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  2. Free algebra - Wikipedia

    en.wikipedia.org/wiki/Free_algebra

    More generally, one can construct the free algebra R E on any set E of generators. Since rings may be regarded as Z-algebras, a free ring on E can be defined as the free algebra Z E . Over a field, the free algebra on n indeterminates can be constructed as the tensor algebra on an n-dimensional vector space.

  3. Macaulay2 - Wikipedia

    en.wikipedia.org/wiki/Macaulay2

    Macaulay2 is built around fast implementations of algorithms useful for computation in commutative algebra and algebraic geometry. This core functionality includes arithmetic on rings, modules, and matrices, as well as algorithms for Gröbner bases, free resolutions, Hilbert series, determinants and Pfaffians, factoring, and similar.

  4. Free object - Wikipedia

    en.wikipedia.org/wiki/Free_object

    In mathematics, the idea of a free object is one of the basic concepts of abstract algebra.Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure.

  5. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers. It is typically taught to secondary school students and at introductory college level in the United States, [5] and builds on their understanding of arithmetic. The use of variables to denote quantities allows ...

  6. National Council of Teachers of Mathematics - Wikipedia

    en.wikipedia.org/wiki/National_Council_of...

    In 1944, NCTM created a postwar plan to help World War II have a lasting effect on math education. Grades 1-6 were considered crucial years to build the foundations of math concepts with the main focus on algebra. In the war years, algebra had one understood purpose: to help the military and industries with the war effort.

  7. Algebra Project - Wikipedia

    en.wikipedia.org/wiki/Algebra_Project

    Each site employs between 30 and 100 high school and college age students part-time, and serves up to 1,000 elementary and middle-school students through on and off site programs. In 2005, the Algebra Project initiated Quality Education as a Civil Right (QECR), a national organizing effort to establish a federal constitutional guarantee of ...

  8. Saxon math - Wikipedia

    en.wikipedia.org/wiki/Saxon_math

    The Saxon Math 1 to Algebra 1/2 (the equivalent of a Pre-Algebra book) curriculum [3] is designed so that students complete assorted mental math problems, learn a new mathematical concept, practice problems relating to that lesson, and solve a variety of problems. Daily practice problems include relevant questions from the current day's lesson ...

  9. Associative algebra - Wikipedia

    en.wikipedia.org/wiki/Associative_algebra

    In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center of A.This is thus an algebraic structure with an addition, a multiplication, and a scalar multiplication (the multiplication by the image of the ring homomorphism of an element of K).

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