abstract algebra


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abstract algebra

[′abz·trakt ′al·jə·brə]
(mathematics)
The study of mathematical systems consisting of a set of elements, one or more binary operations by which two elements may be combined to yield a third, and several rules (axioms) for the interaction of the elements and the operations; includes group theory, ring theory, and number theory.
References in periodicals archive ?
While the book mainly deals with mathematical explanations, it offers some biographical material on physicist Emmy Noether, the founder of modern abstract algebra and a contemporary of Einstein.
The aim of this paper is to give an alternative, purely algebraic proof of the formula in the setting of abstract algebra of MZVs.
Foote, Abstract Algebra, John Wiley and Sons, 2003.
Are arcane results in abstract algebra or topology true, or do they merely follow logically from the axioms and definitions we have chosen?
Smith (Iowa State University, Ames, Iowa) presents abstract algebra as the main tool underlying discrete mathematics and the digital world.
The experts describe the old-school arithmetic as a "spiral" system and S'pore math as an approach that utilizes concrete materials (for example, three oranges), pictorial representation (a drawing of three oranges), and abstract algebra [this is where the message got lost in translation].
In grade nine, kids learn basic algebra, and [right away] abstract algebra is thrown at them in grade 10.
He is led to a discussion of the contributions of Paul Benacerraf and the Bourbaki school to set theory and of Emmy Noether's achievement in abstract algebra.
From Mathematics to Generic Programming comes from a software designer and his colleague who survey the basics of generic programming and the math it's based upon, providing chapters that introduce abstract algebra and connect number theory with programming basics.
This asymmetry puts a greater part of the machinery of abstract algebra for equation solving outside the reach of databases.
It introduces abstract algebra in terms of the integers, other number systems, polynomial rings, more ring theory, groups, and special topics.
Each year, EDGE, a four-week-long summer session, accepts a handful of female students who have completed undergraduate courses in analysis and abstract algebra and have been accepted to graduate programs in math.