Elucidating these reasons, and tracing the implications of the transformation of algebra, will take us from the later decades of the eighteenth century to the 1920s and the milieu in which Moderne Algebra was written.
The reasons for the shift in meaning, and the ways in which structural algebra grew out of old-style classical algebra, are among the major concerns of this book. Modern algebra is in many ways different from school algebra, a subject whose core consists of the explicit solution of equations and modest excursions into geometry. Interestingly, it does not usually include linear algebra or functional analysis, despite the strong links between these branches, and applied mathematicians may well encounter only a first course in groups and nothing else. The primary meaning of the term ‘modern algebra’ is structural algebra: the study of groups, rings, and fields. That it still suffices as an accurate label for much of the work done in the field since is indicative of how powerful the movement was that created the subject. So it confronts a question many students ask themselves: how is it that university-level algebra is so very different from school-level algebra? The term ‘modern algebra’ was decisively introduced by van der Waerden in his book Moderne Algebra (1931), and it is worth discussing what he meant by it, and what was ‘modern’ about it. Rotman Hardcover: 1040 pages Publisher: Prentice Hall 1st edition (2002) 2nd printing (2003) Language: English ISBN: 0130878685 Book Description This books organizing principle is the interplay between groups and rings, Advanced Modern Algebra - Textbook: Rotmans Advanced Modern Algebra. Accordingly, it looks at some of the great success stories in mathematics: Galois theory-the theory of when polynomial equations have algebraic solutions-and algebraic number theory.
More precisely, it looks at some topics in algebra and number theory and follows them from their modest presence in mathematics in the seventeenth and eighteenth centuries into the nineteenth century and sees how they were gradually transformed into what we call modern algebra. This book covers topics in the history of modern algebra.
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