inequalities a journey into linear analysis a journey into lonear analysis

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Inequalities A Journey Into Linear Analysis

Author : D. J. H. Garling
ISBN : 9781139465144
Genre : Mathematics
File Size : 21. 24 MB
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This book contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.

Exploring The Number Jungle

Author : Edward B. Burger
ISBN : 9780821826409
File Size : 66. 33 MB
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Welcome to diophantine analysis--an area of number theory in which we attempt to discover hidden treasures and truths within the jungle of numbers by exploring rational numbers. Diophantine analysis comprises two different but interconnected domains--diophantine approximation and diophantine equations. This highly readable book brings to life the fundamental ideas and theorems from diophantine approximation, geometry of numbers, diophantine geometry and $p$-adic analysis. Through an engaging style, readers participate in a journey through these areas of number theory. Each mathematical theme is presented in a self-contained manner and is motivated by very basic notions. The reader becomes an active participant in the explorations, as each module includes a sequence of numbered questions to be answered and statements to be verified. Many hints and remarks are provided to be freely used and enjoyed. Each module then closes with a Big Picture Question that invites the reader to step back from all the technical details and take a panoramic view of how the ideas at hand fit into the larger mathematical landscape. This book enlists the reader to build intuition, develop ideas and prove results in a very user-friendly and enjoyable environment. Little background is required and a familiarity with number theory is not expected. All that is needed for most of the material is an understanding of calculus and basic linear algebra together with the desire and ability to prove theorems. The minimal background requirement combined with the author's fresh approach and engaging style make this book enjoyable and accessible to second-year undergraduates, and even advanced high school students. The author's refreshing new spin on more traditional discovery approaches makes this book appealing to any mathematician and/or fan of number theory.


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ISBN : UOM:39015079680511
Genre : Best books
File Size : 80. 60 MB
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Analysis On Polish Spaces And An Introduction To Optimal Transportation

Author : D. J. H. Garling
ISBN : 9781108421577
Genre : Mathematics
File Size : 61. 18 MB
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Detailed account of analysis on Polish spaces with a straightforward introduction to optimal transportation.

Approximating Perfection

Author : Leonid P. Lebedev
ISBN : 9781400873258
Genre : Mathematics
File Size : 24. 56 MB
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This is a book for those who enjoy thinking about how and why Nature can be described using mathematical tools. Approximating Perfection considers the background behind mechanics as well as the mathematical ideas that play key roles in mechanical applications. Concentrating on the models of applied mechanics, the book engages the reader in the types of nuts-and-bolts considerations that are normally avoided in formal engineering courses: how and why models remain imperfect, and the factors that motivated their development. The opening chapter reviews and reconsiders the basics of calculus from a fully applied point of view; subsequent chapters explore selected topics from solid mechanics, hydrodynamics, and the natural sciences. Emphasis is placed on the logic that underlies modeling in mechanics and the many surprising parallels that exist between seemingly diverse areas. The mathematical demands on the reader are kept to a minimum, so the book will appeal to a wide technical audience.

Introduction To The Analysis Of Normed Linear Spaces

Author : J. R. Giles
ISBN : 0521653754
Genre : Mathematics
File Size : 70. 8 MB
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This text is ideal for a basic course in functional analysis for senior undergraduate and beginning postgraduate students. John Giles provides insight into basic abstract analysis, which is now the contextual language of much modern mathematics. Although it is assumed that the student has familiarity with elementary real and complex analysis, linear algebra, and the analysis of metric spaces, the book does not assume a knowledge of integration theory or general topology. Its central theme concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. Giles illustrates the general theory with a great variety of example spaces.

Putnam And Beyond

Author : Razvan Gelca
ISBN : 9780387684451
Genre : Mathematics
File Size : 30. 4 MB
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Putnam and Beyond takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis in one and several variables, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research.

Journey Into Dialogic Pedagogy

Author : Eugene Matusov
ISBN : 1606925350
Genre : Education
File Size : 48. 13 MB
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The author came to the decision to embark on this journey into dialogic pedagogy when he firmly realised that education is essentially dialogic. It is not that pedagogy should be dialogic -- he rather argues that it is always dialogic. This is true whether the participants in it, or outside observers of it, realise it or not -- and even when the participants are resistant to dialogue. This statement is in contrast with views that promote dialogic interaction in the classroom as a form of instruction. This conceptualisation contrasts with views that dialogic interaction or conversational instruction are more effective instructional means in comparison to, let's say, a more monologic genre of instruction such as a lecture or a demonstration. This statement is also in contrast with views that assume dialogue is a pedagogical instrument that can be turned on and off. He argues that whatever teachers and students do (or not do) whether in their classrooms or beyond it, they are locked in dialogic relations.

An Introduction To Inequalities

Author : Edwin F. Beckenbach
ISBN : UOM:39015015207627
Genre : Inequalities (Mathematics)
File Size : 75. 58 MB
Format : PDF
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Author : Michael J. Cloud
ISBN : 9783319053110
Genre : Mathematics
File Size : 21. 50 MB
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This book offers a concise introduction to mathematical inequalities for graduate students and researchers in the fields of engineering and applied mathematics. It begins by reviewing essential facts from algebra and calculus and proceeds with a presentation of the central inequalities of applied analysis, illustrating a wide variety of practical applications. The text provides a gentle introduction to abstract spaces, such as metric, normed and inner product spaces. It also provides full coverage of the central inequalities of applied analysis, such as Young's inequality, the inequality of the means, Hölder's inequality, Minkowski's inequality, the Cauchy–Schwarz inequality, Chebyshev's inequality, Jensen's inequality and the triangle inequality. The second edition features extended coverage of applications, including continuum mechanics and interval analysis. It also includes many additional examples and exercises with hints and full solutions that may appeal to upper-level undergraduate and graduate students, as well as researchers in engineering, mathematics, physics, chemistry or any other quantitative science.

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