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Linear algebra is a fundamental area of mathematics, and arguably the most powerful mathematic tool ever deployed. This book uses numerous examples, question and answer sections, and historical biographies to provide an introduction to linear algebra for undergraduates in mathematics, the physical sciences and engineering.

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

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Differential equations in abstract spaces

Banach spaces. --- Differential equations. --- Nonlinear operators. --- Operators, Nonlinear --- 517.91 Differential equations --- Differential equations --- Operator theory --- Functions of complex variables --- Generalized spaces --- Topology --- Banach spaces --- Nonlinear operators --- 517.91 --- Numerical solutions

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For the first time, this book unites different algebraic approaches for discrete optimization and operations research. The presentation of some fundamental directions of this new fast developing area shows the wide range of its applicability. Specifically, the book contains contributions in the following fields: semigroup and semiring theory applied to combinatorial and integer programming, network flow theory in ordered algebraic structures, extremal optimization problems, decomposition principles for discrete structures, Boolean methods in graph theory and applications.

Discrete mathematics --- Algebras, Linear. --- Combinatorial analysis. --- Operations research. --- Operations research --- Combinatorial analysis --- Algebras, Linear --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Combinatorics --- Algebra --- Mathematical analysis --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Calculus of operations --- Line geometry --- Topology

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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.

Ordered algebraic structures --- Operator theory --- Analyse fonctionnelle --- Functional analysis --- Linear operators. --- Banach spaces. --- Operator ideals. --- Linear operators --- Ideals (Algebra) --- Banach spaces --- Operator ideals --- 517.983 --- 517.983 Linear operators. Linear operator equations --- Linear operators. Linear operator equations --- Linear maps --- Maps, Linear --- Operators, Linear --- Functions of complex variables --- Generalized spaces --- Topology --- Functional analysis. --- Espaces d'operateurs lineaires continus --- Espaces de banach --- Ideaux normes --- Operateurs lineaires

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This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that had found a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discussed further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry. The 6th edition includes a systematic treatment of eigenvalues of Riemannian manifolds and several other additions. Also, the entire material has been reorganized in order to improve the coherence of the book. From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. ... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome." Mathematical Reviews "...the material ... is self-contained. Each chapter ends with a set of exercises. Most of the paragraphs have a section ‘Perspectives’, written with the aim to place the material in a broader context and explain further results and directions." Zentralblatt MATH  .

Geometric analysis. --- Geometry, Riemannian. --- Geometry, Riemannian --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Geometric analysis PDEs (Geometric partial differential equations) --- Riemann geometry --- Riemannian geometry --- Mathematics. --- Differential geometry. --- Physics. --- Differential Geometry. --- Theoretical, Mathematical and Computational Physics. --- Generalized spaces --- Geometry, Non-Euclidean --- Semi-Riemannian geometry --- Mathematical analysis --- Global differential geometry. --- Geometry, Differential --- Mathematical physics. --- Physical mathematics --- Physics --- Differential geometry