Advanced Linear Algebra by Nicholas Loehr read online EPUB, PDF, FB2
9781466559028 English 1466559020 Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. The book's 20 chapters are grouped into six main areas: algebraic structures, matrices, structured matrices, geometric aspects of linear algebra, modules, and multilinear algebra. The level of abstraction gradually increases as students proceed through the text, moving from matrices to vector spaces to modules. Each chapter consists of a mathematical vignette devoted to the development of one specific topic. Some chapters look at introductory material from a sophisticated or abstract viewpoint while others provide elementary expositions of more theoretical concepts. Several chapters offer unusual perspectives or novel treatments of standard results. Unlike similar advanced mathematical texts, this one minimizes the dependence of each chapter on material found in previous chapters so that students may immediately turn to the relevant chapter without first wading through pages of earlier material to access the necessary algebraic background and theorems. Chapter summaries contain a structured list of the principal definitions and results. End-of-chapter exercises aid students in digesting the material. Students are encouraged to use a computer algebra system to help solve computationally intensive exercises., This book bridges the gap between the standard material found in introductory linear algebra courses and the more advanced knowledge of linear algebra required in many areas of mathematics, engineering, and the other sciences at the graduate level. The author covers specific areas of linear algebra that sometimes slip through the cracks between the undergraduate and graduate curricula. The topics covered avoid the rigid theorem-proof style and instead provide a narrative account of the topic while retaining the required rigor.
9781466559028 English 1466559020 Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. The book's 20 chapters are grouped into six main areas: algebraic structures, matrices, structured matrices, geometric aspects of linear algebra, modules, and multilinear algebra. The level of abstraction gradually increases as students proceed through the text, moving from matrices to vector spaces to modules. Each chapter consists of a mathematical vignette devoted to the development of one specific topic. Some chapters look at introductory material from a sophisticated or abstract viewpoint while others provide elementary expositions of more theoretical concepts. Several chapters offer unusual perspectives or novel treatments of standard results. Unlike similar advanced mathematical texts, this one minimizes the dependence of each chapter on material found in previous chapters so that students may immediately turn to the relevant chapter without first wading through pages of earlier material to access the necessary algebraic background and theorems. Chapter summaries contain a structured list of the principal definitions and results. End-of-chapter exercises aid students in digesting the material. Students are encouraged to use a computer algebra system to help solve computationally intensive exercises., This book bridges the gap between the standard material found in introductory linear algebra courses and the more advanced knowledge of linear algebra required in many areas of mathematics, engineering, and the other sciences at the graduate level. The author covers specific areas of linear algebra that sometimes slip through the cracks between the undergraduate and graduate curricula. The topics covered avoid the rigid theorem-proof style and instead provide a narrative account of the topic while retaining the required rigor.