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"Any student studying linear algebra will welcome this textbook, which provides a thorough, yet concise, treatment of key topics in university linear algebra courses. Blending practice and theory, the book enables students to practice and master the standard methods as well as understand how they actually work. At every stage the authors take care to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses only on the fundamental topics. Hundreds of examples and exercises, including solutions, give students plenty of hands-on practice End-of-chapter sections summarise material to help students consolidate their learning Ideal as a course text and for self-study Instructors can use the many examples and exercises to supplement their own assignments Both authors have extensive experience of undergraduate teaching and of preparation of distance learning materials"--

Algebra --- Algebras, Linear --- lineaire algebra --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Algebras, Linear - Textbooks

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Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.

Algebras, Linear --- 512.64 --- Linear and multilinear algebra. Matrix theory --- 512.64 Linear and multilinear algebra. Matrix theory --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Algebra --- lineaire algebra --- algebra --- Algebras, Linear - Textbooks

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This book offers a refreshingly concise, manageable introduction to linear algebra: Whereas most treatments of the subject give an exhaustive survey supplemented with applications, this book presents a carefully selected array of the most essential topics that can be thoroughly covered in a single semester. The exposition generally falls in line with the material recommended by the Linear Algebra Curriculum Study Group, but notably deviates in providing an early emphasis on the geometric foundations of linear algebra.  Starting with vectors, lines, and planes in two and three dimensions gives students a more intuitive understanding of the subject and enables an easier grasp of more abstract concepts.  Two important pedagogical devices are also directed to this end: First, throughout the book, the notation is carefully selected to indicate the connections between related quantities; second, in addition to numbering, brief mnemonic titles are appended to theorems and examples, making it easier for the student to internalize and recall important concepts (e.g., it is much more satisfying to recall the Dimension Theorem than to recall Theorem 3.5.1). The focus throughout is primarily on fundamentals, guiding readers to appreciate the elegance and interconnectedness of linear algebra.  At the same time, the text presents a number of interesting, targeted applications, offering a glimpse of how the subject is used in other fields, especially in physics.  A section on computer graphics and a chapter on numerical methods also provide looks at the potential uses of linear algebra, and most sections contain exercises using MATLAB® to put theory into practice in a variety of contexts.  Visuals and problems are included to enhance and reinforce understanding throughout the book, and both students’ and instructors’ solutions manuals (for non-MATLAB exercises) are available online. A Concise Introduction to Linear Algebra builds on the author's previous title on the subject (Introduction to Linear Algebra, Jones & Bartlett, 1996).  With brevity, precision, and rigor, the work is an ideal choice for a standard one-semester course targeted primarily at math or physics majors.  It is a valuable addition to the book collection of anyone who teaches or studies the subject.

Algebras, Linear. --- Algebras, Linear --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Algebra. --- Linear algebra --- Mathematics. --- Matrix theory. --- Mathematical physics. --- Physics. --- Linear and Multilinear Algebras, Matrix Theory. --- General Algebraic Systems. --- Mathematical Physics. --- Mathematical Methods in Physics. --- Theoretical, Mathematical and Computational Physics. --- Mathematical analysis --- Algebra, Universal --- Generalized spaces --- Calculus of operations --- Line geometry --- Topology --- Physical mathematics --- Physics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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Geometry, Riemannian. --- Hermitian structures. --- Riemann, Géométrie de --- Structures hermitiennes --- Differential geometry. Global analysis --- Geometry, Riemannian --- Hermitian structures --- 51 <082.1> --- Structures, Hermitian --- Complex manifolds --- Geometry, Differential --- Kählerian structures --- Riemann geometry --- Riemannian geometry --- Generalized spaces --- Geometry, Non-Euclidean --- Semi-Riemannian geometry --- Mathematics--Series

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  This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics.  It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman’s characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac’s famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group.  This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt  to the presence of gravitational fields that cannot be considered  negligible. The second is to understand some of the basic features of  a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary point-set topology.   The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title.   Reviews of first edition:    “… a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics.” (American Mathematical Society, 1993)    “Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations.” (CHOICE, 1993)  “… his talent in choosing the most significant results and ordering them within the book can’t be denied. The reading of the book is, really, a pleasure.” (Dutch Mathematical Society, 1993)    .

General relativity (Physics) -- Mathematics. --- Generalized spaces. --- Minkowski geometry. --- Special relativity (Physics) -- Mathematics. --- General relativity (Physics) --- Generalized spaces --- Mathematics --- Physics --- Physical Sciences & Mathematics --- Geometry --- Atomic Physics --- Special relativity (Physics) --- Mathematics. --- Relativistic theory of gravitation --- Relativity theory, General --- Ether drift --- Mass energy relations --- Relativity theory, Special --- Restricted theory of relativity --- Special theory of relativity --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Minkowski geometries --- Minkowskian geometry --- Minkowski's geometry --- Manifolds (Mathematics). --- Complex manifolds. --- Physics. --- Gravitation. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Classical and Quantum Gravitation, Relativity Theory. --- Mathematical Methods in Physics. --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Math --- Science --- Properties --- Gravitation --- Calculus of tensors --- Geometry, Non-Euclidean --- Hyperspace --- Cell aggregation --- Mathematical physics. --- Physical mathematics --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation