This anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, "The Best Writing on Mathematics 2011" makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Ian Hacking discusses the salient features that distinguish mathematics from other disciplines of the mind; Doris Schattschneider identifies some of the mathematical inspirations of M. C. Escher's art; Jordan Ellenberg describes compressed sensing, a mathematical field that is reshaping the way people use large sets of data; Erica Klarreich reports on the use of algorithms in the job market for doctors; and much, much more.

In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed physicist and mathematician Freeman Dyson. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

Gottlob Frege (1848 1925) was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of language and philosophical logic. Frege is generally seen (along with Russell and Wittgenstein) as one of the fathers of the analytic method, which dominated philosophy in English-speaking countries for most of the twentieth century. His work is studied today not just for its historical importance but also because many of his ideas are still seen as relevant to current debates in the philosophies of logic, language, mathematics and the mind. The Cambridge Companion to Frege provides a route into this lively area of research.

Matrices offer some of the most powerful techniques in modem mathematics. In the social sciences they provide fresh insights into an astonishing variety of topics. Dominance matrices can show how power struggles in offices or committees develop; Markov chains predict how fast news or gossip will spread in a village; permutation matrices illuminate kinship structures in tribal societies. All these invaluable techniques and many more are explained clearly and simply in this wide-ranging book. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Professor Morgenstern's deep interests in economic time series and problems of measurement are represented by path-breaking articles devoted to the application of modern statistical analysis to temporal economic data. Originally published in 1967. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Mathematical Explorations follows on from the author's previous book, Creative Mathematics, in the same series, and gives the reader experience in working on problems requiring a little more mathematical maturity. The author's main aim is to show that problems are often solved by using mathematics that is not obviously connected to the problem, and readers are encouraged to consider as wide a variety of mathematical ideas as possible. In each case, the emphasis is placed on the important underlying ideas rather than on the solutions for their own sake. To enhance understanding of how mathematical research is conducted, each problem has been chosen not for its mathematical importance, but because it provides a good illustration of how arguments can be developed. While the reader does not require a deep mathematical background to tackle these problems, they will find their mathematical understanding is enriched by attempting to solve them.

Information is a central topic in computer science, cognitive science, and philosophy. In spite of its importance in the "information age," there is no consensus on what information is, what makes it possible, and what it means for one medium to carry information about another. Drawing on ideas from mathematics, computer science, and philosophy, this book addresses the definition and place of information in society. The authors, observing that information flow is possible only within a connected distribution system, provide a mathematically rigorous, philosophically sound foundation for a science of information. They illustrate their theory by applying it to a wide range of phenomena, from file transfer to DNA, from quantum mechanics to speech act theory.

Alfred Tarski, one of the greatest logicians of all time, is widely thought of as 'the man who defined truth'. His mathematical work on the concepts of truth and logical consequence are cornerstones of modern logic, influencing developments in philosophy, linguistics and computer science. Tarski was a charismatic teacher and zealous promoter of his view of logic as the foundation of all rational thought, a bon-vivant and a womanizer, who played the 'great man' to the hilt. Born in Warsaw in 1901 to Jewish parents, he changed his name and converted to Catholicism, but was never able to obtain a professorship in his home country. A fortuitous trip to the United States at the outbreak of war saved his life and turned his career around, even while it separated him from his family for years. By the war's end he was established as a professor of mathematics at the University of California, Berkeley. There Tarski built an empire in logic and methodology that attracted students and distinguished researchers from all over the world. From the cafes of Warsaw and Vienna to the mountains and deserts of California, this first full length biography places Tarski in the social, intellectual and historical context of his times and presents a frank, vivid picture of a personally and professionally passionate man, interlaced with an account of his major scientific achievements.

Lo scibile matematico si espande a un ritmo vertiginoso. Nel corso degli ultimi cinquant'anni sono stati dimostrati piu teoremi che nei precedenti millenni della storia umana. Per illustrare la ricchezza della matematica del Novecento, il presente volume porta sulla ribalta alcuni dei protagonisti di questa straordinaria impresa intellettuale, che ha messo a nostra disposizione nuovi e potenti strumenti per indagare la realta che ci circonda.

Presentando matematici famosi accanto ad altri meno noti al grande pubblico - da Hilbert a Godel, da Turing a Nash, da De Giorgi a Wiles - i ritratti raccolti in questo volume ci presentano personaggi dal forte carisma personale, dai vasti interessi culturali, appassionati nel difendere l'importanza delle proprie ricerche, sensibili alla bellezza, attenti ai problemi sociali e politici del loro tempo.

Ne risulta un affresco che documenta la centralita della matematica nella cultura, non solo scientifica ma anche filosofica, artistica e letteraria, del nostro tempo, in un continuo gioco di scambi e di rimandi, di corrispondenze e di suggestioni.

