추상대수학 - 편집 역사

Pythagoras0: /* 메타데이터 */ 새 문단

2021-02-17T13:01:08Z

메타데이터: 새 문단

Pythagoras0: /* 노트 */ 새 문단

2020-12-21T16:56:23Z

노트: 새 문단

2013년 6월 6일 (목) 16:16에 Pythagoras0님의 편집

2013-06-06T16:16:26Z

2013년 3월 3일 (일) 10:13에 Pythagoras0님의 편집

2013-03-03T10:13:12Z

2013년 1월 12일 (토) 15:21에 Pythagoras0님의 편집

2013-01-12T15:21:03Z

2012년 9월 15일 (토) 05:56에 Pythagoras0님의 편집

2012-09-15T05:56:10Z

2010년 8월 12일 (목) 19:23에 http://bomber0.myid.net/님의 편집

2010-08-12T19:23:33Z

2009년 11월 3일 (화) 21:24에 http://bomber0.myid.net/님의 편집

2009-11-03T21:24:08Z

2009년 10월 15일 (목) 05:46에 http://bomber0.myid.net/님의 편집

2009-10-15T05:46:53Z

2009년 8월 25일 (화) 23:20에 http://bomber0.myid.net/님의 편집

2009-08-25T23:20:50Z

← 이전 판		2021년 2월 17일 (수) 13:01 판
171번째 줄:		171번째 줄:
	===소스===		===소스===
	<references />		<references />
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q159943 Q159943]
		+	===Spacy 패턴 목록===
		+	* [{'LOWER': 'abstract'}, {'LEMMA': 'algebra'}]
		+	* [{'LOWER': 'modern'}, {'LEMMA': 'algebra'}]
		+	* [{'LEMMA': 'algebra'}]
		+	* [{'LEMMA': 'algebraic'}]

