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
{
https://en.wikipedia.org/wiki/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
}
}
== Stone algebra ==
[[Stone_algebra]] =,Stone_algebra . Stone_algebra
[[Ockham_algebra]] =,Ockham_algebra . Ockham_algebra
{
Ockham algebra
'''Ockham algebra'''
오컴 대수 ?
오컴_대수 ??
[[WtEn:Ockham_algebra]] = https://en.wiktionary.org/wiki/Ockham_algebrahttps://en.wikipedia.org/wiki/Ockham_algebra
"Ockham algebra"
Ggl:"Ockham algebra"
}// "Ockham algebra" .... Ggl:"Ockham algebra" Naver:"Ockham algebra" Bing:"Ockham 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:
Contents
- 1. Sub
- 1.1. elementary *
- 1.2. Boolean algebra
- 1.3. collapsing algebra
- 1.4. algebra of sets
- 1.5. algebra of a field AKA k-algebra
- 1.6. sigma-algebra / σ-algebra
- 1.7. Weyl algebra
- 1.8. *-algebra / involutive algebra
- 1.9. symmetric algebra
- 1.10. process algebra
- 1.11. Witt algebra
- 1.12. Lie algebra
- 1.13. De Morgan algebra ( + Ockham algebra + Kleene algebra )
- 1.14. Stone algebra
- 1.15. Hurwitz algebra
- 1.16. composition algebra
- 1.17. division algebra
- 1.18. associative algebra
- 1.19. non-associative algebra
- 1.20. power-associative algebra
- 1.21. differential algebra
- 1.22. Poisson algebra
- 1.23. tensor algebra
- 1.24. bialgebra
- 1.25. quasi-bialgebra
- 1.26. Hopf algebra
- 1.27. coalgebra
- 1.28. cofree coalgebra
- 1.29. measuring coalgebra
- 1.30. free algebra
- 1.31. Jordan algebra
- 1.32. alternative algebra
- 1.33. commutative *
- 1.34. action algebra
- 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
- 2. Sub (-algebra 외)
- 3. 표현들
- 4. 대수학 교재
- 5. 대수학 강의
- 6. bmks ko
1.2.1. + complete Boolean algebra ¶
Boolean_algebra =,Boolean_algebra . Boolean_algebra
{
See VG 불_대수,Boolean_algebra / MK 불_대수,Boolean_algebra
{
See VG 불_대수,Boolean_algebra / MK 불_대수,Boolean_algebra
Boolean_algebra_expression = 불_식,Boolean_expression ? chk
boolean_expression
complete_Boolean_algebra
boolean_expression
complete_Boolean_algebra
1.3. collapsing algebra ¶
collapsing_algebra
Boolean_algebra의 일종, 가끔 forcing{ https://en.wikipedia.org/wiki/Forcing_(mathematics) }을 해서 cardinal_number의 크기,size를 reduce("collapse")(n. 리덕션,reduction). poset(부분순서집합,partially_ordered_set 부분순서집합 부분순서집합 poset )을 사용해 만든 algebra. (we)
https://en.wikipedia.org/wiki/Collapsing_algebra
ko interwiki: 그 붕괴 - Levy_collapse 에 대해. // collapse collapse collapse
https://ko.wikipedia.org/wiki/레비_붕괴
via boolean_algebra
https://en.wikipedia.org/wiki/Collapsing_algebra
ko interwiki: 그 붕괴 - Levy_collapse 에 대해. // collapse collapse collapse
https://ko.wikipedia.org/wiki/레비_붕괴
via boolean_algebra
1.4. algebra of sets ¶
algebra_of_sets =,algebra_of_sets . algebra_of_sets
algebra of sets
https://en.wikipedia.org/wiki/Algebra_of_sets
https://encyclopediaofmath.org/wiki/Algebra_of_sets
https://en.wikipedia.org/wiki/Algebra_of_sets
https://encyclopediaofmath.org/wiki/Algebra_of_sets
"Also called Boolean_algebra or field_of_sets { https://encyclopediaofmath.org/wiki/Field_of_sets } by some authors. "
