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# Science, Technology, and Mathematics > Mathematics

# Abraham Robinson

The Creation of Nonstandard Analysis, A Personal and Mathematical Odyssey

One of the most prominent mathematicians of the twentieth century, Abraham Robinson discovered and developed nonstandard analysis, a rigorous theory of infinitesimals that he used to unite mathematical logic with the larger body of historic and modern mathematics. In this first biography of Robinson, Joseph Dauben reveals the mathematician's personal life to have been a dramatic one: developing his talents in spite of war and ethnic repression, Robinson personally confronted some of the worst political troubles of our times. With the skill and expertise familiar to readers of Dauben's earlier works, the book combines an explanation of Robinson's revolutionary achievements in pure and applied mathematics with a description of his odyssey from Hitler's Germany to the United States via conflict-ridden Palestine and wartime Europe.

Robinson was born in Prussia in 1918. As a boy, he fled with his mother and brother Saul to Palestine. A decade later he narrowly escaped from Paris as the Germans invaded France. Having spent the rest of World War II in England, at the Royal Aircraft Establishment in Farnborough, he began his teaching career at the Royal College of Aeronautics. Subsequently he moved to universities in Canada, Israel, and finally the United States. A joint appointment in mathematics and philosophy at UCLA led to a position at Yale University, where Robinson served as Sterling Professor of Mathematics until his untimely death at the age of fifty-five.

Originally published in 1998.

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.

# Agent_Zero

*The Final Volume of the Groundbreaking Trilogy on Agent-Based Modeling*

In this pioneering synthesis, Joshua Epstein introduces a new theoretical entity: *Agent_Zero*. This software individual, or "agent," is endowed with distinct emotional/affective, cognitive/deliberative, and social modules. Grounded in contemporary neuroscience, these internal components interact to generate observed, often far-from-rational, individual behavior. When multiple agents of this new type move and interact spatially, they collectively generate an astonishing range of dynamics spanning the fields of social conflict, psychology, public health, law, network science, and economics.

Epstein weaves a computational tapestry with threads from Plato, Hume, Darwin, Pavlov, Smith, Tolstoy, Marx, James, and Dostoevsky, among others. This transformative synthesis of social philosophy, cognitive neuroscience, and agent-based modeling will fascinate scholars and students of every stripe. Epstein’s computer programs are provided in the book or on its Princeton University Press website, along with movies of his "computational parables."

*Agent_Zero* is a signal departure in what it includes (e.g., a new synthesis of neurally grounded internal modules), what it eschews (e.g., standard behavioral imitation), the phenomena it generates (from genocide to financial panic), and the modeling arsenal it offers the scientific community.

For generative social science, *Agent_Zero* presents a groundbreaking vision and the tools to realize it.

# Algebra in Context

Introductory Algebra from Origins to Applications

This book’s unique approach to the teaching of mathematics lies in its use of history to provide a framework for understanding algebra and related fields. With Algebra in Context, students will soon discover why mathematics is such a crucial part not only of civilization but also of everyday life. Even those who have avoided mathematics for years will find the historical stories both inviting and gripping. The book’s lessons begin with the creation and spread of number systems, from the mathematical development of early civilizations in Babylonia, Greece, China, Rome, Egypt, and Central America to the advancement of mathematics over time and the roles of famous figures such as Descartes and Leonardo of Pisa (Fibonacci). Before long, it becomes clear that the simple origins of algebra evolved into modern problem solving. Along the way, the language of mathematics becomes familiar, and students are gradually introduced to more challenging problems. Paced perfectly, Amy Shell-Gellasch and J. B. Thoo’s chapters ease students from topic to topic until they reach the twenty-first century. By the end of Algebra in Context, students using this textbook will be comfortable with most algebra concepts, including • Different number bases • Algebraic notation • Methods of arithmetic calculation • Real numbers • Complex numbers • Divisors • Prime factorization • Variation • Factoring • Solving linear equations • False position • Solving quadratic equations • Solving cubic equations • nth roots • Set theory • One-to-one correspondence • Infinite sets • Figurate numbers • Logarithms • Exponential growth • Interest calculations

# American Journal of Mathematics

Vol. 118 (1996) through current issue

The oldest mathematics journal in continuous publication in the Western Hemisphere, *American Journal of Mathematics* ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. *American Journal of Mathematics* is used as a basic reference work in academic libraries, both in the United States and abroad.

# Analysis of Evolutionary Processes

The Adaptive Dynamics Approach and Its Applications

Quantitative approaches to evolutionary biology traditionally consider evolutionary change in isolation from an important pressure in natural selection: the demography of coevolving populations. In *Analysis of Evolutionary Processes*, Fabio Dercole and Sergio Rinaldi have written the first comprehensive book on Adaptive Dynamics (AD), a quantitative modeling approach that explicitly links evolutionary changes to demographic ones. The book shows how the so-called AD canonical equation can answer questions of paramount interest in biology, engineering, and the social sciences, especially economics.

