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Structure And Randomness

Structure and Randomness
by Terence Tao

“In 2007, Terry Tao began a mathematical blog, as an outgrowth of his own website at UCLA. This book is based on a selection of articles from the first year of that blog. These articles discuss a wide range of mathematics and its applications, ranging from expository articles on quantum mechanics, Einstein’s equation E = mc[superscript 2], or compressed sensing, to open problems in analysis, combinatorics, geometry, number theory, and algebra, to lecture series on random matrices, Fourier analysis, or the dichotomy between structure and randomness that is present in many subfields of mathematics, to more philosophical discussions on such topics as the interplay between finitary and infinitary in analysis. Some selected commentary from readers of the blog has also been included at the end of each article.

Space, Structure and Randomness
by Michel Bilodeau, Fernand Meyer, Michel Schmitt

Space, structure, and randomness: these are the three key concepts underlying Georges Matheron’s scientific work. He first encountered them at the beginning of his career when working as a mining engineer, and then they resurfaced in fields ranging from meteorology to microscopy. What could these radically different types of applications possibly have in common? First, in each one only a single realisation of the phenomenon is available for study, but its features repeat themselves in space; second, the sampling pattern is rarely regular, and finally there are problems of change of scale.

This volume is divided in three sections on random sets, geostatistics and mathematical morphology. They reflect his professional interests and his search for underlying unity. Some readers may be surprised to find theoretical chapters mixed with applied ones. We have done this deliberately. GM always considered that the distinction between the theory and practice was purely academic.

When GM tackled practical problems, he used his skill as a physicist to extract the salient features and to select variables which could be measured meaningfully and whose values could be estimated from the available data. Then he used his outstanding ability as a mathematician to solve the problems neatly and efficiently. It was his capacity to combine a physicist’s intuition with a mathematician’s analytical skills that allowed him to produce new and innovative solutions to difficult problems.

The book should appeal to graduate students and researchers working in mathematics, probability, statistics, physics, spatial data analysis, and image analysis. In addition it will be of interest to those who enjoy discovering links between scientific disciplines that seem unrelated at first glance. In writing the book the contributors have tried to put GM’s ideas into perspective. During his working life, GM was a genuinely creative scientist. He developed innovative concepts whose usefulness goes far beyond the confines of the discipline for which they were originally designed. This is why his work remains as pertinent today as it was when it was first written.

Structure and Randomness
by Terence Tao

There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and non-rigorous to be discussed in the formal literature. Traditionally, it was a matter of luck and location as to who learned such folklore mathematics. But today, such bits and pieces can be communicated effectively and efficiently via the semiformal medium of research blogging. This book grew from such a blog. In 2007, Terry Tao began a mathematical blog, as an outgrowth of his own website at UCLA. This book is based on a selection of articles from the first year of that blog. These articles discuss a wide range of mathematics and its applications, ranging from expository articles on quantum mechanics, Einstein’s equation $E=mc^2$, or compressed sensing, to open problems in analysis, combinatorics, geometry, number theory, and algebra, to lecture series on random matrices, Fourier analysis, or the dichotomy between structure and randomness that is present in many subfields of mathematics, to more philosophical discussions on such topics as the interplay between finitary and infinitary in analysis. Some selected commentary from readers of the blog has also been included at the end of each article. While the articles vary widely in subject matter and level, they should be broadly accessible to readers with a general graduate mathematics background; the focus in many articles is on the “big picture” and on informal discussion, with technical details largely being left to the referenced literature.

Geometry, Structure and Randomness in Combinatorics
by Jiří Matousek, Jaroslav Nešetřil, Marco Pellegrini

​This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.

Computational Analysis of Randomness in Structural Mechanics
by Christian Bucher

Proper treatment of structural behavior under severe loading – such as the performance of a high-rise building during an earthquake – relies heavily on the use of probability-based analysis and decision-making tools. Proper application of these tools is significantly enhanced by a thorough understanding of the underlying theoretical and computational concepts as provided by this book.

Detailing the computational aspects of stochastic analysis within the field of structural mechanics, this book first presents a few motivating examples that demonstrate the various random effects within the context of simple structural analysis models. It moreover briefly reviews the fundamental concepts from continuum mechanics and puts them in the perspective of modern numerical tools, such as the finite element method. More advanced topics are developed step by step while gradually increasing the complexity of the structural and probabilistic analyses.

This volume is intended for structural analysts and advanced students who wish to explore the benefits of stochastic analysis. It will provide researchers and decision makers working on structural and infrastructural systems with the necessary probabilistic information needed for strategic developments in construction, inspection and maintenance.

Fooled by Randomness
by Nassim Nicholas Taleb

Fooled by Randomness is a standalone book in Nassim Nicholas Taleb’s landmark Incerto series, an investigation of opacity, luck, uncertainty, probability, human error, risk, and decision-making in a world we don’t understand. The other books in the series are The Black Swan, Antifragile, Skin in the Game, and The Bed of Procrustes.

