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Books > Science & Mathematics > Mathematics > Algebra
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Fundamental Structures of Algebra and Discrete Mat Mathematics (Hardcover)
Loot Price: R5,619
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Fundamental Structures of Algebra and Discrete Mat Mathematics (Hardcover)
Expected to ship within 18 - 22 working days
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Structures are defined by laws of composition, rules of generation,
and relations. The objects on which these laws operate may be
numbers, geometric objects like points and lines, or abstract
symbols. Algebra is the study of mathematical laws, with a search
for general principles that do not depend on what the objects are.
Fundamental Structures of Algebra and Discrete Mathematics is an
introduction to the twelve basic kinds of structures - sets,
ordered sets, groups, rings, fields, vector spaces, graphs,
lattices, matroids, topological spaces, universal algebras, and
categories - that underlie algebra and discrete mathematics.
Beginning with the most basic type of structure, sets, this unique
reference provides a detailed look at the theoretical underpinning
of each structure, shedding light on the significance of each
structure as well as their interrelation. Using a self-contained
approach that requires little previous knowledge of mathematical
definitions, results, or methods, the book examines selected key
aspects of these structures, including closure systems, generators,
substructures, homomorphisms and congruences, equational axioms,
connections with basic set theory, finiteness conditions,
combinatorial properties, and discrete algorithmic procedures.
Several classical results are proved, including the Abel-Ruffini
theorem on unsolvability by radicals, Helly's theorem on
intersecting convex sets, and a simplified version of the
Godel-Herbrand completeness theorem. Many of the results are
relevant to current research. Highly interactive in approach, the
book features numerous exercises and examples woven throughout the
text that allow the reader to become fully acquainted withthe
character and function of each structure. Additional questions,
designed to stretch the reader's analytical skills, appear at the
end of each section. Similar to a grammar book that explains the
fundamental structures essential to mastering a language,
Fundamental Structures of Algebra and Discrete Mathematics is a
systematic examination of the basic algebraic structures needed to
understand and manipulate advanced mathematical concepts. A
cornerstone reference that is both a clear primer and rigorous
study guide, Fundamental Structures of Algebra and Discrete
Mathematics is indispensable to the student and professional
seeking to learn or use the methods of modern algebra.
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