After introducing the basics of evolutionary processes and classifying available modeling approaches, Dercole and Rinaldi give a detailed presentation of the derivation of the AD canonical equation, an ordinary differential equation that focuses on evolutionary processes driven by rare and small innovations. The authors then look at important features of evolutionary dynamics as viewed through the lens of AD. They present their discovery of the first chaotic evolutionary attractor, which calls into question the common view that coevolution produces exquisitely harmonious adaptations between species. And, opening up potential new lines of research by providing the first application of AD to economics, they show how AD can explain the emergence of technological variety.

*Analysis of Evolutionary Processes* will interest anyone looking for a self-contained treatment of AD for self-study or teaching, including graduate students and researchers in mathematical and theoretical biology, applied mathematics, and theoretical economics.

# Archimedes

This classic study by the eminent Dutch historian of science E. J. Dijksterhuis (1892-1965) presents the work of the Greek mathematician and mechanical engineer to the modern reader. With meticulous scholarship, Dijksterhuis surveys the whole range of evidence on Archimedes' life and the 2000-year history of the manuscripts and editions of the text, and then undertakes a comprehensive examination of all the extant writings.

Originally published in 1987.

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.

# Bayesian Field Theory

Ask a traditional mathematician the likely outcome of a coin-toss, and he will reply that no evidence exists on which to base such a prediction. Ask a Bayesian, and he will examine the coin, conclude that it was probably not tampered with, and predict five hundred heads in a thousand tosses; a subsequent experiment would then be used to refine this prediction. The Bayesian approach, in other words, permits the use of prior knowledge when testing a hypothesis. Long the province of mathematicians and statisticians, Bayesian methods are applied in this ground-breaking book to problems in cutting-edge physics. Joerg Lemm offers practical examples of Bayesian analysis for the physicist working in such areas as neural networks, artificial intelligence, and inverse problems in quantum theory. The book also includes nonparametric density estimation problems, including, as special cases, nonparametric regression and pattern recognition. Thought-provoking and sure to be controversial, Bayesian Field Theory will be of interest to physicists as well as to other specialists in the rapidly growing number of fields that make use of Bayesian methods.

# Beyond Banneker

Black Mathematicians and the Paths to Excellence

*An in-depth look at the lives, experiences, and professional careers of Black mathematicians in the United States.*

# Bioéthique

Méthode et complexité

Les problèmes qui ont motivé la théorie et la pratique de la bioéthique dans les années 1960 et 1970 ont changé de nature. Les enjeux en bioéthique relèvent désormais de macro problèmes complexes, interreliés, qui touchent à la fois des populations entières et de nombreuses institutions sociales. L'auteure nous invite à une exploration méthodologique en bioéthique permettant de faire ressortir la complexité d'enjeux éthiques tels que l'euthanasie, le clonage et le commerce du gène et nous propose des moyens d'aborder cette complexité. Les écrits d'Edgar Morin sur la méthode et la complexité guident la réflexion.

# Borges and Mathematics

Borges and Mathematics is a short book of essays that explores the scientific thinking of the Argentine writer Jorge Luis Borges (1899-1986). Around half of the book consists of two “lectures” focused on mathematics. The rest of the book reflects on the relationship between literature, artistic creation, physics, and mathematics more generally. Written in a way that will be accessible even to those “who can only count to ten,” the book presents a bravura demonstration of the intricate links between the worlds of sciences and arts, and it is a thought-provoking call to dialog for readers from both traditions. The author, Guillermo Martínez, is both a recognized writer, whose murder mystery The Oxford Murders has been translated into thirty-five languages, and a PhD in mathematics. Contents: Borges and Mathematics: First Lecture; Borges and Mathematics: Second Lecture; The Golem and Artificial Intelligence; The Short Story as Logical System; A Margin Too Narrow; Euclid, or the Aesthetics of Mathematical Reasoning; Solutions and Disillusions; The Pythagorean Twins; The Music of Chance (Interview with Gregory Chaikin); Literature and Rationality; Who’s Afraid of the Big Bad One?; A Small, Small God; God’s Sinkhole. This book was originally published in Spanish as Borges y la matemática (2003). It has been translated with generous support from the Latino Cultural Center at Purdue University. Key points: • Presents complex mathematical and literary concepts in a way that is accessible to non-specialists. • Promotes dialog between readers from both humanist and scientific traditions. • Expands understanding of the Argentine writer, Jorge Luis Borges, including presenting some never-before-translated work.