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.

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.

An Introduction to Sociolinguistics (6版)

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【簡介】 Sociolinguistics is the study of the interaction between language and society. In this classic introductory work, Janet Holmes and Nick Wilson examine the role of language in a variety of social contexts, considering both how language works and how it can be used to signal and interpret various aspects of social identity. Divided into three parts, this book explains basic sociolinguistic concepts in the light of classic approaches, as well as introducing more recent research.This sixth edition has been revised and updated throughout, using key concepts and examples to guide the reader through this fascinating area, including: - New material on gender, social media and online use of language, codeswitching, and language policy- An updated companion website that is fully cross- referenced within this book and features video and audio materials and links to useful websites- Revised examples and exercises that include new material from Asia and South America- Fully updated further reading and references sectionsAn Introduction to Sociolinguistics is an essential introductory text for all students of sociolinguistics and a splendid point of reference for students of English language studies, linguistics, and applied linguistics.