

1.42. ADDHERE

ADDHERE
ADDHERE

2. Sub (-algebra 외)

2.2. algebraic propositional logic

algebraic_propositional_logic =,algebraic_propositional_logic =,algebraic_propositional_logic . algebraic_propositional_logic (local에도 writing)


//copied from VG:명제논리,propositional_logic
https://plato.stanford.edu/entries/logic-algebraic-propositional/
{
algebraic_propositional_logic (w) . Sub? 앞에 algebraic이 붙으면 달라지는 것은? QQQ


algebraic propositional logic


2.3. algebra system

혹시 CAS가 아닌 algebra system이 있는지... 글쎄?

aka computer_algebra ?? (그냥 생각)

aka algebraic_system ?? (그냥생각, 아닐 듯)

2.3.1. computer algebra system (CAS)

컴퓨터대수시스템 ?
computer algebra system
computer_algebra_system =,computer_algebra_system . computer_algebra_system |=,CAS CAS
CAS
WtEn:CAS
WtEn:computer_algebra_system
WpSp:Computer_algebra_system ?
WpEn:Computer_algebra_system ?
Computer_algebra_system

Rel.
symbolic_computation?
symbolic_computing?
아무튼
symbolic_ 등등 과 관련... 왜냐?
실제 수,number보단 기호,symbol 심벌,symbol을 manipulation의 대상으로 사용.
rel. symbolic_logic ...

2.3.1.1. 각종 CAS systems

Ex. / Sub:
매트랩,MATLAB
옥타브,Octave .... MATLAB_and_Octave curr. VG:MATLAB_and_Octave
Xcas =,Xcas . Xcas - Giac의 UI라고 함.
{


Giac =,Giac . Giac
{
free/opensource CAS.


이것들은 notebook_interface를 쓰는 일이 많음.... WtEn:notebook_interface ?

3. 표현들

표현 '대수학': 학문 분야임을 명확히 나타냄
(대수학을 줄여 대수로 부르기도 함)
하지만 '대수학'이 아닌 '대수'도 따로 있음. 대수학에서 다루는 대상,object.

표현 '대수':
'대수학'의 줄임말일 수도 있고 아닐 수도 있음. tbw

[https]수학백과: 가측 공간 처음부분 참조


Suffix -대수:

학문 분야명으로 쓰이는
_algebra는 거의 항상 -대수(학)으로 번역하면 무난. (다만 다른 것으로 번역될 수 있음, 아래 서술)

칼큘러스,calculus에서 어떤 _calculus 는 -대수(학)으로 번역되기도 함.
저기에는 정립된 번역이 없으며 -계산(법), -연산, -논리 등의 번역도 자주 보임.


Suffix -algebra:

수학의 분야명으로 쓰이는 suffix _algebra 중에서 어떤 것은 _logic , _calculus 와 완전히 구분되지 않음.
i.e.
앨지브라,algebra / 로직,logic / 칼큘러스,calculus의 경계선은 명확하지 않은 경우가 많음.

본질은 같은 것을 어떤 관점으로 / 어떤 방식으로 / .... 집중해서, 해석하는지 / 분석하는지 / 다루는지 ..... 에 따라 이름이 달라지는 듯
대체로 _algebra 는 대수적 관점, _logic 은 수리논리적 관점, _calculus 는 계산적 관점 ???

ex. 다음 것들은 비슷.

Boolean_algebra and Boolean_logic
propositional_logic and propositional_calculus
*th-order_calculus and *th-order_logic

...

그리고
logical_calculus Srch:logical_calculus
algebra_of_logic = logic_algebra = 논리대수 = Boolean_algebra[1]


Prefix algebraic- and algebraically-



ex.
Algebraic Propositional Logic
https://plato.stanford.edu/entries/logic-algebraic-propositional/
algebraic_propositional_logic

4.1. Serge Lang Algebra

Serge Lang
Serge_Lang
Algebra
Garduate Texts in Mathematics
Springer
두꺼운


4.2. Weibel - Homological Algebra

4.3. Hartshorne - Algebraic Geometry

Hartshorne - Algebraic Geometry
Ggl:Hartshorne Algebraic Geometry

Robin Hartshorne
Algebraic Geometry
Graduate Texts in Mathematics
Springer


algebraic_geometry 대수기하 대수기하학
KmsE:algebraic geom at @DATE

5. 대수학 강의

5.1. 오장헌

현대대수학1
세종대학교 오장헌
2015년 1학기
http://kocw.net/home/cview.do?cid=0d182cad13104050
평점 good
"The object of this course is to study the notion and theory of a 군,group.
One should be able to classify분류,classification groups of up to 오더,order 10.
Should be ablle to apply Sylow Theorems실로우_정리,쉴로브_정리,Sylow_theorem{ =,Sylow_theorem . Sylow_theorem Ndict:Sylow theorem WtEn:Sylow_theorem WpEn:Sylow_theorem -> https://en.wikipedia.org/wiki/Sylow_theorems https://ko.wikipedia.org/wiki/쉴로브_정리 ... Ggl:Sylow theorem / 실로우 via KmsE:sylow / 쉴로브 via 수백. } to solve various problems about groups.