1.6. sigma-algebra / σ-algebra ¶
sigma-algebra =,sigma-algebra . sigma-algebra // VG 시그마대수,sigma-algebra (incl. 보렐_시그마대수,Borel_sigma-algebra )
σ-algebra (also σ-field)
https://mathworld.wolfram.com/Sigma-Algebra.html
https://www.proofwiki.org/wiki/Definition:Sigma-Algebra
https://en.wikipedia.org/wiki/Σ-algebra
https://ko.wikipedia.org/wiki/시그마_대수
https://ncatlab.org/nlab/show/sigma-algebra
시그마 대수
시그마 대수
σ-algebra
σ-algebra
}https://mathworld.wolfram.com/Sigma-Algebra.html
https://www.proofwiki.org/wiki/Definition:Sigma-Algebra
https://en.wikipedia.org/wiki/Σ-algebra
https://ko.wikipedia.org/wiki/시그마_대수
https://ncatlab.org/nlab/show/sigma-algebra
시그마 대수
시그마 대수
σ-algebra
σ-algebra
}
bmks en
Understanding F-Algebras - School of Haskell | School of Haskell
https://www.schoolofhaskell.com/user/bartosz/understanding-algebras
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
....
f-algebra
}
l대수,l-algebra {Understanding F-Algebras - School of Haskell | School of Haskell
https://www.schoolofhaskell.com/user/bartosz/understanding-algebras
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
....
f-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
}
{
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 = C*-algebra
involutive_algebra
=,*-algebra =,star-algebra =,involutive_algebra .
involutive algebra
https://en.wikipedia.org/wiki/*-algebra
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 대합_(수학) = https://ko.wikipedia.org/wiki/대합_(수학) involution }
involutive_algebra
=,*-algebra =,star-algebra =,involutive_algebra .
involutive algebra
https://en.wikipedia.org/wiki/*-algebra
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 대합_(수학) = https://ko.wikipedia.org/wiki/대합_(수학) involution }
1.9. symmetric algebra ¶
symmetric_algebra =,symmetric_algebra . symmetric_algebra
https://en.wikipedia.org/wiki/Symmetric_algebra
https://ko.wikipedia.org/wiki/대칭_대수
대칭성,symmetry?
https://en.wikipedia.org/wiki/Symmetric_algebra
https://ko.wikipedia.org/wiki/대칭_대수
대칭성,symmetry?
1.11. Witt algebra ¶
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 ) ¶
De_Morgan_algebra =,De_Morgan_algebra . De_Morgan_algebra
드모르간_대수,De_Morgan_algebra ?
{
De Morgan algebra
De_Morgan_algebra
= https://en.wiktionary.org/wiki/De_Morgan_algebra
De_Morgan_algebra
= https://en.wikipedia.org/wiki/De_Morgan_algebra
"De Morgan algebra"
De Morgan algebra
드모르간_대수,De_Morgan_algebra ?
{
De Morgan algebra
De_Morgan_algebra
= https://en.wiktionary.org/wiki/De_Morgan_algebra
De_Morgan_algebra
= https://en.wikipedia.org/wiki/De_Morgan_algebra
"De Morgan algebra"
De Morgan algebra
Hyper: (up)
Ockham_algebra =,Ockham_algebra . Ockham_algebra
{
Ockham algebra
오컴 대수 ?
오컴_대수 ??
Ockham_algebra = https://en.wiktionary.org/wiki/Ockham_algebra
https://en.wikipedia.org/wiki/Ockham_algebra
}// "Ockham algebra" .... Ockham algebra Ockham algebra Ockham algebra
Ockham_algebra =,Ockham_algebra . Ockham_algebra
{
Ockham algebra
오컴 대수 ?
