Top 10 recommendation analysis stein 2022
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1. Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis) (Bk. 3)
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Princeton University PressDescription
Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science.
After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises.
As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels.
Also available, the first two volumes in the Princeton Lectures in Analysis:
2. Fourier Analysis: An Introduction (Princeton Lectures in Analysis, Volume 1)
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Princeton University PressDescription
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.
The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression.
In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest.
The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
3. Complex Analysis (Princeton Lectures in Analysis, No. 2)
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Princeton University PressDescription
With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle.
With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory.
Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences.
The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
4. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
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Used Book in Good ConditionDescription
This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, Lsup estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.
5. Functional Analysis: Introduction to Further Topics in Analysis (Princeton Lectures in Analysis) (Bk. 4)
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Princeton University PressDescription
This is the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. Beginning with the basic facts of functional analysis, this volume looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. The authors then use the Baire category theorem to illustrate several points, including the existence of Besicovitch sets. The second half of the book introduces readers to other central topics in analysis, such as probability theory and Brownian motion, which culminates in the solution of Dirichlet's problem. The concluding chapters explore several complex variables and oscillatory integrals in Fourier analysis, and illustrate applications to such diverse areas as nonlinear dispersion equations and the problem of counting lattice points. Throughout the book, the authors focus on key results in each area and stress the organic unity of the subject.
- A comprehensive and authoritative text that treats some of the main topics of modern analysis
- A look at basic functional analysis and its applications in harmonic analysis, probability theory, and several complex variables
- Key results in each area discussed in relation to other areas of mathematics
- Highlights the organic unity of large areas of analysis traditionally split into subfields
- Interesting exercises and problems illustrate ideas
- Clear proofs provided
6. Introduction to Algorithms, 3rd Edition (The MIT Press)
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MIT Press MADescription
A new edition of the essential text and professional reference, with substantial new material on such topics as vEB trees, multithreaded algorithms, dynamic programming, and edge-based flow.
Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor.
The first edition became a widely used text in universities worldwide as well as the standard reference for professionals. The second edition featured new chapters on the role of algorithms, probabilistic analysis and randomized algorithms, and linear programming. The third edition has been revised and updated throughout. It includes two completely new chapters, on van Emde Boas trees and multithreaded algorithms, substantial additions to the chapter on recurrence (now called Divide-and-Conquer), and an appendix on matrices. It features improved treatment of dynamic programming and greedy algorithms and a new notion of edge-based flow in the material on flow networks. Many new exercises and problems have been added for this edition. The international paperback edition is no longer available; the hardcover is available worldwide.
7. Jungian Analysis (Reality of the Psyche Series)
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Used Book in Good ConditionDescription
This is a revised, updated, and expanded edition of a classic work, a groundbreaking survey of the Jungian approach to therapy in its most important applications. The majority of the contributions have been completely rewritten or replaced, while the remainder have been thoroughly revised.Jungian Analysis comprises 18 definitive essays by eminent Jungian authorities on specific aspects of Jungian thought and practice. Each contribution is written in a personal tone and style, and presents the history and state of the art on the chosen topic, with a reference list for further reading.
8. Poetry into Song: Performance and Analysis of Lieder
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Focusing on the music of the great song composers--Schubert, Schumann, Brahms, Wolf, and Strauss--Poetry Into Song offers a systematic introduction to the performance and analysis of Lieder . Part I, "The Language of Poetry," provides chapters on the themes and imagery of German Romanticism and the methods of analysis for German Romantic poetry. Part II, "The Language of the Performer," deals with issues of concern to performers: texture, temporality, articulation, and interpretation of notation and unusual rhythm accents and stresses. Part III provides clearly defined analytical procedures for each of four main chapters on harmony and tonality, melody and motive, rhythm and meter, and form. The concluding chapter compares different settings of the same text, and the volume ends with several appendices that offer text translations, over 40 pages of less accessible song scores, a glossary of technical terms, and a substantial bibliography. Directed toward students in both voice and theory, and toward all singers, the authors establish a framework for the analysis of song based on a process of performing, listening, and analyzing, designed to give the reader a new understanding of the reciprocal interaction between performance and analysis. Emphasizing the masterworks, the book features numerous poetic texts, as well as a core repertory of songs. Examples throughout the text demonstrate points, while end of chapter questions reinforce concepts and provide opportunities for directed analysis. While there are a variety of books on Lieder and on German Romantic poetry, none combines performance, musical analysis, textual analysis, and the interrelation between poetry and music in the systematic, thorough way of Poetry Into Song.9. Structure and Style: The Study and Analysis of Musical Forms (Classic Reprint)
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Excerpt from Structure and Style: The Study and Analysis of Musical FormsThe forms with which this book is concerned are those found in Western music. The idiom, form, and aesthetics of Oriental mus1c make it so markedly different from Western music that only a sep arate study could do it justice.
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10. Engaging Music: Essays in Music Analysis
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The first collection of its kind, Engaging Music: Essays in Music Analysis includes twenty-two selections by highly esteemed contemporary music theorists, sixteen of which were written especially for this volume. Featuring work by such luminaries as Charles Burkhart, Edward T. Cone, Allen Forte, David B. Lewin, and Carl Schachter, the book is an ideal text for undergraduate and graduate courses in form and analysis. It also serves as an invaluable reference for music teachers, students, and musicians.Opening with an introduction to writing analytical essays, Engaging Music then presents introductory readings that describe analytical approaches to rhythm, meter, and phrase; pitch (twelve-tone music); form in jazz and rock music; and musical ambiguity. The following essays offer exemplary models of analysis that cover a wide range of composers, from the Baroque (Purcell and Bach) and the Classical (Beethoven, Haydn, and Mozart) to the 19th-century (Brahms, Chopin, Schubert, Schumann, and Wagner) and the early 20th-century (Bartk, Schoenberg and Webern). The selections explore a diversity of genres--from opera to music for computer-generated tape--and a variety of analytical approaches, from Schenkerian to feminist. The volume also includes analyses of popular music (from jazz to a Sarah MacLachlan song) and of a relatively recent work by Barbara Kolb. A comprehensive glossary defines terms and concepts that may be unfamiliar to students, and a selected bibliography suggests other appropriate readings. Reflecting the broad spectrum of current interests and perspectives in the field, Engaging Music provides a unique window into the multifaceted world of music theory and analysis.
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