Download or read book Modern Algebra and the Rise of Mathematical Structures written by Leo Corry and published by Birkhäuser. This book was released on 2012-12-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A History of Abstract Algebra written by Israel Kleiner and published by Springer Science & Business Media. This book was released on 2007-10-02 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the history of abstract algebra. It shows how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved.
Download or read book Abstract Algebra written by Stephen Lovett and published by CRC Press. This book was released on 2015-07-13 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Download or read book Elementary Overview Of Mathematical Structures An Algebra Topology And Categories written by Marco Grandis and published by World Scientific. This book was released on 2020-08-12 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.
Download or read book Modern Algebra written by John R. Durbin and published by John Wiley & Sons. This book was released on 2008-12-31 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modern Algebra written by Mary P. Dolciani and published by T. Nelson & Sons (Canada). This book was released on 1962 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebra written by Saunders Mac Lane and published by American Mathematical Society. This book was released on 2023-10-10 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Episodes in the History of Modern Algebra 1800 1950 written by Jeremy J. Gray and published by American Mathematical Soc.. This book was released on 2011-08-31 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modern Algebra written by Mary P. Dolciani and published by . This book was released on 1965 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Essentials of Modern Algebra written by Cheryl Chute Miller and published by . This book was released on 2012-08-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for the undergraduate one or two semester course in modern algebra, also called abstract algebra. Features groups, rings, and fields and provides numerous exercises and projects.
Download or read book Modern Algebra Abstract Algebra written by and published by Krishna Prakashan Media. This book was released on with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modern Algebra written by Mary P. Dolciani and published by . This book was released on 1970 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modern Algebra written by Mary P. Dolciani and published by [Regina : Sask. Department of Education, 1973]. (Winnipeg : Xerox of Canada). This book was released on 1973 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modern Algebra with Applications written by William J. Gilbert and published by Wiley-Interscience. This book was released on 1976-11-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book blends the theoretical with the practical in the instruction of modern algebra. Modern algebra is usually taught from the point of view of its intrinsic interest, without using applications. Many readers lose interest when they do not see the relevance of the subject and often become skeptical of the explanation that the material will be used later. The author believes by providing interesting and nontrivial applications, the student will better appreciate and understand the subject.
Download or read book Mathematics of the 19th Century written by A.N. Kolmogorov and published by Springer Science & Business Media. This book was released on 1998-03-24 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The editors of the present series had originally intended to publish an integrated work on the history of mathematics in the nineteenth century, passing systemati cally from one discipline to another in some natural order. Circumstances beyond their control, mainly difficulties in choosing authors, led to the abandonment of this plan by the time the second volume appeared. Instead of a unified mono graph we now present to the reader a series of books intended to encompass all the mathematics of the nineteenth century, but not in the order of the accepted classification of the component disciplines. In contrast to the first two books of The Mathematics of the Nineteenth Century, which were divided into chapters, this third volume consists of four parts, more in keeping with the nature of the publication. 1 We recall that the first book contained essays on the history of mathemati 2 cal logic, algebra, number theory, and probability, while the second covered the history of geometry and analytic function theory. In the present third volume the reader will find: 1. An essay on the development of Chebyshev's theory of approximation of functions, later called "constructive function theory" by S. N. Bernshtein. This highly original essay is due to the late N. I. Akhiezer (1901-1980), the author of fundamental discoveries in this area. Akhiezer's text will no doubt attract attention not only from historians of mathematics, but also from many specialists in constructive function theory.
Download or read book Mathematical Structures written by Karl Dahlke and published by . This book was released on 2015-05-04 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is chapter 1 of a series of book. The entire series is an introduction to combinatory, number theory, topology, groups, rings, fields, modules, algebraic and integral extensions, noncommutative algebra, algebraic number theory, algebraic geometry, algebraic topology, and even more. The title of the series is Abstract Algebra and Discrete Mathematics.The focus is on breadth, rather than depth. Excellent books already exist for any one of these topics in detail, and I don't want to reinvent that wheel. Instead, this book knits them all together, providing a foundation for each topic in turn. By analogy, you might point your backyard telescope to every corner of the galaxy, in an effort to comprehend its scope, beauty, and diversity. You might not understand the Crab Nebula in all its detail, this is not the Hubble Space Telescope, but you should walk away with an appreciation for the vastness and the wonder of the galaxy, in this case, the galaxy of modern mathematics. If, from time to time, you find yourself saying, "How did anybody ever think of that?", then I have succeeded.Each chapter builds on the information that has gone before, and forward references are rare, though they do happen from time to time. I hope this series of books is more accessible than a sea of disconnected web pages, which is the hallmark of most math websites.This book is Chapter 1, Data Structures,By Karl Dahlke and Kermit Rose, Copyright (c) 2015Table of ContentsPage 04 1.01 Properties of ArithmeticPage 05 1.02 Modular MathPage 05 1.03 HomomorphismPage 08 1.04 Casting out NinesPage 09 1.05 Monomorphism, Epimorphism, IsomorphismPage 11 1.06 Discrete LogsPage 13 1.07 Binary SearchPage 14 1.08 Function CompositionPage 14 1.09 PermutationsPage 17 1.10 Even and Odd PermutationsPage 19 1.11 MatricesPage 23 1.12 Linear FunctionsPage 25 1.13 Matrix as FunctionPage 27 1.14 DeterminantPage 33 1.15 Gaussian EliminationPage 36 1.16 Elementary Row OperationsPage 37 1.17 The Determinant of the ProductPage 38 1.18 Matrix Identities and Inverses Page 43 1.19 OrthogonalPage 44 1.20 Determinant equals VolumePage 46 1.21 The Gram Schmidt ProcessPage 47 1.22 The Shoelace FormulaPage 50 1.23 Orthonormal and Rotations Page 55 1.24 Cross Product Page 57 1.25 Vandermonde MatrixPage 58 1.26 A Matrix of Matrices Page 59 1.27 Complex Numbers and the Gaussian IntegersPage 61 1.28 Eisenstein IntegersPage 63 1.29 QuaternionsPage 64 1.30 Half Integer QuaternionsPage 65 1.31 Projective Space and an Interesting HomomorphismPage 68 1.32 The Square Root of a Rotation Page 69 1.33 The Hairy Ball Theorem Page 70 1.34 Generalized Euclidean SpacePage 71 1.35 PolynomialsPage 72 1.36 Synthetic Division, Roots, and GCDPage 74 1.37 Formal DerivativePage 75 1.38 Power and Laurent SeriesPage 76 1.39 p-adic Numbers