오컴_대수 ??
Ockham_algebra = https://en.wiktionary.org/wiki/Ockham_algebra
https://en.wikipedia.org/wiki/Ockham_algebra
}// "Ockham algebra" .... Ockham algebra Ockham algebra Ockham algebra
1.17. division algebra ¶
나눗셈대수,division_algebra
=나눗셈대수,division_algebra =,division_algebra . 나눗셈대수 division_algebra
{
division algebra
=나눗셈대수,division_algebra =,division_algebra . 나눗셈대수 division_algebra
{
division algebra
나눗셈대수 ? - Yes (kms https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=division algebra )
division_algebra
= https://en.wiktionary.org/wiki/division_algebra
= https://en.wikipedia.org/wiki/Division_algebra
= https://en.wiktionary.org/wiki/division_algebra
- A linear algebra such that its non-zero vectors form a multiplicative_group.
- 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( unity element ).)
= https://en.wikipedia.org/wiki/Division_algebra
division algebra
at 2023-08-19 - 사원수,quaternion { quaternion quaternion VG: 사원수,quaternion } 팔원수,octonion =팔원수,octonion =,octonion { octonion octonion octonion 팔원수 https://ko.wikipedia.org/wiki/팔원수 https://en.wikipedia.org/wiki/Octonion octonion } 에 대한 수학백과 항목 두 곳에서만 언급중.
} // "division algebra" .... division algebra1.18. associative algebra ¶
1.19. non-associative algebra ¶
AKA distributive algebra = distributive_algebra =,distributive_algebra .
"or distributive algebra"
"or distributive algebra"
1.20. power-associative algebra ¶
power-associative_algebra =,power-associative_algebra . power-associative_algebra
power-associative algebra
power-associative algebra
power-associative algebra
power-associative algebra
"power-associative algebra"
power-associative algebra
power-associative algebra
"power-associative algebra"
1.25. quasi-bialgebra ¶
https://en.wikipedia.org/wiki/Quasi-bialgebra
bialgebra
coassociativity { coassociativity https://en.wikipedia.org/wiki/Coassociativity is redir to coalgebra }
bialgebra
coassociativity { coassociativity https://en.wikipedia.org/wiki/Coassociativity is redir to coalgebra }
1.28. cofree coalgebra ¶
cofree_coalgebra =,cofree_coalgebra . cofree_coalgebra
cofree_coalgebra
cofree coalgebra
https://en.wikipedia.org/wiki/Cofree_coalgebra
cofree_coalgebra
cofree coalgebra
https://en.wikipedia.org/wiki/Cofree_coalgebra
1.31. Jordan algebra ¶
Jordan_algebra =,Jordan_algebra . Jordan_algebra
Jordan algebra
https://en.wiktionary.org/wiki/Jordan_algebra
https://ko.wikipedia.org/wiki/요르단_대수
https://en.wikipedia.org/wiki/Jordan_algebra
Jordan algebra
"Jordan algebra"
Jordan algebra
https://en.wiktionary.org/wiki/Jordan_algebra
https://ko.wikipedia.org/wiki/요르단_대수
https://en.wikipedia.org/wiki/Jordan_algebra
Jordan algebra
"Jordan algebra"
1.32. alternative algebra ¶
alternative algebra
alternative_algebra =,alternative_algebra =,alternative_algebra . alternative_algebra
{
alternative_algebra = https://en.wiktionary.org/wiki/alternative_algebra#English
alternative_algebra =,alternative_algebra =,alternative_algebra . alternative_algebra
{
alternative_algebra = https://en.wiktionary.org/wiki/alternative_algebra#English
"alternative algebra"
alternative algebra
alternative algebra
alternative algebra
alternative algebra
alternative algebra
alternative algebra
alternative algebra
alternative algebra
}
1.33. commutative * ¶
commutative algebra = commutative_algebra =,commutative_algebra . commutative_algebra |=,commalg .
