**Author**: G. H. Hardy,J. E. Littlewood,G. Pólya

**Publisher:**Cambridge University Press

**ISBN:**9780521358804

**Category:**Mathematics

**Page:**324

**View:**6693

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# Search Results for: inequalities-cambridge-mathematical-library

**Author**: G. H. Hardy,J. E. Littlewood,G. Pólya

**Publisher:** Cambridge University Press

**ISBN:** 9780521358804

**Category:** Mathematics

**Page:** 324

**View:** 6693

This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and lucidly both the statement and proof of all the standard inequalities of analysis. The authors were well-known for their powers of exposition and made this subject accessible to a wide audience of mathematicians.

**Author**: H. Davenport

**Publisher:** Cambridge University Press

**ISBN:** 9781139441230

**Category:** Mathematics

**Page:** N.A

**View:** 6819

Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added.

**Author**: D. J. H. Garling

**Publisher:** Cambridge University Press

**ISBN:** 1139465147

**Category:** Mathematics

**Page:** N.A

**View:** 4106

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.
*Theorems, Techniques and Selected Problems*

**Author**: Zdravko Cvetkovski

**Publisher:** Springer Science & Business Media

**ISBN:** 3642237924

**Category:** Mathematics

**Page:** 444

**View:** 8814

This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving inequalities. It is written for all middle and high-school students, as well as for graduate and undergraduate students. School teachers and trainers for mathematical competitions will also gain benefit from this book.

**Author**: Sean P. Meyn,Richard L. Tweedie

**Publisher:** Springer Science & Business Media

**ISBN:** 144713267X

**Category:** Mathematics

**Page:** 550

**View:** 4691

Markov Chains and Stochastic Stability is part of the Communications and Control Engineering Series (CCES) edited by Professors B.W. Dickinson, E.D. Sontag, M. Thoma, A. Fettweis, J.L. Massey and J.W. Modestino. The area of Markov chain theory and application has matured over the past 20 years into something more accessible and complete. It is of increasing interest and importance. This publication deals with the action of Markov chains on general state spaces. It discusses the theories and the use to be gained, concentrating on the areas of engineering, operations research and control theory. Throughout, the theme of stochastic stability and the search for practical methods of verifying such stability, provide a new and powerful technique. This does not only affect applications but also the development of the theory itself. The impact of the theory on specific models is discussed in detail, in order to provide examples as well as to demonstrate the importance of these models. Markov Chains and Stochastic Stability can be used as a textbook on applied Markov chain theory, provided that one concentrates on the main aspects only. It is also of benefit to graduate students with a standard background in countable space stochastic models. Finally, the book can serve as a research resource and active tool for practitioners.

**Author**: Nicholas D. Kazarinoff

**Publisher:** Courier Corporation

**ISBN:** 0486798178

**Category:** Mathematics

**Page:** 96

**View:** 9139

Mathematical analysis is largely a systematic study and exploration of inequalities — but for students the study of inequalities often remains a foreign country, difficult of access. This book is a passport to that country, offering a background on inequalities that will prepare undergraduates (and even high school students) to cope with the concepts of continuity, derivative, and integral. Beginning with explanations of the algebra of inequalities and conditional inequalities, the text introduces a pair of ancient theorems and their applications. Explorations of inequalities and calculus cover the number e, examples from the calculus, and approximations by polynomials. The final sections present modern theorems, including Bernstein's proof of the Weierstrass approximation theorem and the Cauchy, Bunyakovskii, Hölder, and Minkowski inequalities. Numerous figures, problems, and examples appear throughout the book, offering students an excellent foundation for further studies of calculus.
*Differential Geometric and Analytic Perspectives*

**Author**: Isaac Chavel

**Publisher:** Cambridge University Press

**ISBN:** 9780521802673

**Category:** Mathematics

**Page:** 268

**View:** 2588

This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.

**Author**: Edwin F. Beckenbach,Richard Bellman

**Publisher:** N.A

**ISBN:** N.A

**Category:** Inequalities (Mathematics)

**Page:** 133

**View:** 4960

**Author**: David Williams

**Publisher:** Cambridge University Press

**ISBN:** 1139642987

**Category:** Mathematics

**Page:** N.A

**View:** 2918

Probability theory is nowadays applied in a huge variety of fields including physics, engineering, biology, economics and the social sciences. This book is a modern, lively and rigorous account which has Doob's theory of martingales in discrete time as its main theme. It proves important results such as Kolmogorov's Strong Law of Large Numbers and the Three-Series Theorem by martingale techniques, and the Central Limit Theorem via the use of characteristic functions. A distinguishing feature is its determination to keep the probability flowing at a nice tempo. It achieves this by being selective rather than encyclopaedic, presenting only what is essential to understand the fundamentals; and it assumes certain key results from measure theory in the main text. These measure-theoretic results are proved in full in appendices, so that the book is completely self-contained. The book is written for students, not for researchers, and has evolved through several years of class testing. Exercises play a vital rôle. Interesting and challenging problems, some with hints, consolidate what has already been learnt, and provide motivation to discover more of the subject than can be covered in a single introduction.
*An Introduction to the Art of Mathematical Inequalities*

**Author**: J. Michael Steele

**Publisher:** Cambridge University Press

**ISBN:** 9780521546775

**Category:** Mathematics

**Page:** 306

**View:** 1887

This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.

**Author**: Godfrey Harold Hardy

**Publisher:** American Mathematical Soc.

**ISBN:** 0821826492

**Category:** Mathematics

**Page:** 396

**View:** 9310

Review of the original edition: This is an inspiring textbook for students who know the theory of functions of real and complex variables and wish further knowledge of mathematical analysis. There are no problems displayed and labelled ``problems,'' but one who follows all of the arguments and calculations of the text will find use for his ingenuity and pencil. The book deals with interesting and important problems and topics in many fields of mathematical analysis, to an extent very much greater than that indicated by the titles of the chapters. It is, of course, an indispensable handbook for those interested in divergent series. It assembles a considerable part of the theory of divergent series, which has previously existed only in periodical literature. Hardy has greatly simplified and improved many theories, theorems and proofs. In addition, numerous acknowledgements show that the book incorporates many previously unpublished results and improvements of old results, communicated to Hardy by his colleagues and by others interested in the book. --Mathematical Reviews
*Preparing for University*

**Author**: Stephen Siklos

**Publisher:** Open Book Publishers

**ISBN:** 1783741449

**Category:** Mathematics

**Page:** 186

**View:** 5098

This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to university-style mathematics. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics.

**Author**: J. C. Burkill,H. Burkill

**Publisher:** Cambridge University Press

**ISBN:** 9780521523431

**Category:** Mathematics

**Page:** 526

**View:** 4689

A classic calculus text reissued in the Cambridge Mathematical Library. Clear and logical, with many examples.

**Author**: Godfrey Harold Hardy,E. M. Wright,Roger Heath-Brown,Joseph Silverman

**Publisher:** Oxford University Press

**ISBN:** 9780199219865

**Category:** Mathematics

**Page:** 621

**View:** 2776

An Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. This Sixth Edition has been extensively revised and updated to guide today's students through the key milestones and developments in number theory. Updates include a chapter on one of the mostimportant developments in number theory -- modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader and the clarityof exposition is retained throughout making this textbook highly accessible to undergraduates in mathematics from the first year upwards.

**Author**: E. T. Whittaker,G. N. Watson

**Publisher:** Cambridge University Press

**ISBN:** 1107268583

**Category:** Mathematics

**Page:** N.A

**View:** 6377

This classic text is known to and used by thousands of mathematicians and students of mathematics throughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principal transcendental functions.

**Author**: G. H. Hardy

**Publisher:** Cambridge University Press

**ISBN:** 1107493668

**Category:** Mathematics

**Page:** 72

**View:** 3306

Originally published in 1910 as number twelve in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides an up-to-date version of Du Bois-Reymond's Infinitärcalcül by the celebrated English mathematician G. H. Hardy. This tract will be of value to anyone with an interest in the history of mathematics or the theory of functions.

**Author**: A. Zygmund

**Publisher:** Cambridge University Press

**ISBN:** 9780521890533

**Category:** Mathematics

**Page:** 747

**View:** 6992

Both volumes of classic text on trigonometric series, with a foreword by Robert Fefferman.

**Author**: Avner Ash,Peter Scholze

**Publisher:** Cambridge University Press

**ISBN:** 0521739551

**Category:** Mathematics

**Page:** 230

**View:** 8249

The new edition of this celebrated and long-unavailable book preserves the original book's content and structure and its unrivalled presentation of a universal method for the resolution of a class of singularities in algebraic geometry.

**Author**: Daniel Huybrechts,Manfred Lehn

**Publisher:** Cambridge University Press

**ISBN:** 1139485822

**Category:** Mathematics

**Page:** N.A

**View:** 2967

Now back in print, this highly regarded book has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces, which include moduli spaces in positive characteristic, moduli spaces of principal bundles and of complexes, Hilbert schemes of points on surfaces, derived categories of coherent sheaves, and moduli spaces of sheaves on Calabi–Yau threefolds. The authors review changes in the field since the publication of the original edition in 1997 and point the reader towards further literature. References have been brought up to date and errors removed. Developed from the authors' lectures, this book is ideal as a text for graduate students as well as a valuable resource for any mathematician with a background in algebraic geometry who wants to learn more about Grothendieck's approach.
*From Competitions to Research*

**Author**: Dierk Schleicher,Malte Lackmann

**Publisher:** Springer Science & Business Media

**ISBN:** 9783642195334

**Category:** Mathematics

**Page:** 220

**View:** 9811

This Invitation to Mathematics consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is about. We hope that it will also be of interest to teachers or more advanced mathematicians who would like to learn about exciting aspects of mathematics outside of their own work or specialization. Together with a team of young ``test readers'', editors and authors have taken great care, through a substantial ``active editing'' process, to make the contributions understandable by the intended readership.

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