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In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including:    a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments  The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula.  Review of the first edition:  This is an excellent book. 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Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature.    Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrödinger operators, operators on graphs, and the spectral theory of Riemannian manifolds.       Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49737082601745,"sku":"NGR9783030380014","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3030380017.jpg?v=1751284701"},{"product_id":"differential-geometry-book-loring-w-tu-9783319550824","title":"Differential Geometry","description":"This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of  de Rham cohomology is required for the last third of the text.Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included.  Differential geometry, as its name implies, is the study of geometry using differential calculus. 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A masterly elucidation of modern graph theory.”     Bulletin of the Institute of Combinatorics and its Applications    “Succeeds dramatically ... a hell of a good book.” MAA Reviews    “A highlight of the book is what is by far the best account in print of the Seymour-Robertson theory of graph minors.” Mathematika     “ ... like listening to someone explain mathematics.” Bulletin of the AMS","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49737530310929,"sku":"NGR9783662536216","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":53522324422929,"sku":"NLS9783662536216","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3662536218.jpg?v=1751096477"},{"product_id":"measure-integration-real-analysis-book-sheldon-axler-9783030331429","title":"Measure, Integration \u0026 Real Analysis","description":"This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49737643884817,"sku":"NGR9783030331429","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":49794618818833,"sku":"CIN3030331423G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50994993299729,"sku":"GOR010857948","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51060255785233,"sku":"NIN9783030331429","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3030331423.jpg?v=1751030588"},{"product_id":"mathematical-logic-book-heinz-dieter-ebbinghaus-9783030738389","title":"Mathematical Logic","description":"What is a mathematical proof? 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On the other hand, this difficulty can be overcome--even in the framework of first-order logic-by developing mathematics in set-theoretic terms. 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The second edition has been adapted, expanded, and aptly retitled from Lee’s earlier book, Riemannian Manifolds: An Introduction to Curvature.  Numerous exercises and problem sets provide the student with opportunities to practice and develop skills; appendices contain a brief review of essential background material. While demonstrating the uses of most of the main technical tools needed for a careful study of Riemannian manifolds, this text focuses on ensuring that the student develops an intimate acquaintance with the geometric meaning of curvature. The reasonably broad coverage begins with a treatment of indispensable tools for working with Riemannian metrics such as connections and geodesics. 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The main ideas of the subject, motivated as in the original papers, are introduced here in an intuitive and accessible way…The book is an excellent introduction designed for a one-semester graduate course, containing exercises and problems which encourage students to practice working with the new notions and develop skills for later use. By citing suitable references for detailed study, the reader is stimulated to inquire into further research. (C.-L. 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