值此2024年3月14日第六屆國際數學日來臨之際，我們精選12本美國數學學會出版的經典外文數學著作。這些經典之作將引領您深入數學的豐富世界，探索其深奧的奧秘，體驗數學之美。讀者現可通過 Ebook Central 平臺探索這些珍貴的學術資源，讓我們共同在知識的海洋中遨遊，慶祝數學的無限魅力。
Lectures on Quasiconformal Mappings
《擬共形映射講義》
作者： Lars V. Ahlfors
內容簡介：
Lars Ahlfors’s Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmüller spaces, including the Bers embedding and the Teichmüller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmüller spaces from these lecture notes.
A Course in Metric Geometry
《度量幾何學教程》
作者：Dmitri Burago，Yuri Burago等
內容簡介：
Metric geometry is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations.
The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Carathéodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with “easy-to-touch” mathematical objects using “easy-to-visualize” methods.
A Course in Minimal Surfaces
《極小曲面教程》
作者： Tobias Holck Colding，William P. Minicozzi lI
內容簡介：
Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein’s classical work, and even Lebesgue’s definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces.
This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science.
Fourier Analysis
《傅立葉分析》
作者： Javier Duoandikoetxea
內容簡介：
Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by Calderón and Zygmund. The text was born from a graduate course taught at the Universidad Autónoma de Madrid and incorporates lecture notes from a course taught by José Luis Rubio de Francia at the same university.
Motivated by the study of Fourier series and integrals, classical topics are introduced, such as the Hardy-Littlewood maximal function and the Hilbert transform. The remaining portions of the text are devoted to the study of singular integral operators and multipliers. Both classical aspects of the theory and more recent developments, such as weighted inequalities, BMO spaces, and the T1 theorem, are discussed.
An Introduction to Complex Analysis and Geometry
《複分析與幾何引論》
作者：John P. D’Angelo
內容簡介：
An Introduction to Complex Analysis and Geometry provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics. The book developed from courses given in the Campus Honors Program at the University of Illinois Urbana-Champaign. These courses aimed to share with students the way many mathematics and physics problems magically simplify when viewed from the perspective of complex analysis. The book begins at an elementary level but also contains advanced material.
Partial Differential Equations
《偏微分方程》
作者： Lawrence C. Evans
內容簡介：
This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE.
Function Theory of One Complex Variable
《單複變函數論》
作者： Robert E. Greene，StevenG. Krantz
內容簡介：
Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples and exercises that illustrate this point.
The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem, and the Bergman kernel. The authors also treat Hp spaces and Painlevé’s theorem on smoothness to the boundary for conformal maps.
Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems
《微分幾何中嘉當的活動標架法和外微分系統初步》
作者：Thomas A. lvey，J.M. Landsberg
內容簡介：
This book is an introduction to Cartan’s approach to differential geometry. Two central methods in Cartan’s geometry are the theory of exterior differential systems and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems.
It begins with the classical geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally with motivating examples leading to definitions, theorems, and proofs.
Representations of Algebraic Groups
《代數群表示論》
作者： Jens Carsten Jantzen
內容簡介：
Back in print from the AMS, the first part of this book is an introduction to the general theory of representations of algebraic group schemes. Here, Janzten describes important basic notions: induction functors, cohomology, quotients, Frobenius kernels, and reduction mod p, among others. The second part of the book is devoted to the representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, the Borel-Bott-Weil theorem and Weyl’s character formula, and Schubert schemes and line bundles on them.
Lectures on the Orbit Method《軌道法講義》
作者： A. A. Kirillov
內容簡介：
The orbit method was introduced by the author, A. A. Kirillov, in the 1960s and remains a useful and powerful tool in areas such as Lie theory, group representations, integrable systems, complex and symplectic geometry, and mathematical physics. This book describes the essence of the orbit method for non-experts and gives the first systematic, detailed, and self-contained exposition of the method. It starts with a convenient “User’s Guide” and contains numerous examples. It can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.
1001 Problems in Classical Number Theory
《經典數論中的1001個問題》
作者： Jean-Marie De Koninck，Armel Mercier
內容簡介：
In the spirit of The Book of the One Thousand and One Nights, the authors offer 1001 problems in number theory in a way that entices the reader to immediately attack the next problem. Whether a novice or an experienced mathematician, anyone fascinated by numbers will find a great variety of problems—some simple, others more complex—that will provide them with a wonderful mathematical experience.
Complex Proofs of Real Theorems
《實定理的複證明》
作者： Peter D. Lax，Lawrence Zalcman
內容簡介：
Complex Proofs of Real Theorems is an extended meditation on Hadamard’s famous dictum, “The shortest and best way between two truths of the real domain often passes through the imaginary one.” Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics.
美國數學學會及其電子書簡介
美國數學學會（American Mathematical Society，AMS）是美國數學領域推動數學研究和數學教育的知名組織，本身為一非營利機構，旨在促進關於數學之研究，並且對數學教育提供協助與建議以及促進各國數學家之交流活動等等。
美國數學學會於1888年成立至今130多年來，已經出版了非常大量高品質之高等數學領域的書籍，包括19世紀以來數學專業領域的各種會議論文集(Proceedings)、專書(Monograph)以及專論(Memoirs)。
Ebook Central 平臺
ProQuest Ebook Central 平臺（簡稱EBC），是一個綜合類的外文電子書平臺，共收錄全球2400多家著名大學出版社、專業出版商、學術出版機構出版的近200萬種電子書，以近年來新出版的圖書為主，並會定期更新電子書資源。EBC 主要內容覆蓋電腦科學、經濟、商業、文學、語言、歷史、藝術、哲學與教育學等全學科領域。涉及50多種語言，覆蓋英語、德語、法語、西班牙語、葡萄牙語、阿拉伯語等。
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