Fooled by Randomness is the word-of-mouth sensation that will change the way you think about business and the world. Nassim Nicholas Taleb–veteran trader, renowned risk expert, polymathic scholar, erudite raconteur, and New York Times bestselling author of The Black Swan–has written a modern classic that turns on its head what we believe about luck and skill.

This book is about luck–or more precisely, about how we perceive and deal with luck in life and business. Set against the backdrop of the most conspicuous forum in which luck is mistaken for skill–the world of trading–Fooled by Randomness provides captivating insight into one of the least understood factors in all our lives. Writing in an entertaining narrative style, the author tackles major intellectual issues related to the underestimation of the influence of happenstance on our lives.

The book is populated with an array of characters, some of whom have grasped, in their own way, the significance of chance: the baseball legend Yogi Berra; the philosopher of knowledge Karl Popper; the ancient world’s wisest man, Solon; the modern financier George Soros; and the Greek voyager Odysseus. We also meet the fictional Nero, who seems to understand the role of randomness in his professional life but falls victim to his own superstitious foolishness.

However, the most recognizable character of all remains unnamed–the lucky fool who happens to be in the right place at the right time–he embodies the “survival of the least fit.” Such individuals attract devoted followers who believe in their guru’s insights and methods. But no one can replicate what is obtained by chance.

Are we capable of distinguishing the fortunate charlatan from the genuine visionary? Must we always try to uncover nonexistent messages in random events? It may be impossible to guard ourselves against the vagaries of the goddess Fortuna, but after reading Fooled by Randomness we can be a little better prepared.

Named by Fortune One of the Smartest Books of All Time

A Financial Times Best Business Book of the Year

Advances in Computation and Intelligence
by Jingnan Liu, Zhihua Cai, Chengyu Hu, Zhuo Kang, Yong Liu

LNCS 6382 is the ?rst volume of the proceedings of the Fifth International Symposium on Intelligence Computation and Applications (ISICA 2010)held in Wuhan, China, October 22–24, 2010. Fifty-three papers among 267 submissions were selected and included in LNCS 6382. The symposium featured the most up-to-date research in ant colony and particle swarm optimization, di?erential evolution, distributed computing, – netic algorithms, multi-agent systems, multi-objective and dynamic optimi- tion, robot intelligence, statistical learning, and system design. LNCS 6382 is dedicated to the memory of Lishan Kang. ISICA conferences were one of the ?rst series of international conferences on computational intel- gence that combine elements of learning, adaptation, evolution and fuzzy logic to create programs as alternative solutions to arti?cial intelligence. The idea for ISICA came about after Lishan Kang organized on international symposium on evolutionary computation at Wuhan University in 2000. After he was – vited to be the Director of the School of Computer Science, China University of Geosciences, he wondered whether he could establish such discussion forums on computational intelligence at China University of Geosciences. With support from his university, the School of Computer Science organizedthe ?rst ISICA in 2005, in which some of the leading ?gures from the scienti?c computing world were invited, including H. -P. Schwefel, Germany, M. Schoenauer, France, D. J. Evans, UK, T. Higuchi, Japan, Z. Michalewicz, Australia, and X. Yao, UK.

Compactness and Contradiction
by Terence Tao

There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and nonrigorous to be discussed in the formal literature. Traditionally, it was a matter

Statistics in Musicology
by Jan Beran

Traditionally, statistics and music are not generally associated with each other. However, …intelligent… music software, computer digitization, and other advanced techniques and technologies have precipitated the need for standard statistical models to answer basic musicological questions. Statistics In Musicology presents an unprecedented introduction to statistical and mathematical methods developed for use in music analysis, music theory, and performance theory. It explores concrete methods for data generation and numerical encoding of musical data and serves as a practical reference for a wide audience, including statisticians, mathematicians, musicologists, and musicians.

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by Elliott H. Lieb, Michael Loss

This is an excellent textbook on analysis and it has several unique features: Proofs of heat kernel estimates, the Nash inequality and the logarithmic Sobolev inequality are topics that are seldom treated on the level of a textbook. Best constants in several inequalities, such as Young’s inequality and the logarithmic Sobolev inequality, are also included. A thorough treatment of rearrangement inequalities and competing symmetries appears in book form for the first time. There is an extensive treatment of potential theory and its applications to quantum mechanics, which, again, is unique at this level. Uniform convexity of $L^p$ space is treated very carefully. The presentation of this important subject is highly unusual for a textbook. All the proofs provide deep insights into the theorems. This book sets a new standard for a graduate textbook in analysis. –Shing-Tung Yau, Harvard University For some number of years, Rudin’s “Real and Complex”, and a few other analysis books, served as the canonical choice for the book to use, and to teach from, in a first year grad analysis course. Lieb-Loss offers a refreshing alternative: It begins with a down-to-earth intro to measure theory, $L^p$ and all that … It aims at a wide range of essential applications, such as the Fourier transform, and series, inequalities, distributions, and Sobolev spaces–PDE, potential theory, calculus of variations, and math physics (Schrodinger’s equation, the hydrogen atom, Thomas-Fermi theory … to mention a few). The book should work equally well in a one-, or in a two-semester course. The first half of the book covers the basics, and the rest will be great for students to have, regardless of whether or not it gets to be included in a course. –Palle E. T. Jorgensen, University of Iowa

How to Think about Analysis
by Lara Alcock

Analysis (sometimes called Real Analysis or Advanced Calculus) is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the student’s existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these.

