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 : 30. 68 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 : 64. 7 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 : 28. 11 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 : 44. 15 MB
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Detailed account of analysis on Polish spaces with a straightforward introduction to optimal transportation.

Putnam And Beyond

Author : Razvan Gelca
ISBN : 9780387684451
Genre : Mathematics
File Size : 26. 85 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.

Life In Crisis

Author : Peter Redfield
ISBN : 9780520955189
Genre : Social Science
File Size : 24. 13 MB
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Life in Crisis tells the story of Médecins Sans Frontières (Doctors Without Borders or MSF) and its effort to "save lives" on a global scale. Begun in 1971 as a French alternative to the Red Cross, the MSF has grown into an international institution with a reputation for outspoken protest as well as technical efficiency. It has also expanded beyond emergency response, providing for a wider range of endeavors, including AIDS care. Yet its seemingly simple ethical goal proves deeply complex in practice. MSF continually faces the problem of defining its own limits. Its minimalist form of care recalls the promise of state welfare, but without political resolution or a sense of well-being beyond health and survival. Lacking utopian certainty, the group struggles when the moral clarity of crisis fades. Nevertheless, it continues to take action and innovate. Its organizational history illustrates both the logic and the tensions of casting humanitarian medicine into a leading role in international affairs.

Optimal Control Of Partial Differential Equations Involving Pointwise State Constraints Regularization And Applications

Author : Irwin Yousept
ISBN : 9783867276689
Genre :
File Size : 74. 68 MB
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A Course In Mathematical Analysis

Author : D. J. H. Garling
ISBN : 9781107032040
Genre : Mathematics
File Size : 51. 88 MB
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"The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. Volume I focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theoryit describes many applications, including a chapter on Fourier series. It also includes a Prologue in which the author introduces the axioms of set theory and uses them to construct the real number system. Volume II goes on to consider metric and topological spaces, and functions of several variables. Volume III covers complex analysis and the theory of measure and integration"--

Qualitative Computing

Author : Françoise Chatelin
ISBN : 9789814322928
Genre : Mathematics
File Size : 32. 36 MB
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Introduction to Qualitative Computing; Hypercomputation in Dickson Algebras; Scales of Complexity and Linear Reachability; Singular Values for the Multiplication Maps; Computation Beyond Classical Logic; Complexification of the Arithmetic; Homotopic Deviation in Linear Algebra; The Discrete and the Continuous; Arithmetic in the Alternative Dickson Division Algebras; The Real and the Complex.

Approximating Perfection

Author : Leonid P. Lebedev
ISBN : 9781400873258
Genre : Mathematics
File Size : 90. 45 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.

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