“…The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. …”
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“…The term 'Abstract Algebra' serves the purpose of distinguishing its advanced features from those of Classical Algebra. …”
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“…Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines-linear algebra, abstract algebra, and number theory-into one compr…”
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“…The intended audience will have had exposure to proof writing, but not necessarily to abstract algebra. That audience will be well prepared by this text for a second-semester course focusing on algebraic number theory. …”
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“…In this volume, the authors close the gap between abstract mathematical approaches, such as abstract algebra, number theory, nonlinear functional analysis, partial differential equations, methods of nonlinear and multi-valued analysis, on the one hand, and practical applications in nonlinear mechanics, decision making theory and control theory on the other. …”
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“…This book is the first volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. …”
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“…Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.…”
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“…This book is the second volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. …”
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“…Required background includes a standard course in abstract algebra and some knowledge of topology. The volume contains many exercises. …”
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“…This textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. …”
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“…Since not all control researchers today are exposed to geometric control theory, the book also adopts a tutorial style by way of examples that illustrate the geometric and abstract algebra concepts used in linear geometric control. …”
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“…Basic knowledge of abstract algebra is enough to read one third of the book. …”
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“…Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. …”
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“…Substantial progress on their existence has resulted from advances in algebraic design theory using deep connections with linear algebra, abstract algebra, finite geometry, number theory, and combinatorics. …”
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“…And a short overview of some aspects of abstract algebra is given at the end of the corresponding chapters. …”
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“…Sivakumar, IMAGE, No. 47, Fall 2011Always mathematically constructive, this book helps readers delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.-L'enseignement Mathématique, January-June 2007, Vol. 53, No. 1-2.…”
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“…Prerequisites include standard courses in abstract algebra and functional analysis.…”
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“…A wide range of subjects are covered, ranging from abstract algebra, including Lie algebras, commutative semigroups, and differential geometry, to optimization and control in real world problems such as fluid mechanics, the numerical simulation of cancer PDE models, and the stability of certain dynamical systems. …”
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“…The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles.Contents: Mathematical Structures Abstract Algebra Vector Algebras Topological Spaces Algebraic Topology Manifolds Lie Groups Clifford Groups Riemannian Manifolds Fiber Bundles Categories and Functors  Readership: Students in mathematics and physics who want to explore a level deeper into actual mathematical content.…”
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“…It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.…”
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