← 이전 판		2020년 12월 21일 (월) 16:56 판
123번째 줄:		123번째 줄:
	[[분류:교과목]]		[[분류:교과목]]
	[[분류:추상대수학]]		[[분류:추상대수학]]
		+
		+	== 노트 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q159943 Q159943]
		+	===말뭉치===
		+	# Theory and Applications is an open source textbook designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner.<ref name="ref_32c6abca">[http://abstract.ups.edu/ Abstract Algebra: Theory and Applications (A Free Textbook)]</ref>
		+	# Five of them will be taking college courses in differential equations, abstract algebra and discrete mathematics as 10th-graders at Pasadena High School this fall.<ref name="ref_cfa4eaf5">[https://www.merriam-webster.com/dictionary/abstract%20algebra Definition of Abstract Algebra by Merriam-Webster]</ref>
		+	# At the height of her mathematical powers, doing new work on abstract algebra, Noether died after an operation on an ovarian cyst.<ref name="ref_cfa4eaf5" />
		+	# If the operations satisfy familiar arithmetic rules (such as associativity, commutativity, and distributivity) the set will have a particularly “rich” algebraic structure.<ref name="ref_fd0599a4">[https://www.britannica.com/science/modern-algebra Modern algebra \| mathematics]</ref>
		+	# Sets with the richest algebraic structure are known as fields.<ref name="ref_fd0599a4" />
		+	# In fact, finite fields motivated the early development of abstract algebra.<ref name="ref_fd0599a4" />
		+	# Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems.<ref name="ref_53cb43d7">[https://mathworld.wolfram.com/AbstractAlgebra.html Abstract Algebra -- from Wolfram MathWorld]</ref>
		+	# discrete mathematics are sometimes considered branches of abstract algebra.<ref name="ref_53cb43d7" />
		+	# In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.<ref name="ref_f9c755ac">[https://en.wikipedia.org/wiki/Abstract_algebra Abstract algebra]</ref>
		+	# Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras.<ref name="ref_f9c755ac" />
		+	# Algebraic structures, with their associated homomorphisms, form mathematical categories.<ref name="ref_f9c755ac" />
		+	# As in other parts of mathematics, concrete problems and examples have played important roles in the development of abstract algebra.<ref name="ref_f9c755ac" />
		+	# But the richness of abstract algebra comes from the idea that you can use abstractions of a concept that are easy to understand to explain more complex behavior!<ref name="ref_9d850f01">[https://math.stackexchange.com/questions/855828/what-is-abstract-algebra-essentially What is Abstract Algebra essentially?]</ref>
		+	# This site contains many of the definitions and theorems from the area of mathematics generally called abstract algebra.<ref name="ref_84fa5ed8">[http://www.math.niu.edu/~beachy/aaol/contents.html ABSTRACT ALGEBRA ON LINE: Contents]</ref>
		+	# It is intended for undergraduate students taking an abstract algebra class at the junior/senior level, as well as for students taking their first graduate algebra course.<ref name="ref_84fa5ed8" />
		+	# Algebra has also played a significant role in clarifying and highlighting notions of logic, at the core of exact philosophy for millennia.<ref name="ref_6874edf0">[https://plato.stanford.edu/entries/algebra/ Algebra (Stanford Encyclopedia of Philosophy)]</ref>
		+	# A number of branches of mathematics have found algebra such an effective tool that they have spawned algebraic subbranches.<ref name="ref_6874edf0" />
		+	# Groups, rings and fields only scratch the surface of abstract algebra.<ref name="ref_6874edf0" />
		+	# Boolean algebras abstract the algebra of sets.<ref name="ref_6874edf0" />
		+	# "Abstract Algebra" is a clearly written, self-contained basic algebra text for graduate students, with a generous amount of additional material that suggests the scope of contemporary algebra.<ref name="ref_a30cf7c2">[https://www.springer.com/gp/book/9780387715674 Pierre Antoine Grillet]</ref>
		+	# The last chapters, on universal algebras and categories, including tripleability, give valuable general views of algebra.<ref name="ref_a30cf7c2" />
		+	# This book is on abstract algebra (abstract algebraic systems), an advanced set of topics related to algebra, including groups, rings, ideals, fields, and more.<ref name="ref_cbc73e9b">[https://en.wikibooks.org/wiki/Abstract_Algebra Wikibooks, open books for an open world]</ref>
		+	# Primarily, we will follow Wikibooks' Abstract Algebra textbook.<ref name="ref_7cd593b6">[https://en.wikiversity.org/wiki/Introduction_to_Abstract_Algebra Introduction to Abstract Algebra]</ref>
		+	# A good textbook to pick up is Topics in Algebra by I.N. Herstein.<ref name="ref_7cd593b6" />
		+	# Shed the societal and cultural narratives holding you back and let step-by-step A First Course in Abstract Algebra textbook solutions reorient your old paradigms.<ref name="ref_17f28728">[https://www.slader.com/textbook/9780201763904-a-first-course-in-abstract-algebra-7th-edition/ Solutions to A First Course in Abstract Algebra (9780201763904) :: Homework Help and Answers :: Slader]</ref>
		+	# Unlock your A First Course in Abstract Algebra PDF (Profound Dynamic Fulfillment) today.<ref name="ref_17f28728" />
		+	# This course develops in the theme of "Arithmetic congruence, and abstract algebraic structures.<ref name="ref_ceda1da5">[https://math.gatech.edu/courses/math/4107 Georgia Institute of Technology]</ref>
		+	# This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences.<ref name="ref_8424066c">[https://www.degruyter.com/view/title/319702?language=en Abstract Algebra]</ref>
		+	# Abstract Algebra with Applications provides a friendly and concise introduction to algebra, with an emphasis on its uses in the modern world.<ref name="ref_2eef2cc6">[https://www.cambridge.org/core_title/gb/491143 Abstract algebra applications]</ref>
		+	# Perhaps no other subject of undergraduate mathematics is as challenging to learn (and to teach) as abstract algebra.<ref name="ref_2eef2cc6" />
		+	# Many of the applications of modern algebra are explained in a thoughtful way that will help motivate students to study abstract concepts.<ref name="ref_2eef2cc6" />
		+	# Abstract Algebra by Dummit & Foote is a standard textbook used by colleges and universities.<ref name="ref_99735e06">[https://www.socratica.com/subject/abstract-algebra Abstract Algebra]</ref>
		+	# It covers all the topics for a solid first course in Abstract Algebra.<ref name="ref_99735e06" />
		+	# Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication.<ref name="ref_c51bd267">[https://www.worldscientific.com/worldscibooks/10.1142/9853 Abstract Algebra]</ref>
		+	# Noether went into research and more or less invented the field of abstract algebra.<ref name="ref_92aa58b2">[https://cosmosmagazine.com/physics/woman-who-invented-abstract-algebra/ The inventor of abstract algebra]</ref>
		+	# The main aim of the course is to introduce you to basic concepts from abstract algebra, especially the notion of a group.<ref name="ref_eea5599c">[https://www.kcl.ac.uk/study/courses-data/modules/4/Introduction-To-Abstract-Algebra-4ccm121a Introduction To Abstract Algebra]</ref>
		+	# The course will help prepare you for further study in abstract algebra as well as familiarize you with tools essential in many other areas of mathematics.<ref name="ref_eea5599c" />
		+	# Computational Problems in Abstract Algebra provides information pertinent to the application of computers to abstract algebra.<ref name="ref_213c6e05">[https://www.sciencedirect.com/book/9780080129754/computational-problems-in-abstract-algebra Computational Problems in Abstract Algebra]</ref>
		+	# The final chapter deals with the computational problems related to invariant factors in linear algebra.<ref name="ref_213c6e05" />
		+	# Mathematicians as well as students of algebra will find this book useful.<ref name="ref_213c6e05" />
		+	===소스===
		+	<references />

