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Identifier	Thesis 1817
Author	Baker, Justice-Taylor
Title	The Evolution of the Abstract Group Concept
Publisher	Central Connecticut State University
Date	2006
Resource Type	Master's Thesis
Notes	Abstract algebra is, at its core, the study of algebraic structures. As the name implies, these structures can be studied in the abstract. Therefore universal properties can be examined and proven generally, as opposed to being studied number system by number system. This generalization allowed the concepts of elementary algebra, which pervade all of mathematics and the natural sciences, to be axiomatically defined and examined. A direct consequence of the breadth and reach of elementary algebra is seen in the diverse applications of the first of these abstract algebraic structures, groups, and the study of their inherent properties, group theory. Yet even with the role abstract groups play in mathematics and science, their process of discovery is somewhat in dispute. Many texts attribute the generation of abstract groups to Evariste Galois, who first used the term group in 1830. Others credit English mathematician Arthur Cayley, but disagree on the date of discovery, either 1854 or 1878. Some see groups as the inevitable consequence of the study of algebraic equations; while others see evidence of group theory structures in geometry, number theory and even the earliest recorded mathematics dating to the early Egyptians. The overall significance of abstract groups, though, is not in debate. As Hans Wussing wrote in the most complete examination of the history of groups, The Genesis of the Abstract Group Concept (1969): The history of the rise of group theory is the history of a mathematical discipline that has aided the advance of algebra in two distinct ways: as the earliest example of the evolution of an abstract algebraic structure and, … as "midwife" of modern algebra. (Wussing, 1984, pg. 15-16)
Subject	Algebra, Abstract
Department	Department of Mathematical Sciences
Advisor	Chen, Yuanquian
Type	Text
Digital Format	application/pdf
Language	eng
OCLC number	Thesis 1817
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