2021년 2월 17일 (수) 07:46에 Pythagoras0님의 편집

2021-02-17T07:46:08Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-26T12:04:46Z

메타데이터: 새 문단

Pythagoras0: /* 노트 */ 새 문단

2020-12-22T06:41:30Z

노트: 새 문단

새 문서

== 노트 ==

===위키데이터===
* ID : [https://www.wikidata.org/wiki/Q874429 Q874429]
===말뭉치===
# Cube can be represented using group theory.<ref name="ref_8cdd3504">[https://www.britannica.com/science/group-theory group theory | Definition, Axioms, & Applications]</ref>
# So that’s all well and good, but what does any of this have to do with group theory?<ref name="ref_e4f03ea5">[https://medium.com/cantors-paradise/an-invitation-to-group-theory-c81e21ab739a Introduction to Group Theory]</ref>
# In the above section we described group theory formalism applied to graphs.<ref name="ref_a36bda63">[https://tbiomed.biomedcentral.com/articles/10.1186/1742-4682-8-21 Review and application of group theory to molecular systems biology]</ref>
# The study of groups is known as group theory.<ref name="ref_8bdf167a">[https://mathworld.wolfram.com/Group.html Group -- from Wolfram MathWorld]</ref>
# There are many groups on Group Theory in the library, and some of these might be helpful for parts of the module, but no single book is likely to cover the whole syllabus.<ref name="ref_010c9a23">[https://warwick.ac.uk/fac/sci/maths/undergrad/ughandbook/year4/ma442/ MA442 Group Theory]</ref>
# In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.<ref name="ref_02cef63c">[https://en.wikipedia.org/wiki/Group_theory Group theory]</ref>
# Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra.<ref name="ref_02cef63c" />
# The early history of group theory dates from the 19th century.<ref name="ref_02cef63c" />
# The theory of transformation groups forms a bridge connecting group theory with differential geometry.<ref name="ref_02cef63c" />
# Group Theory is the mathematical application of symmetry to an object to obtain knowledge of its physical properties.<ref name="ref_064d871e">[https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Group_Theory/Group_Theory_and_its_Application_to_Chemistry Group Theory and its Application to Chemistry]</ref>
# one needs to take a look at the theory portion of the Group Theory topic or refer to one of the reference text listed at the bottom of the page.<ref name="ref_064d871e" />
# When one thinks of group theory applications one doesn't necessarily associated it with everyday life or a simple toy like a Rubik's cube.<ref name="ref_064d871e" />
# The character table contains a wealth of information, for a more detailed discussion of the character table can be found in Group Theory Theoretical portion of the chemWiki.<ref name="ref_064d871e" />
# Symmetry operations and symmetry elements are two basic and important concepts in group theory.<ref name="ref_6aef3327">[https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Group_Theory/Group_Theory%3A_Theory Group Theory: Theory]</ref>
# Since the symmetry point group have all the properties of a group, there are also several subgroups that we can find in a perticular symmetry point group.<ref name="ref_6aef3327" />
# The Geometric Group Theory Page provides information and resources about geometric group theory and low-dimensional topology, although the links sometimes stray into neighboring fields.<ref name="ref_046371c0">[https://web.math.ucsb.edu/~jon.mccammond/geogrouptheory/ Geometric Group Theory]</ref>
# Rather we must take the view that group theory is the abstraction of ideas that were common to a number of major areas which were being studied essentially simultaneously.<ref name="ref_c3e1d538">[https://mathshistory.st-andrews.ac.uk/HistTopics/Development_group_theory/ Group theory]</ref>
# Although the beginnings of permutation group theory can be seen in this work, Lagrange never composes his permutations so in some sense never discusses groups at all.<ref name="ref_c3e1d538" />
# Abel , in, gave the first accepted proof of the insolubility of the quintic, and he used the existing ideas on permutations of roots but little new in the development of group theory.<ref name="ref_c3e1d538" />
# Group theory really came of age with the book by Burnside published in.<ref name="ref_c3e1d538" />
# This teacher package brings together all Plus articles on group theory.<ref name="ref_8b8f8143">[https://plus.maths.org/content/teacher-package-group-theory Teacher package: Group theory]</ref>
# Articles in this category explore applications of group theory.<ref name="ref_8b8f8143" />
# The article explains how group theory was used to show that you can solve a Rubik's cube in 26 steps.<ref name="ref_8b8f8143" />
# An account of how group theory is used to study the shape of viruses.<ref name="ref_8b8f8143" />
# After novel geometries such as hyperbolic and projective geometry had emerged, Klein used group theory to organize them in a more coherent way.<ref name="ref_3d3815ad">[https://en.wikipedia.org/wiki/Group_(mathematics) Group (mathematics)]</ref>
# The third field contributing to group theory was number theory.<ref name="ref_3d3815ad" />
# Likewise, group theory helps predict the changes in physical properties that occur when a material undergoes a phase transition, for example, from a cubic to a tetrahedral crystalline form.<ref name="ref_3d3815ad" />
# Listing all finite simple groups was a major achievement in contemporary group theory.<ref name="ref_3d3815ad" />
# Appendices review the basic concepts of group theory , ring theory, and linear algebra.<ref name="ref_0322db10">[https://www.thefreedictionary.com/group+theory group theory]</ref>
# Broadly speaking, group theory is the study of symmetry.<ref name="ref_0852391e">[https://kconrad.math.uconn.edu/math216/whygroups.html Why is group theory important?]</ref>
# When we are dealing with an object that appears symmetric, group theory can help with the analysis.<ref name="ref_0852391e" />
# Within mathematics itself, group theory is very closely linked to symmetry in geometry.<ref name="ref_0852391e" />
# Classical problems in algebra have been resolved with group theory.<ref name="ref_0852391e" />
# The spatial symmetries of V(r) can be analyzed by standard group theory.<ref name="ref_49b314d1">[https://www.nature.com/articles/s41467-018-07935-y Floquet group theory and its application to selection rules in harmonic generation]</ref>
# Today, the group theory has multiple facets and widespread applications in a broad range of science, including not only mathematics and physics but also chemistry.<ref name="ref_491bc331">[https://www.intechopen.com/books/symmetry-group-theory-and-mathematical-treatment-in-chemistry/group-theory-from-a-mathematical-viewpoint Group Theory from a Mathematical Viewpoint]</ref>
# In chemistry, group theory is used to study the symmetries and the crystal structures of molecules.<ref name="ref_491bc331" />
# One of the origins of the group theory goes back to the study of the solvability of algebraic equations by Galois in the nineteenth century.<ref name="ref_491bc331" />
# By using group theory, he classified Euclidean geometry and non-Euclidean geometry.<ref name="ref_491bc331" />
===소스===
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2021년 2월 17일 (수) 07:46에 Pythagoras0님의 편집

Pythagoras0: /* 메타데이터 */ 새 문단

Pythagoras0: /* 노트 */ 새 문단