{"title":"Sheldon Axler","description":"Sheldon Axler is Professor of Mathematics at San Francisco State University. He has won teaching awards at MIT and Michigan State University. His career achievements include the Mathematical Association of America's Lester R. Ford Award for expository writing, election as Fellow of the American Mathematical Society, over a decade as Dean of the College of Science \u0026amp; Engineering at San Francisco State University, member of the Council of the American Mathematical Society, member of the Board of Trustees of the Mathematical Sciences Research Institute, and Editor-in-Chief of the Mathematical Intelligencer. His previous publications include the widely used textbook Linear Algebra Done Right.","products":[{"product_id":"measure-integration-real-analysis-hardcover","title":"Measure, Integration \u0026 Real Analysis - Hardcover","description":"\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics.\u003c\/p\u003e\u003cp\u003eMotivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on \u003cb\u003eR\u003c\/b\u003e\u003ci\u003e\u003csup\u003en\u003c\/sup\u003e\u003c\/i\u003e.\u003c\/p\u003e\u003cp\u003eChapters on Banach spaces, \u003ci\u003eL\u003csup\u003ep\u003c\/sup\u003e\u003c\/i\u003e spaces, and Hilbert spaces showcase major results such as the Hahn-Banach Theorem, Hölder's Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability.\u003c\/p\u003e\u003cp\u003eExtensively class tested at multiple universities and written by an award-winning mathematical expositor, \u003ci\u003eMeasure, Integration \u0026amp; Real Analysis\u003c\/i\u003e is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic \u003ci\u003eSupplement for Measure, Integration \u0026amp; Real Analysis\u003c\/i\u003ethat is freely available online. For errata and updates, visit https: \/\/measure.axler.net\/\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics.\u003c\/p\u003e\u003cp\u003eMotivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on \u003cb\u003eR\u003c\/b\u003e\u003ci\u003e\u003csup\u003en\u003c\/sup\u003e\u003c\/i\u003e.\u003c\/p\u003e\u003cp\u003eChapters on Banach spaces, \u003ci\u003eL\u003csup\u003ep\u003c\/sup\u003e\u003c\/i\u003e spaces, and Hilbert spaces showcase major results such as the Hahn-Banach Theorem, Hölder's Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability.\u003c\/p\u003e\u003cp\u003eExtensively class tested at multiple universities and written by an award-winning mathematical expositor, \u003ci\u003eMeasure, Integration \u0026amp; Real Analysis\u003c\/i\u003e is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic \u003ci\u003eSupplement for Measure, Integration \u0026amp; Real Analysis\u003c\/i\u003e that isfreely available online.\u003c\/p\u003e","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":51376789291231,"sku":"9783030331429","price":97.18,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0813\/8958\/4607\/files\/Q3zXXSekUD9783030331429.webp?v=1789225341"},{"product_id":"linear-algebra-done-right-hardcover","title":"Linear Algebra Done Right - Hardcover","description":"\u003cp\u003e\u003c\/p\u003e\u003cp\u003eNow available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added.\u003c\/p\u003e\u003cp\u003eThe novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eNo prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the reviews of previous editions: \u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eAltogether, the text is a didactic masterpiece\u003c\/i\u003e. -- \u003cb\u003ezbMATH\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eThe determinant-free proofs are elegant and intuitive\u003c\/i\u003e. -- \u003cb\u003eAmerican Mathematical Monthly\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eThe most original linear algebra book to appear in years, it certainly belongs in every undergraduate library\u003c\/i\u003e -- \u003cb\u003eCHOICE\u003c\/b\u003e\u003cb\u003e\u003cbr\u003e\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eNow available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added.\u003c\/p\u003e\u003cp\u003eThe novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions.\u003c\/p\u003e\u003cp\u003eNo prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom reviews of previous editions: \u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eAltogether, the text is a didactic masterpiece.\u003c\/i\u003e -- \u003cb\u003ezbMATH\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eThe determinant-free proofs are elegant and intuitive.\u003c\/i\u003e -- \u003cb\u003eAmerican Mathematical Monthly\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eThe most original linear algebra book to appear in years, it certainly belongs in every undergraduate library\u003c\/i\u003e -- \u003cb\u003eCHOICE\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":51376804987103,"sku":"9783031410253","price":97.18,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0813\/8958\/4607\/files\/FwwFw3iA0j9783031410253.webp?v=1789225384"}],"url":"https:\/\/blackandbarhe.com\/collections\/sheldon-axler.oembed","provider":"Black \u0026 Barhe Bookstore","version":"1.0","type":"link"}