@@ 1번째 줄: / 1번째 줄: @@
-==간단한 요약==
+==개요==
 * 현대대수학의 기본적인 언어이자 대상인, 군, 환, 체의 기본적인 용어 및 이론을 공부함.
 * 갈루아 이론 - 군론을 통해 확장체 혹은 대수방정식의 해가 가진 대칭성을 들여다 봄.
@@ 8번째 줄: / 7번째 줄: @@
 ==선수 과목 또는 알고 있으면 좋은 것들==
-*  고교 수준의 대수학<br>
+*  고교 수준의 대수학
 ** 다항식, 다항방정식
-*  기초적인 선형대수학<br>
+*  기초적인 선형대수학
-**  기저, 차원, 선형사상, 행렬, 행렬식<br>
+**  기저, 차원, 선형사상, 행렬, 행렬식
 ==다루는 대상==
-*  군(group)<br>
+*  군(group)
 ** 대칭성을 기술하는 언어
 ** 항등원, 역원,
-*  환(ring)<br>
+*  환(ring)
 ** 덧셈, 뺄셈, 곱하기가 가능하며, 덧셈과 곱셈 사이에 분배법칙이 성립.
 ** 정수의 집합, 다항식의 집합, n x n 행렬들의 집합
-*  체(field)<br>
+*  체(field)
 ** 실수, 복소수와 같이 사칙연산이 가능.
-**  좀더 일반적으로 곱셈의 교환법칙을 가정하지 않는 경우는 division ring이라 부름.<br>  <br>
+**  좀더 일반적으로 곱셈의 교환법칙을 가정하지 않는 경우는 division ring이라 부름.
 ==중요한 개념 및 정리==
@@ 40번째 줄: / 41번째 줄: @@
 * [[대수학의 기본정리]](The fundamental theorem of algebras)의 대수적 증명은 가능한가?
-* [[해밀턴의 사원수(quarternions)|해밀턴의 사원수]]<br>
+* [[해밀턴의 사원수(quarternions)|해밀턴의 사원수]]
-**  아래 참고할만한 자료<br>
+**  아래 참고할만한 자료
 *** [http://www.jstor.org/stable/2315349 The Impossibility of a Division Algebra of Vectors in Three Dimensional Space]
-*** [http://www.jstor.org/stable/2689449 Hamilton's Discovery of Quaternions]<br>
+*** [http://www.jstor.org/stable/2689449 Hamilton's Discovery of Quaternions]
 * [[가우스와 정17각형의 작도]]
 * [[그리스 3대 작도 불가능문제]]를 군론을 통해 해결할 수 있음.
 * [[5차방정식과 근의 공식|일반적인 5차 이상의 방정식의 대수적 해가 존재하지 않음에 대한 아벨의 증명]]
-*  유클리드 도메인이 아닌 PID<br>
+*  유클리드 도메인이 아닌 PID
-**  아래 참고할만한 자료<br>
+**  아래 참고할만한 자료
 *** [http://www.jstor.org/stable/2322908 A Principal Ideal Domain That Is Not a Euclidean Domain]
 * [[7개의 프리즈 패턴]]
@@ 59번째 줄: / 60번째 줄: @@
 * [[초등정수론|정수론]]
 * [[선형대수학]]
-* [[리만곡면론|대수곡선론]]<br>
+* [[리만곡면론|대수곡선론]]
 ** 대수기하학 입문으로서의 대수곡선론
-* [[대수적위상수학]]<br>
+* [[대수적위상수학]]
-**  군론<br>
+**  군론
 *** fundamental group을 정의하기 위해 필요
 *** covering space의 deck transformation group
-**  유한생성 아벨군의 기본정리<br>
+**  유한생성 아벨군의 기본정리
 *** 호몰로지를 이해하기 위해 필요
-*  조합론<br>
+*  조합론
 ** 번사이드 보조정리
@@ 77번째 줄: / 78번째 줄: @@
 * 펠릭스 클라인의 '정이십면체와 5차방정식'
-*  semisimple rings<br>
+*  semisimple rings
 ** [[아틴-웨더번 정리(Artin–Wedderburn theorem)]]
 * 유한군의 표현론
@@ 83번째 줄: / 84번째 줄: @@
 * [[Classical groups]]
-−
 ==표준적인 교과서==
-* [http://www.amazon.com/First-Course-Abstract-Algebra-7th/dp/0201763907 A First Course in Abstract Algebra]<br>
+* John B. Fraleigh [http://www.amazon.com/First-Course-Abstract-Algebra-7th/dp/0201763907 A First Course in Abstract Algebra]
-** John B. Fraleigh
-==추천도서 및 보조교재==
+==관련도서==
-* [http://www.amazon.com/exec/obidos/ASIN/0817646841/ebooksclub-20/ A History of Abstract Algebra]<br>
+* Israel Kleiner [http://www.amazon.com/exec/obidos/ASIN/0817646841/ebooksclub-20/ A History of Abstract Algebra]
@@ 99번째 줄: / 102번째 줄: @@
 ==관련논문==
-* [http://www.jstor.org/stable/2975015 The Evolution of Algebra 1800-1870]<br>
