Elementary algebra: Difference between revisions
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imported>Rodw m Disambiguating links to Operation (link changed to Operation (mathematics)) using DisamAssist. |
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[[File:Polynomialdeg2.svg|thumb|right|200px|Two-dimensional plot (red curve) of the algebraic equation <math>y = x^2 - x - 2</math>.]] | [[File:Polynomialdeg2.svg|thumb|right|200px|Two-dimensional plot (red curve) of the algebraic equation <math>y = x^2 - x - 2</math>.]] | ||
'''Elementary algebra''', also known as '''high school algebra''' or '''college algebra''',<ref>Pierce, R., [https://www.mathsisfun.com/algebra/index-college.html College Algebra], ''Maths is Fun'', accessed 28 August 2023</ref> encompasses the basic concepts of [[algebra]]. It is often contrasted with [[arithmetic]]: arithmetic deals with specified [[number]]s,<ref>[[Herbert Ellsworth Slaught|H.E. Slaught]] and N.J. Lennes, ''Elementary algebra'', Publ. Allyn and Bacon, 1915, [https://books.google.com/books?id=gLii_eO4dNsC&dq=%22Elementary%20algebra%22%20letters&pg=PA1 page 1] (republished by Forgotten Books)</ref> whilst algebra introduces numerical [[variable (mathematics)|variables]] (quantities without fixed values).<ref>Lewis Hirsch, Arthur Goodman, ''Understanding Elementary Algebra With Geometry: A Course for College Students'', Publisher: Cengage Learning, 2005, {{ISBN|0534999727}}, 9780534999728, 654 pages, [https://books.google.com/books?id=7hdK4RSub5cC&q=generalization&pg=PA2 page 2]</ref> | '''Elementary algebra''', also known as '''high school algebra''' or '''college algebra''',<ref>Pierce, R., [https://www.mathsisfun.com/algebra/index-college.html College Algebra], ''Maths is Fun'', accessed 28 August 2023</ref> encompasses the basic concepts of [[algebra]]. It is often contrasted with [[arithmetic]]: arithmetic deals with specified [[number]]s,<ref>[[Herbert Ellsworth Slaught|H.E. Slaught]] and N.J. Lennes, ''Elementary algebra'', Publ. Allyn and Bacon, 1915, [https://books.google.com/books?id=gLii_eO4dNsC&dq=%22Elementary%20algebra%22%20letters&pg=PA1 page 1] (republished by Forgotten Books)</ref> whilst algebra introduces numerical [[variable (mathematics)|variables]] (quantities without fixed values).<ref>Lewis Hirsch, Arthur Goodman, ''Understanding Elementary Algebra With Geometry: A Course for College Students'', Publisher: Cengage Learning, 2005, {{ISBN|0534999727}}, 9780534999728, 654 pages, [https://books.google.com/books?id=7hdK4RSub5cC&q=generalization&pg=PA2 page 2]</ref> In arithmetic, [[Operation (mathematics)|operations]] (such as addition and subtraction) can only be performed on numbers. In algebra, operations can be performed on numbers, variables, and [[Term (arithmetic)|terms]]. Unlike [[abstract algebra]], elementary algebra is not concerned with [[algebraic structure]]s outside the realm of [[real number|real]] and [[complex number]]s. | ||
It is typically taught to [[secondary school]] students and at introductory college level in the [[United States]],<ref name=leff /> and builds on their understanding of [[arithmetic]]. The use of variables to denote quantities allows general relationships between quantities to be formally and concisely expressed, and thus enables solving a broader scope of problems. Many quantitative relationships in [[science]] and mathematics are expressed as algebraic [[equation]]s. | It is typically taught to [[secondary school]] students and at introductory college level in the [[United States]],<ref name=leff /> and builds on their understanding of [[arithmetic]]. The use of variables to denote quantities allows general relationships between quantities to be formally and concisely expressed, and thus enables solving a broader scope of problems. Many quantitative relationships in [[science]] and mathematics are expressed as algebraic [[equation]]s. | ||
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== References == | == References == | ||
*[[Leonhard Euler]], '' [[Elements of Algebra]]'', 1770. English translation [[Tarquin Press]], 2007, {{ISBN|978-1-899618-79-8}}, also online digitized editions<ref>[http://web.mat.bham.ac.uk/C.J.Sangwin/euler/ Euler's Elements of Algebra<!-- Bot generated title -->] {{webarchive|url=https://web.archive.org/web/20110413234352/http://web.mat.bham.ac.uk/C.J.Sangwin/euler/ |date=2011-04-13 }}</ref> 2006,<ref>{{cite web|url=https://books.google.com/books?id=X8yv0sj4_1YC&q=euler+elements|title=Elements of Algebra|first1=Leonhard|last1=Euler|first2=John|last2=Hewlett|first3=Francis|last3=Horner|first4=Jean|last4=Bernoulli|first5=Joseph Louis|last5=Lagrange|date=4 May 2018|publisher=Longman, Orme|access-date=4 May 2018|via=Google Books}}</ref> 1822. | *[[Leonhard Euler]], '' [[Elements of Algebra]]'', 1770. English translation [[Tarquin Press]], 2007, {{ISBN|978-1-899618-79-8}}, also online digitized editions<ref>[http://web.mat.bham.ac.uk/C.J.Sangwin/euler/ Euler's Elements of Algebra<!-- Bot generated title -->] {{webarchive|url=https://web.archive.org/web/20110413234352/http://web.mat.bham.ac.uk/C.J.Sangwin/euler/ |date=2011-04-13 }}</ref> 2006,<ref>{{cite web|url=https://books.google.com/books?id=X8yv0sj4_1YC&q=euler+elements|title=Elements of Algebra|first1=Leonhard|last1=Euler|first2=John|last2=Hewlett|first3=Francis|last3=Horner|first4=Jean|last4=Bernoulli|first5=Joseph Louis|last5=Lagrange|date=4 May 2018|publisher=Longman, Orme|access-date=4 May 2018|via=Google Books}}</ref> 1822. | ||
*Charles Smith, ''[ | *Charles Smith, ''[https://digital.library.cornell.edu/cgi/t/text/text-idx?c=math;idno=smit025 A Treatise on Algebra]'', in [https://historical.library.cornell.edu/math Cornell University Library Historical Math Monographs]. | ||
*Redden, John. [http://catalog.flatworldknowledge.com/bookhub/reader/128?e=fwk-redden-ch01 ''Elementary Algebra''] {{Webarchive|url=https://web.archive.org/web/20160610165651/http://catalog.flatworldknowledge.com/bookhub/reader/128?e=fwk-redden-ch01 |date=2016-06-10 }}. Flat World Knowledge, 2011 | *Redden, John. [http://catalog.flatworldknowledge.com/bookhub/reader/128?e=fwk-redden-ch01 ''Elementary Algebra''] {{Webarchive|url=https://web.archive.org/web/20160610165651/http://catalog.flatworldknowledge.com/bookhub/reader/128?e=fwk-redden-ch01 |date=2016-06-10 }}. Flat World Knowledge, 2011 | ||
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