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algebra
algebra
algebra 1. The investigation of mathematical properties of data, such as numbers, and of operations on data, such as the addition and multiplication of numbers.
2. A collection of
sets together with a collection of
operations over those sets. Many examples involve only one set, such as the following: (a) the set
N = {0,1,2,…} of natural numbers together with, for example, the operations of addition, subtraction, and multiplication;(b) the set
B = {TRUE, FALSE} of Boolean truth values together with the operations AND, OR, and NOT (see also
Boolean algebra);(c) the set of all finite strings over a set of symbols together with the operation of
concatenation;(d) a set of sets together with the operations of
union,
intersection, and
complement (see also
set algebra).
In computer science, however, it is natural to consider algebras involving more than one set. These are called
many-sorted algebras, in contrast to
single-sorted algebras with only one set. For example, in programming languages there are different
data types such as Boolean, integer, real, character, etc., as well as user-defined types. Operations on elements of these types can then be seen as giving rise to a many-sorted algebra. By stating axioms that define properties of these operations, an
abstract data type can be specified. See also
algebraic structure,
signature.
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Smarandache Bcc-algebras.
Magazine article from: Scientia Magna; 6/1/2005; ; 700+ words
; ...Smarandache BCC-algebras and Smarandache...Smarandache BCC-algebra; Smarandache BCC...notion of BCC-algebras by using a dual...sense of Komori. An algebra (X; *, 0) of...not contain BCC-algebras of order 4. Based...Smarandache BCC-algebra is defined to be...
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 "Record (Stockton, CA)")
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Algebra proficiency slipping in S.J.: Years after state steps up pace, many still struggle to adapt to tougher eighth-grade standards.
Newspaper article from: Record (Stockton, CA); 8/27/2007; 700+ words
; ...STOCKTON -- Students who do not learn algebra cannot expect to fulfill graduation requirements...standards, trying to figure out how to teach algebra in eighth grade and how to ready students...percent of students in public schools taking algebra showed proficiency on 2007 standardized...
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Algebra = X in One School, Y in Another; Teaching Inconsistent as Standards Waver
Newspaper article from: The Washington Post; 8/19/2002; ; 700+ words
; ...articles After taking Maryland's state algebra test this year, Susan Gruenspecht's...County wanted to know: Where was the algebra? They were not alone. University of...Jerome Dancis called the test "pretend algebra." Montgomery County parent John Hoven...
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Algebra Poses a Problem of Timing; Not Taking Class Early Could Close Gateway to Sciences
Newspaper article from: The Washington Post; 8/18/2002; ; 700+ words
; ...40 percent of its eighth-graders in algebra last school year, compared with 20 percent...disparities exist throughout the country as algebra becomes the focus of a major overhaul...said they want every student completing algebra -- a gateway to higher math and science...
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'Algebra Readiness' - the Key to Math Success for California's Students
Newspaper article from: U.S. Newswire; 3/19/2008; 700+ words
; ...Panel centered around the importance of algebra readiness, a priority already identified...consideration of innovative, research-based algebra- readiness courses from Pearson, customized...s report underscores the importance of algebra-readiness instruction and validates...
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Algebra: changing the equation: support programs decrease math anxiety and help students succeed.(CURRICULUM)
Magazine article from: District Administration; 5/1/2008; ; 700+ words
; ...scientists, she highlighted the importance of algebra. "The panel's research showed that if students do well in algebra, then they are more likely to succeed...all school districts provide access to algebra for all prepared students--including...
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'Algebra Readiness' - the Key to Math Success for California's Students.
PR Newswire; 3/19/2008; 700+ words
; ...Schools to Build Solid Foundation for Algebra SACRAMENTO, Calif., March 19 /PRNewswire...Panel centered around the importance of algebra readiness, a priority already identified...consideration of innovative, research-based algebra- readiness courses from Pearson, customized...
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Algebra requirement will cost schools billions, O'Connell says
Newspaper article from: Oakland Tribune; 8/12/2008; ; 700+ words
; ...for California's new eighth-grade Algebra I requirement to work, the state superintendent...middle school students to be tested in Algebra I by the end of eighth grade. "We cannot...but saying all kids are going to pass Algebra I, well, that is a big order," said...
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Algebra's at-risk solution: districts deploy software to enhance and accelerate algebra instruction.(AT-RISK STUDENTS)
Magazine article from: District Administration; 10/1/2006; ; 700+ words
; Algebra wields an incredible amount of power in...Los Angeles Superintendent Roy Romer says algebra triggers more dropouts than any other single...standards are evolving. More states require algebra for high school graduation, which means...
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The algebra divide: essentials on education data and analysis from research authority AEL.(Appalachia Educational Laboratory)
Magazine article from: District Administration; 10/1/2003; 700+ words
; Algebra is a gateway to better math scores on standardized...districts or states that do not require algebra for graduation from high school, many...the math section will cover not only Algebra I and Geometry but some concepts from Algebra...
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Algebra
Book article from: Mathematics
Algebra Algebra is a branch of mathematics that uses variables to solve equations. When...that are given, the unknown variable(s) can be determined. Early Algebra The history of algebra began in ancient Egypt and Babylon. The Rhind...
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Algebras
Dictionary entry from: New Dictionary of the History of Ideas
ALGEBRAS. The word algebra refers to a theory...called "common algebra." But especially...nineteenth century other algebras were developed...philological" mode the algebra furnishes in some...applications of algebras. The most important...
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Boolean Algebra
Book article from: Computer Sciences
Boolean Algebra In 1847 George Boole (1815 – 1864), an English...logic. His combination of ideas from classical logic and algebra resulted in what is called Boolean algebra. Using variables and symbols, Boole designed a language...
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Boolean algebra
Encyclopedia entry from: The Gale Encyclopedia of Science
Boolean algebra Boolean algebra is often referred to as the algebra of logic. The English mathematician George Boole (1815 – 1864), who is largely responsible for its beginnings, was the first to apply algebraic techniques to logical...
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initial algebra
Book article from: A Dictionary of Computing
initial algebra An algebra A , from some class of algebras C , such that for every algebra B in C there is a unique homomorphism...recursive enumerable then the initial algebra is semicomputable . Initial algebras have importance for the semantics...
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