+* I. G. Bashmakova and A. N. Rudakov [http://www.jstor.org/stable/2975015 The Evolution of Algebra 1800-1870] , <cite>The American Mathematical Monthly</cite>, Vol. 102, No. 3 (Mar., 1995), pp. 266-270
-** I. G. Bashmakova and A. N. Rudakov , <cite>The American Mathematical Monthly</cite>, Vol. 102, No. 3 (Mar., 1995), pp. 266-270
+* [http://www.jstor.org/stable/2690312 The Evolution of Group Theory: A Brief Survey]
 ** Israel Kleiner, <cite>Mathematics Magazine</cite>, Vol. 59, No. 4 (Oct., 1986), pp. 195-215
-* [http://www.jstor.org/stable/2690624 A History of Lagrange's Theorem on Groups]<br>
+* [http://www.jstor.org/stable/2690624 A History of Lagrange's Theorem on Groups]
 ** Richard L. Roth, <cite>Mathematics Magazine</cite>, Vol. 74, No. 2 (Apr., 2001), pp. 99-108
-* [http://www.jstor.org/stable/2689449 Hamilton's Discovery of Quaternions]<br>
+* [http://www.jstor.org/stable/2689449 Hamilton's Discovery of Quaternions]
 ** B. L. van der Waerden, <cite>Mathematics Magazine</cite>, Vol. 49, No. 5 (Nov., 1976), pp. 227-234
-* [http://www.jstor.org/stable/2974935 The Genesis of the Abstract Ring Concept]<br>
+* [http://www.jstor.org/stable/2974935 The Genesis of the Abstract Ring Concept]
 ** Israel Kleiner, <cite>The American Mathematical Monthly</cite>, Vol. 103, No. 5 (May, 1996), pp. 417-424
-* [http://www.jstor.org/stable/2691011 A Historically Focused Course in Abstract Algebra]<br>
+* [http://www.jstor.org/stable/2691011 A Historically Focused Course in Abstract Algebra]
 ** Israel Kleiner, <cite>Mathematics Magazine</cite>, Vol. 71, No. 2 (Apr., 1998), pp. 105-111
-* [http://www.jstor.org/stable/2325119 Galois Theory for Beginners]<br>
+* [http://www.jstor.org/stable/2325119 Galois Theory for Beginners]
 ** John Stillwell, <cite>The American Mathematical Monthly</cite>, Vol. 101, No. 1 (Jan., 1994), pp. 22-27
-* [http://www.jstor.org/stable/2974763 Niels Hendrik Abel and Equations of the Fifth Degree]<br>
+* [http://www.jstor.org/stable/2974763 Niels Hendrik Abel and Equations of the Fifth Degree]
 ** Michael I. Rosen, <cite>The American Mathematical Monthly</cite>, Vol. 102, No. 6 (Jun. - Jul., 1995), pp. 495-505
 * [http://www.jstor.org/stable/2322908 A Principal Ideal Domain That Is Not a Euclidean Domain]
 ** Oscar A. Campoli, <cite>The American Mathematical Monthly</cite>, Vol. 95, No. 9 (Nov., 1988), pp. 868-871
-* [http://www.jstor.org/stable/2974984 Principal Ideal Domains are Almost Euclidean]<br>
+* [http://www.jstor.org/stable/2974984 Principal Ideal Domains are Almost Euclidean]
 ** John Greene, <cite>The American Mathematical Monthly</cite>, Vol. 104, No. 2 (Feb., 1997), pp. 154-156
 [[분류:교과목]]
 [[분류:추상대수학]]

