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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Elementary algebra ： ウィキペディア英語版 Elementary algebra Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics. It is typically taught to secondary school students and builds on their understanding of arithmetic. Whereas arithmetic deals with specified numbers,〔H.E. Slaught and N.J. Lennes, ''Elementary algebra'', Publ. Allyn and Bacon, 1915, (page 1 ) (republished by Forgotten Books)〕 algebra introduces quantities without fixed values, known as variables.〔Lewis Hirsch, Arthur Goodman, ''Understanding Elementary Algebra With Geometry: A Course for College Students'', Publisher: Cengage Learning, 2005, ISBN 0534999727, 9780534999728, 654 pages, (page 2 )〕 This use of variables entails a use of algebraic notation and an understanding of the general rules of the operators introduced in arithmetic. Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers. 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. Most quantitative results in science and mathematics are expressed as algebraic equations. ==Algebraic notation == (詳細は3x^2 - 2xy + c has the following components: 256px 1 : Exponent (power), 2 : Coefficient, 3 : term, 4 : operator, 5 : constant, $x,\; y$ : variables A ''coefficient'' is a numerical value which multiplies a variable (the operator is omitted). A ''term'' is an addend or a summand, a group of coefficients, variables, constants and exponents that may be separated from the other terms by the plus and minus operators.〔Richard N. Aufmann, Joanne Lockwood, ''Introductory Algebra: An Applied Approach'', Publisher Cengage Learning, 2010, ISBN 1439046042, 9781439046043, (page 78 )〕 Letters represent variables and constants. By convention, letters at the beginning of the alphabet (e.g. $a,\; b,\; c$) are typically used to represent constants, and those toward the end of the alphabet (e.g. $x,\; y$ and $z$) are used to represent variables.〔William L. Hosch (editor), ''The Britannica Guide to Algebra and Trigonometry'', Britannica Educational Publishing, The Rosen Publishing Group, 2010, ISBN 1615302190, 9781615302192, (page 71 )〕 They are usually written in italics.〔James E. Gentle, ''Numerical Linear Algebra for Applications in Statistics'', Publisher: Springer, 1998, ISBN 0387985425, 9780387985428, 221 pages, (E. Gentle page 183 )〕 Algebraic operations work in the same way as arithmetic operations,〔Horatio Nelson Robinson, ''New elementary algebra: containing the rudiments of science for schools and academies'', Ivison, Phinney, Blakeman, & Co., 1866, (page 7 )〕 such as addition, subtraction, multiplication, division and exponentiation.〔Ron Larson, Robert Hostetler, Bruce H. Edwards, ''Algebra And Trigonometry: A Graphing Approach'', Publisher: Cengage Learning, 2007, ISBN 061885195X, 9780618851959, 1114 pages, (page 6 )〕 and are applied to algebraic variables and terms. Multiplication symbols are usually omitted, and implied when there is no space between two variables or terms, or when a coefficient is used. For example, $3\; \backslash times\; x^2$ is written as $3x^2$, and $2\; \backslash times\; x\; \backslash times\; y$ may be written $2xy$.〔Sin Kwai Meng, Chip Wai Lung, Ng Song Beng, "Algebraic notation", in ''Mathematics Matters Secondary 1 Express Textbook'', Publisher Panpac Education Pte Ltd, ISBN 9812738827, 9789812738820, (page 68 )〕 Usually terms with the highest power (exponent), are written on the left, for example, $x^2$ is written to the left of $x$. When a coefficient is one, it is usually omitted (e.g. $1x^2$ is written $x^2$).〔David Alan Herzog, ''Teach Yourself Visually Algebra'', Publisher John Wiley & Sons, 2008, ISBN 0470185597, 9780470185599, 304 pages, (page 72 )〕 Likewise when the exponent (power) is one, (e.g. $3x^1$ is written $3x$).〔John C. Peterson, ''Technical Mathematics With Calculus'', Publisher Cengage Learning, 2003, ISBN 0766861899, 9780766861893, 1613 pages, (page 31 )〕 When the exponent is zero, the result is always 1 (e.g. $x^0$ is always rewritten to $1$).〔Jerome E. Kaufmann, Karen L. Schwitters, ''Algebra for College Students'', Publisher Cengage Learning, 2010, ISBN 0538733543, 9780538733540, 803 pages, (page 222 )〕 However $0^0$, being undefined, should not appear in an expression, and care should be taken in simplifying expressions in which variables may appear in exponents. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Elementary algebra」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.