1.35. information * / valuation * ¶
information algebra / valuation algebra
정보대수
값매김대수
정보대수
값매김대수
https://en.wikipedia.org/wiki/Information_algebra#Connections
information algebra / valuation algebra information algebra / valuation algebra
information algebra / valuation algebra information algebra / valuation algebra
2.2. algebraic propositional logic ¶
algebraic_propositional_logic =,algebraic_propositional_logic =,algebraic_propositional_logic . algebraic_propositional_logic (local에도 writing)
//copied from 명제논리,propositional_logic
https://plato.stanford.edu/entries/logic-algebraic-propositional/
{
algebraic_propositional_logic (w) . Sub? 앞에 algebraic이 붙으면 달라지는 것은? QQQ
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
CAS
computer_algebra_system
Computer_algebra_system ?
Computer_algebra_system ?
Computer_algebra_system
computer algebra system
computer_algebra_system =,computer_algebra_system . computer_algebra_system |=,CAS CAS
CAS
CAS
computer_algebra_system
Computer_algebra_system ?
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.
symbolic_computation?
symbolic_computing?
아무튼
symbolic_ 등등 과 관련... 왜냐?
실제 수,number보단 기호,symbol 심벌,symbol을 manipulation의 대상으로 사용.
2.3.1.1. 각종 CAS systems ¶
Ex. / Sub:
매트랩,MATLAB
옥타브,Octave .... MATLAB_and_Octave curr. MATLAB_and_Octave
Xcas =,Xcas . Xcas - Giac의 UI라고 함.
{
매트랩,MATLAB
옥타브,Octave .... MATLAB_and_Octave curr. MATLAB_and_Octave
Xcas =,Xcas . Xcas - Giac의 UI라고 함.
{
Giac ?
Giac
Giac
}
매스매티카,Mathematica or Wolfram_Mathematica - installed 프로그램,program/소프트웨어,software.
Wolfram_Alpha - 웹사이트,website/online service/앱,app.
...
Giac
Giac
}
매스매티카,Mathematica or Wolfram_Mathematica - installed 프로그램,program/소프트웨어,software.
Wolfram_Alpha - 웹사이트,website/online service/앱,app.
...
3. 표현들 ¶
표현 '대수':
'대수학'의 줄임말일 수도 있고 아닐 수도 있음. tbw
'대수학'의 줄임말일 수도 있고 아닐 수도 있음. tbw
수학백과: 가측 공간 처음부분 참조
Suffix -대수:
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.
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 ???
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
propositional_logic and propositional_calculus
*th-order_calculus and *th-order_logic
...
Prefix algebraic- and algebraically-
ex.
Algebraic Propositional Logic
https://plato.stanford.edu/entries/logic-algebraic-propositional/
algebraic_propositional_logic
Algebraic Propositional Logic
https://plato.stanford.edu/entries/logic-algebraic-propositional/
algebraic_propositional_logic
4.2. Weibel - Homological Algebra ¶
An introduction to homological algebra
Cambridge studies in advanced mathematics 38
4.3. Hartshorne - Algebraic Geometry ¶
Robin Hartshorne
Algebraic Geometry
Graduate Texts in Mathematics
Springer
Algebraic Geometry
Graduate Texts in Mathematics
Springer
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 Sylow theorem Sylow_theorem Sylow_theorem -> https://en.wikipedia.org/wiki/Sylow_theorems https://ko.wikipedia.org/wiki/쉴로브_정리 ... Sylow theorem / 실로우 via sylow / 쉴로브 via 수백. } to solve various problems about groups.
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 Sylow theorem Sylow_theorem Sylow_theorem -> https://en.wikipedia.org/wiki/Sylow_theorems https://ko.wikipedia.org/wiki/쉴로브_정리 ... Sylow theorem / 실로우 via sylow / 쉴로브 via 수백. } to solve various problems about groups.