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 ?
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.
Anna Titova, assistant professor of mathematics and chairwoman of the mathematics department, will present "Understanding Abstract Concepts in the Context of Abstract Algebra," at the sixteenth annual Conference on Research in Undergraduate Mathematics Education, which will be held Feb.
Unlike the first edition, material covered in the author's A First Course in Abstract Algebra, third ed.
Abstract algebra has only appeared in the last 200 years.
We are not talking just straight forward abstract algebra, juggling inter-related multiple but known and fixed factors.
3 Which French mathematician laid the foundations for a major branch of abstract algebra and was killed in a dual at the age of 20?
Those improvements, along with faster computers and better software engineering, eventually produced an agile reasoning system called Otter, aimed at questions in abstract algebra and formal logic.