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 ?
The second updated edition of Essentials of Modern Algebra isn't for beginners, but is a top pick for undergrads taking a one- or two-semester course in abstract algebra, serving as a progressive tutorial that explains concepts and then provides self-test exercises.
The material should be accessible to anyone who has completed a first set of proof-based mathematics courses such as abstract algebra and analysis, they say, and requires no prior knowledge of mathematical logic.
The aim of this paper is to give an alternative, purely algebraic proof of the formula in the setting of abstract algebra of MZVs.
Let us define an abstract algebra U generated by [[a.sub.i] :1 [less than or equal to] i [less than or equal to] n} over a finite field g.
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?
Synopsis: Now in a newly updated and expanded second edition, "Introduction to Abstract Algebra" by academician Jonathan D.
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.
After her work with abstract algebra, Noether began studying physics, which led to her greatest discovery: Noether's Theorem.
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. "Pure mathematicians," he finds, "appear to themselves as well as to others to be exploring a realm of abstract objects with fixed objective properties and relations." That being the case, it is a challenge to the Aristotelian philosopher of science to explain how pure mathematics is really about universais that could be and sometimes are realized in nonabstract, physical reality.