← 이전 판		2013년 3월 3일 (일) 10:13 판
121번째 줄:		121번째 줄:
	** John Greene, <cite>The American Mathematical Monthly</cite>, Vol. 104, No. 2 (Feb., 1997), pp. 154-156		** John Greene, <cite>The American Mathematical Monthly</cite>, Vol. 104, No. 2 (Feb., 1997), pp. 154-156
	[[분류:교과목]]		[[분류:교과목]]
		+	[[분류:추상대수학]]

← 이전 판		2013년 1월 12일 (토) 15:21 판
120번째 줄:		120번째 줄:
	* [http://www.jstor.org/stable/2974984 Principal Ideal Domains are Almost Euclidean]<br>		* [http://www.jstor.org/stable/2974984 Principal Ideal Domains are Almost Euclidean]<br>
	** John Greene, <cite>The American Mathematical Monthly</cite>, Vol. 104, No. 2 (Feb., 1997), pp. 154-156		** John Greene, <cite>The American Mathematical Monthly</cite>, Vol. 104, No. 2 (Feb., 1997), pp. 154-156
		+	[[분류:교과목]]

@@ 29번째 줄: / 29번째 줄: @@
 * [[순환군]]
 * [[군론(group theory)|군론]]
-* [[search?q=%EC%9C%A0%ED%95%9C%EC%83%9D%EC%84%B1%20%EC%95%84%EB%B2%A8%EA%B5%B0%EC%9D%98%20%EA%B8%B0%EB%B3%B8%EC%A0%95%EB%A6%AC&parent id=1940206|유한생성 아벨군의 기본정리]]
+* [[유한생성 아벨군의 기본정리]]
 * [[#|체론(field theory)]]
 * ideal
@@ 78번째 줄: / 78번째 줄: @@
 * 펠릭스 클라인의 '정이십면체와 5차방정식'
 *  semisimple rings<br>
-** Artin–Wedderburn theorem
+** [[search?q=Artin%E2%80%93Wedderburn%20theorem&parent id=1940206|Artin–Wedderburn theorem]]
 * 유한군의 표현론
 * [[대수적수론|대수적정수론]]

@@ 115번째 줄: / 115번째 줄: @@
 ** <cite>The American Mathematical Monthly</cite>, Vol. 106, No. 9 (Nov., 1999), pp. 859-863
 * [http://www.jstor.org/stable/4146920 The Arithmetic of Algebraic Numbers: An Elementary Approach]<br>
-** Chi-Kwong Li and David Lutzer
+** Chi-Kwong Li and David Lutzer, <cite>The College Mathematics Journal</cite>, Vol. 35, No. 4 (Sep., 2004), pp. 307-309
 * [http://www.jstor.org/stable/2689449 Hamilton's Discovery of Quaternions]<br>
 ** B. L. van der Waerden
@@ 129번째 줄: / 128번째 줄: @@
 ** Israel Kleiner
 ** <cite>Mathematics Magazine</cite>, Vol. 71, No. 2 (Apr., 1998), pp. 105-111
 * [http://www.jstor.org/stable/2325119 Galois Theory for Beginners]<br>
 ** John Stillwell