{"title":"Elias M. Stein","description":"\u003cp\u003eElias M. Stein was a renowned mathematician whose contributions to the field of analysis have left an indelible mark on the scientific community. His work, spanning decades, has been instrumental in developing the way we understand and apply mathematical concepts across various domains.\u003c\/p\u003e\n\n\u003cp\u003eThis collection brings together some of Stein's most influential works, perfect for anyone interested in deepening their understanding of advanced mathematics. Each book is a cornerstone in its respective area of study:\u003c\/p\u003e\n\n\u003cul\u003e\n  \u003cli\u003e\n\u003cem\u003eComplex Analysis\u003c\/em\u003e: Dive into the intricate world of complex numbers and analytic functions, where Stein elucidates the profound connections between calculus, geometry, and topology.\u003c\/li\u003e\n  \u003cli\u003e\n\u003cem\u003eFourier Analysis\u003c\/em\u003e: Discover the beauty of Fourier theory, a fundamental tool in both pure and applied mathematics, and essential for anyone working with signal processing, heat diffusion, and quantum mechanics.\u003c\/li\u003e\n  \u003cli\u003e\n\u003cem\u003eFunctional Analysis\u003c\/em\u003e: Uncover the abstract yet powerful branch of analysis that intersects with operator theory and the study of vector spaces, offering applications in physics and beyond.\u003c\/li\u003e\n  \u003cli\u003e\n\u003cem\u003eReal Analysis\u003c\/em\u003e: Explore the rigorous foundations of calculus, providing vital insights into differentiable functions, integration, and measure theory.\u003c\/li\u003e\n\u003c\/ul\u003e\n\n\u003cp\u003eWhether you're a student, an academic, or simply a lover of mathematics, Elias M. Stein's work provides profound insights, and complex problem-solving techniques and inspires continued exploration in the fields of Science \u0026amp; Nature.\u003c\/p\u003e","products":[{"product_id":"complex-analysis-by-rami-shakarchi-9780691113852","title":"Complex Analysis","description":"\u003cdiv class=\"book-description\"\u003e\n\u003cp\u003eWith 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.\u003c\/p\u003e\n\n\u003cp\u003eWith 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, \u003cem\u003eComplex Analysis\u003c\/em\u003e will be welcomed by students of mathematics, physics, engineering, and other sciences.\u003c\/p\u003e\n\n\u003cp\u003eThe 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 \u003cem\u003eComplex Analysis\u003c\/em\u003e 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.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":46854291063020,"sku":"9780691113852","price":92.0,"currency_code":"NZD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/1125663482434.jpg?v=1759239870"},{"product_id":"fourier-analysis-by-rami-shakarchi-9780691113845","title":"Fourier Analysis","description":"\u003cdiv class=\"book-description\"\u003e\n\u003cp\u003eThis 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.\u003c\/p\u003e\n\n\u003cp\u003eIt 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.\u003c\/p\u003e\n\n\u003cp\u003eThe 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.\u003c\/p\u003e\n\n\u003cp\u003eIn organising 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.\u003c\/p\u003e\n\n\u003cp\u003e\u003ci\u003eThe Princeton Lectures in Analysis\u003c\/i\u003e 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 \u003ci\u003eFourier Analysis\u003c\/i\u003e is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences.\u003c\/p\u003e\n\n\u003cp\u003eStein 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.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":46854536921324,"sku":"9780691113845","price":338.0,"currency_code":"NZD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/9780691113845.jpg?v=1759246023"},{"product_id":"functional-analysis-by-rami-shakarchi-9780691113876","title":"Functional Analysis","description":"\u003cdiv class=\"book-description\"\u003e\n\u003cp\u003eThis 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, highlighting their roles in harmonic analysis. The authors then use the Baire category theorem to illustrate several points, including the existence of Besicovitch sets.\u003c\/p\u003e\n\n\u003cp\u003eThe 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.\u003c\/p\u003e\n\n\u003cp\u003eThroughout the book, the authors focus on key results in each area and stress the organic unity of the subject.\u003c\/p\u003e\n\n\u003cp\u003e\u003cem\u003eFunctional Analysis\u003c\/em\u003e offers a comprehensive and authoritative treatment of some of the main topics of modern analysis. It provides a look at basic functional analysis and its applications in harmonic analysis, probability theory, and several complex variables, discussing key results in each area in relation to other areas of mathematics and highlighting the organic unity of large areas of analysis traditionally split into subfields.\u003c\/p\u003e\n\n\u003cp\u003eThe book contains interesting exercises and problems that illustrate ideas, along with clear proofs to aid understanding.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":46854542524652,"sku":"9780691113876","price":215.99,"currency_code":"NZD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/9780691113876.jpg?v=1759246274"},{"product_id":"real-analysis-by-rami-shakarchi-9780691113869","title":"Real Analysis","description":"\u003cdiv class=\"book-description\"\u003e\n\u003cp\u003e\u003ci\u003eReal Analysis\u003c\/i\u003e 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.\u003c\/p\u003e\n\n\u003cp\u003eThis 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 L\u003csub\u003e2\u003c\/sub\u003e theory.\u003c\/p\u003e\n\n\u003cp\u003eThey 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.\u003c\/p\u003e\n\n\u003cp\u003eEach 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, \u003ci\u003eReal Analysis\u003c\/i\u003e is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":46998569386220,"sku":"9780691113869","price":319.0,"currency_code":"NZD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/473c6e85b2632e53318126a1f4c6db7f.jpg?v=1763237159"}],"url":"https:\/\/bookhero.pro\/collections\/elias-m-stein.oembed","provider":"Book Hero","version":"1.0","type":"link"}