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Modern Algebra And The Rise Of Mathematical Structures

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Modern Algebra And The Rise Of Mathematical Structures

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Author : Leo Corry
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Modern Algebra And The Rise Of Mathematical Structures written by Leo Corry and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-1800s to 1930, and then considers attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.

Abstract Algebra

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Author : Stephen Lovett
language : en
Publisher: CRC Press
Release Date : 2015-07-13

Abstract Algebra written by Stephen Lovett and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-13 with Mathematics categories.

A Discovery-Based Approach to Learning about Algebraic Structures Abstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester introductory course to a full two-semester sequence. The book presents the core topics of structures in a consistent order: Definition of structure Motivation Examples General properties Important objects Description Subobjects Morphisms Subclasses Quotient objects Action structures Applications The text uses the general concept of an algebraic structure as a unifying principle and introduces other algebraic structures besides the three standard ones (groups, rings, and fields). Examples, exercises, investigative projects, and entire sections illustrate how abstract algebra is applied to areas of science and other branches of mathematics. "Lovett (Wheaton College) takes readers through the variegated landscape of algebra, from elementary modular arithmetic through groups, semigroups, and monoids, past rings and fields and group actions, beyond modules and algebras, to Galois theory, multivariable polynomial rings, and Gröbner bases." Choice Reviewed: Recommended

Episodes In The History Of Modern Algebra 1800 1950

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Author : Jeremy J. Gray
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-08-31

Episodes In The History Of Modern Algebra 1800 1950 written by Jeremy J. Gray and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-31 with Mathematics categories.

Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a ``rising sea'' in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics.

Modern Algebra Text Large Print Structure And Method Book One

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Author : Mary P. Dolciani
language : en
Publisher: [Regina : Sask. Department of Education, 1973]. (Winnipeg : Xerox of Canada)
Release Date : 1973

Modern Algebra Text Large Print Structure And Method Book One written by Mary P. Dolciani and has been published by [Regina : Sask. Department of Education, 1973]. (Winnipeg : Xerox of Canada) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Algebra categories.

Elementary Overview Of Mathematical Structures An Algebra Topology And Categories

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Author : Marco Grandis
language : en
Publisher: World Scientific
Release Date : 2020-08-12

Elementary Overview Of Mathematical Structures An Algebra Topology And Categories written by Marco Grandis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-12 with Mathematics categories.

'The presentation is modeled on the discursive style of the Bourbaki collective, and the coverage of topics is rich and varied. Grandis has provided a large selection of exercises and has sprinkled orienting comments throughout. For an undergraduate library where strong students seek an overview of a significant portion of mathematics, this would be an excellent acquisition. Summing up: Recommended.'CHOICESince the last century, a large part of Mathematics is concerned with the study of mathematical structures, from groups to fields and vector spaces, from lattices to Boolean algebras, from metric spaces to topological spaces, from topological groups to Banach spaces.More recently, these structured sets and their transformations have been assembled in higher structures, called categories.We want to give a structural overview of these topics, where the basic facts of the different theories are unified through the 'universal properties' that they satisfy, and their particularities stand out, perhaps even more.This book can be used as a textbook for undergraduate studies and for self-study. It can provide students of Mathematics with a unified perspective of subjects which are often kept apart. It is also addressed to students and researchers of disciplines having strong interactions with Mathematics, like Physics and Chemistry, Statistics, Computer Science, Engineering.

Algebra

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Author : Saunders Mac Lane
language : en
Publisher: American Mathematical Society
Release Date : 2023-10-10

Algebra written by Saunders Mac Lane and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-10 with Mathematics categories.

This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach—emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s—was popularized for the graduate level in the 1940s and 1950s to some degree by the authors' publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors.

Modern Algebra

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Author : John R. Durbin
language : en
Publisher: John Wiley & Sons
Release Date : 2008-12-31

Modern Algebra written by John R. Durbin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-31 with Mathematics categories.

Engineers and computer scientists who need a basic understanding of algebra will benefit from this accessible book. The sixth edition includes many carefully worked examples and proofs to guide them through abstract algebra successfully. It introduces the most important kinds of algebraic structures, and helps them improve their ability to understand and work with abstract ideas. New and revised exercise sets are integrated throughout the first four chapters. A more in-depth discussion is also included on Galois Theory. The first six chapters provide engineers and computer scientists with the core of the subject and then the book explores the concepts in more detail.

Modern Algebra And The Rise Of Mathematical Structures

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