This collection of new essays offers a "state-of-the-art" conspectus of major trends in the philosophy of logic and philosophy of mathematics. A distinguished group of philosophers addresses issues at the center of contemporary debate: semantic and set-theoretic paradoxes, the set/class distinction, foundations of set theory, mathematical intuition and many others. The volume includes Hilary Putnam's 1995 Alfred Tarski lectures published here for the first time. The essays are presented to honor the work of Charles Parsons.

Durante la II guerra mondiale hanno avuto luogo numerosi risultati di rilievo nel campo della crittografia militare. Uno dei meno conosciuti e quello usato dal servizio di intelligence svedese, nei confronti del codice tedesco per le comunicazioni strategiche con i comandi dei paesi occupati nel nord Europa, le cui linee passavano per la Svezia. In tal modo, durante la fase piu critica della guerra la direzione politica e militare svedese era in grado di seguire i piani e le disposizioni dei Tedeschi, venendo a conoscenza dei piu arditi progetti per modificare la propria politica, tenendo la Svezia fuori dalla guerra.

La violazione del codice tedesco e narrata in dettaglio, per la prima volta, con elementi che gli permettono di essere un ottima introduzione al campo della crittografia, oltre che un ritratto vitale e umano della societa del tempo: una disperata condizione bellica, l'intrigo politico e spionistico, il genio del matematico Arne Beurling, le difficolta e i trucchi del mestiere, e il lavoro sistematico e oscuro di una folla di decrittatori.

The design inference uncovers intelligent causes by isolating their key trademark: specified events of small probability. Just about anything that happens is highly improbable, but when a highly improbable event is also specified (i.e. conforms to an independently given pattern) undirected natural causes lose their explanatory power. Design inferences can be found in a range of scientific pursuits from forensic science to research into the origins of life to the search for extraterrestrial intelligence. This challenging and provocative 1998 book shows how incomplete undirected causes are for science and breathes new life into classical design arguments. It will be read with particular interest by philosophers of science and religion, other philosophers concerned with epistemology and logic, probability and complexity theorists, and statisticians.

Guicciardini presents a comprehensive survey of both the research and teaching of Newtonian calculus, the calculus of "fluxions", over the period between 1700 and 1810. Although Newton was one of the inventors of calculus, the developments in Britain remained separate from the rest of Europe for over a century. While it is usually maintained that after Newton there was a period of decline in British mathematics, the author's research demonstrates that the methods used by researchers of the period yielded considerable success in laying the foundations and investigating the applications of the calculus. Even when "decline" set in, in mid century, the foundations of the reform were being laid, which were to change the direction and nature of the mathematics community. The book considers the importance of Isaac Newton, Roger Cotes, Brook Taylor, James Stirling, Abraham de Moivre, Colin Maclaurin, Thomas Bayes, John Landen and Edward Waring. This will be a useful book for students and researchers in the history of science, philosophers of science and undergraduates studying the history of mathematics.

Philosophical considerations, which are often ignored or treated casually, are given careful consideration in this introduction. Thomas Forster places the notion of inductively defined sets (recursive datatypes) at the center of his exposition resulting in an original analysis of well established topics. The presentation illustrates difficult points and includes many exercises. Little previous knowledge of logic is required and only a knowledge of standard undergraduate mathematics is assumed.

Questo volume raccoglie lo scambio epistolare tra Cantor e Dedekind, finora edito parte in tedesco e parte in francese. Sara la prima edizione italiana completa di questo fondamentale carteggio, in cui si vedono nascere la nozione di cardinale e ordinale transfiniti, in cui si dimostra la non numerabilita dell'insieme dei numeri reali R e si leggono i primi tentativi e le correzioni alla costruzione di una biiezione tra R e R2, e le discussioni fra Cantor e Dedekind sull'invarianza della nozione di dimensione. "Pochi scritti matematici possono competere - scrive Pietro Nastasi nell'Introduzione - con questa corrispondenza nell'evidenziare il complesso intreccio psicologico che presiede all'invenzione matematica. E nessun lavoro storiografico potrebbe far emergere, meglio di queste lettere, la differenza fra le due personalita implicate: focosa e fantasiosa quella di Cantor, pacata e critica quella del piu anziano amico".

Professor Morgenstern's deep interests in economic time series and problems of measurement are represented by path-breaking articles devoted to the application of modern statistical analysis to temporal economic data. Originally published in 1967. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This book introduces the reader to Serres' unique manner of 'doing philosophy' that can be traced throughout his entire oeuvre: namely as a novel manner of bearing witness. It explores how Serres takes note of a range of epistemologically unsettling situations, which he understands as arising from the short-circuit of a proprietary notion of capital with a praxis of science that commits itself to a form of reasoning which privileges the most direct path (simple method) in order to expend minimal efforts while pursuing maximal efficiency. In Serres' universal economy, value is considered as a function of rarity, not as a stock of resources. This book demonstrates how Michel Serres has developed an architectonics that is coefficient with nature. Mathematic and Information in the Philosophy of Michel Serres acquaints the reader with Serres' monist manner of addressing the universality and the power of knowledge - that is at once also the anonymous and empty faculty of incandescent, inventive thought. The chapters of the book demarcate, problematize and contextualize some of the epistemologically unsettling situations Serres addresses, whilst also examining the particular manner in which he responds to and converses with these situations.

Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. "Mind and Nature" is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished.

Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, "The Open World" (1932) and "Mind and Nature" (1934), each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life.

A survey of recent developments both in the classical and modern fields of the theory. Contents include: The complex analytic structure of the space of closed Riemann surfaces; Complex analysis on noncompact Riemann domains; Proof of the Teichmuller-Ahlfors theorem; The conformal mapping of Riemann surfaces; On certain coefficients of univalent functions; Compact analytic surfaces; On differentiable mappings; Deformations of complex analytic manifolds. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This distinctive anthology includes many of the most important recent contributions to the philosophy of mathematics. The featured papers are organized thematically, rather than chronologically, to provide the best overview of philosophical issues connected with mathematics and the development of mathematical knowledge. Coverage ranges from general topics in mathematical explanation and the concept of number, to specialized investigations of the ontology of mathematical entities and the nature of mathematical truth, models and methods of mathematical proof, intuitionistic mathematics, and philosophical foundations of set theory.

This volume explores the central problems and exposes intriguing new directions in the philosophy of mathematics, making it an essential teaching resource, reference work, and research guide.

The book complements "Philosophy of Logic: An Anthology" and "A Companion to Philosophical Logic, "also edited by Dale Jacquette (Blackwell 2001).

Presenter l'analyse de base en suivant grosso modo l'ordre suivant laquelle elle a ete decouverte, voici le fil conducteur de cet ouvrage. Complete par un grand nombre de dessins, d'exemples et de contre-exemples, cet ouvrage est redige avec un veritable souci de pedagogie. Il est truffe de remarques historiques et de commentaires explicitant la motivation profonde des developpements exposes.

"Geschichte der Analysis" ist von einem internationalen Expertenteam geschrieben und stellt die gegenwartig umfassendste Darstellung der Herausbildung und Entwicklung dieser mathematischen Kerndisziplin dar. Der tiefgreifende begriffliche Wandel, den die Analysis im Laufe der Zeit durchgemacht hat, wird ebenso dargestellt, wie auch der Einfluss, den vor allem physikalische Probleme gehabt haben. Biographische und philosophische Hintergrunde werden ausgeleuchtet und ihre Relevanz fur die Theorieentwicklung gezeigt. Neben der eigentlichen Geschichte der Analysis bis ungefahr 1900 enthalt das Buch Spezialkapitel uber die Entwicklung der analytischen Mechanik im 18. Jahrhundert, Randwertprobleme der mathematischen Physik im 19. Jahrhundert, die Theorie der komplexen Funktionen, die Grundlagenkrise sowie historische Uberblicke uber die Variationsrechnung, Differentialgleichungen und Funktionalanalysis."

L'opera, pubblicata, anche per questa edizione, come Supplemento alla rivista LETTERA MATEMATICA, e frutto del convegno 'Matematica e Cultura' organizzato a Venezia nel Marzo 1998. Il convegno, giunto nel Marzo 1998 alla sua seconda edizione, si propone come un ponte tra i diversi aspetti del sapere umano. Pur avendo come punto di riferimento la matematica, si rivolge a tutti coloro che hanno curiosita e interessi culturali anche e soprattutto al di fuori della matematica. Nel volume si parla pertanto di musica, cinema, di arte, di filosofia, di letteratura, di internet e mass-media.

This publication includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728-1777) written in the 1760s: Vorlaufige Kenntnisse fur die, so die Quadratur und Rectification des Circuls suchen and Memoire sur quelques proprietes remarquables des quantites transcendentes circulaires et logarithmiques. The translations are accompanied by a contextualised study of each of these works and provide an overview of Lambert's contributions, showing both the background and the influence of his work. In addition, by adopting a biographical approach, it allows readers to better get to know the scientist himself. Lambert was a highly relevant scientist and polymath in his time, admired by the likes of Kant, who despite having made a wide variety of contributions to different branches of knowledge, later faded into an undeserved secondary place with respect to other scientists of the eighteenth century. In mathematics, in particular, he is famous for his research on non-Euclidean geometries, although he is likely best known for having been the first who proved the irrationality of pi. In his Memoire, he conducted one of the first studies on hyperbolic functions, offered a surprisingly rigorous proof of the irrationality of pi, established for the first time the modern distinction between algebraic and transcendental numbers, and based on such distinction, he conjectured the transcendence of pi and therefore the impossibility of squaring the circle.

Matrices offer some of the most powerful techniques in modem mathematics. In the social sciences they provide fresh insights into an astonishing variety of topics. Dominance matrices can show how power struggles in offices or committees develop; Markov chains predict how fast news or gossip will spread in a village; permutation matrices illuminate kinship structures in tribal societies. All these invaluable techniques and many more are explained clearly and simply in this wide-ranging book.

Originally published in 1986.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.