The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.

The Way of Analysis
by Robert S. Strichartz

The Way of Analysis gives a thorough account of real analysis in one or several variables, from the construction of the real number system to an introduction of the Lebesgue integral. The text provides proofs of all main results, as well as motivations, examples, applications, exercises, and formal chapter summaries. Additionally, there are three chapters on application of analysis, ordinary differential equations, Fourier series, and curves and surfaces to show how the techniques of analysis are used in concrete settings.

Analysis I
by Herbert Amann, Joachim Escher

Logical thinking, the analysis of complex relationships, the recognition of und- lying simple structures which are common to a multitude of problems — these are the skills which are needed to do mathematics, and their development is the main goal of mathematics education. Of course, these skills cannot be learned ‘in a vacuum’. Only a continuous struggle with concrete problems and a striving for deep understanding leads to success. A good measure of abstraction is needed to allow one to concentrate on the essential, without being distracted by appearances and irrelevancies. The present book strives for clarity and transparency. Right from the beg- ning, it requires from the reader a willingness to deal with abstract concepts, as well as a considerable measure of self-initiative. For these e?orts, the reader will be richly rewarded in his or her mathematical thinking abilities, and will possess the foundation needed for a deeper penetration into mathematics and its applications. Thisbookisthe?rstvolumeofathreevolumeintroductiontoanalysis.It- veloped from courses that the authors have taught over the last twenty six years at theUniversitiesofBochum,Kiel,Zurich,BaselandKassel.Sincewehopethatthis book will be used also for self-study and supplementary reading, we have included far more material than can be covered in a three semester sequence. This allows us to provide a wide overview of the subject and to present the many beautiful and important applications of the theory. We also demonstrate that mathematics possesses, not only elegance and inner beauty, but also provides e?cient methods for the solution of concrete problems.

Analysis I
by Terence Tao

This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

Handbook of Water Analysis
by Leo M.L. Nollet, Leen S. P. De Gelder

This work details water sampling and preservation methods by enumerating the different ways to measure physical, chemical, organoleptical, and radiological characteristics. It provides step-by-step descriptions of separation, residue determination, and cleanup techniques for a variety of fresh- and salt-waters. It also discusses information regarding the analysis and detection of bacteria and algae.

Data Collection and Analysis
by Roger Sapsford, Victor Jupp

In simple and non-technical terms, the Second Edition of Data Collection and Analysis illustrates a wide range of techniques and approaches used in social research projects. Always accessible and engaging, this comprehensive text covers both quantitative and qualitative approaches to data collection and analysis in social research, considering both the structure and logic of research projects and the ethics and politics of research.

A wide range of examples illustrate the text and a set of exercises runs throughout the book to aid the reader in understanding and planning research projects.

Building on the strengths of the First Edition, this new and expanded version includes:

– The addition of chapter introductions, summaries and key terms to guide the reader through the text

– Three brand new chapters focusing on: research and information on the Net; discourse research; ethnographic and discursive qualitative analysis

– Up-to-date examples of research in action

– New material on questionnaire design, composite measurement and techniques of quantitative and qualitative interviewing

An invaluable guide for students from across the social sciences, this wide-ranging volume is also a key resource for practitioners in a variety of applied areas including nursing, social work, the criminal justice system, teaching and education.

Analysis I
by Roger Godement

Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.

Dictionary of the Theatre
by Patrice Pavis

Patrice Pavis is one of France’s most brilliant academics and a leading expert internationally in the theory of theatre. Dictionary of the Theatre is an English translation of Pavis’s acclaimed Dictionnaire du théâtre, now in its second printing in France.

This encyclopedic dictionary includes theoretical, technical, and semiotic terms and concepts. Alphabetical entries range from ‘absurd’ to ‘word scenery’ and treat the reader to a vast panoply of theatre and theory. The extended discussions are supported by useful examples drawn from the international repertoire of plays and playwrights, both classic and contemporary. The Foreword is by Marvin Carlson.

This dictionary is remarkably well integrated, partly because of its excellent system of cross-referencing, but also because it represents the vision and scholarship of a single, recognized authority. There is no other source like it available and it will be warmly welcomed by the English-language theatre world.