An Introduction to Microlocal Analysis

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Microlocal analysis provides a powerful, versatile, and modular perspective on the analysis of linear partial differential equations. This text, developed from a first-year graduate course, provides an accessible introduction and develops, from first principles, the core notions and results including pseudodifferential operators, wave front sets, and propagation phenomena. The reader is assumed to have some exposure to functional analysis and the theory of smooth manifolds. With detailed proofs, a wealth of exercises of varying levels of difficulty, and connections to contemporary research in general relativity, the book serves as both a comprehensive textbook for graduate students and a useful reference for researchers.

Elliptic Partial Differential Equations from an Elementary Viewpoint: What the Laplacian Is Good for (1版)

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【簡介】 This book offers a captivating journey through the world of elliptic partial differential equations (PDEs) and their surprising appearances across science, engineering, and even everyday life. Blending mathematical rigor with an accessible and engaging style, it introduces the Laplace operator and elliptic PDEs through diverse real-world phenomena, from physics and biology to artificial intelligence and image processing.Readers will explore fundamental topics such as diffusion, wave propagation, and fluid dynamics, alongside unexpected applications - including pattern formation in nature, traffic jams, quantum mechanics, and even the mathematics behind fighting pandemics and cancer. With a focus on both intuition and formalism, the book provides a wealth of examples, historical insights, and thought-provoking problems that make the subject come alive.Awarded the prestigious Book Prize of the Unione Matematica Italiana, this work has been praised as ＂a remarkable journey through delightful applications of elliptic PDEs, all while maintaining the highest standards of mathematical rigor.＂ Whether you are a student, researcher, or simply curious about how mathematics shapes the world around us, this book will challenge and inspire you.

Axiomatic Arithmetic: An Introduction to Number Systems (1版)

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【簡介】 The goal of this book is to construct and explore the properties of the most commonly encountered number systems, beginning with the Peano axioms for the natural numbers. The systems discussed include the natural numbers, integers, rational numbers, real numbers, and complex numbers.Along the way, the book covers a range of related topics such as the ring-theoretic properties of integers, Euclid’s algorithm, the fundamental theorem of arithmetic, modular arithmetic, and cardinality. It also delves into decimal and continued fraction representations of the reals, the rational zeroes theorem, Liouville’s approximation theorem, the extended real number system, and the fundamental theorem of algebra.The book contains 233 exercises with detailed solutions provided at the end, making it well-suited for self-study. These exercises also introduce additional number systems including the quaternions, octonions, and p-adic numbers.The intended audience is first- or second-year undergraduate students in Mathematics or the Applied Sciences who have completed a first course in Calculus. It may also be valuable to school teachers interested in the foundations of algebra and calculus, as well as students in teacher education programs.This book can serve as a supplementary text for introductory courses in real analysis or algebra. It also includes 57 figures to aid understanding throughout.

Souvenr of an Outbound Life (1版)

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【簡介】 　　Fascinated by her grandfather’s seafaring life on a freighter and triggered by her own turbulent arrival to Iceland one winter, Crystal Kwan ends up buying a one-way ticket to Paris where her outbound life unfolds.  Under the influence of great artists, architects and writers who travelled far both physically and creatively, she is tempted to do the same: to record serendipitous, at times overwhelming moments through writing, sketching and photography. Four themes of “souvenirs”, each a result of a particular type of travel, portray different ways of seeing as she comes face to face with the world. Be it creative or contemplative, memorable or regrettable, the greatest souvenir harnessed throughout all journeys is the transformative power of travel.