front cover of Handbook of Quantitative Ecology
Handbook of Quantitative Ecology
Justin Kitzes
University of Chicago Press, 2022
An essential guide to quantitative research methods in ecology and conservation biology, accessible for even the most math-averse student or professional.

Quantitative research techniques have become increasingly important in ecology and conservation biology, but the sheer breadth of methods that must be understood—from population modeling and probabilistic thinking to modern statistics, simulation, and data science—and a lack of computational or mathematics training have hindered quantitative literacy in these fields. In this book, ecologist Justin Kitzes addresses those challenges for students and practicing scientists alike.

Requiring only basic algebra and the ability to use a spreadsheet, Handbook of Quantitative Ecology is designed to provide a practical, intuitive, and integrated introduction to widely used quantitative methods. Kitzes builds each chapter around a specific ecological problem and arrives, step by step, at a general principle through the process of solving that problem. Grouped into five broad categories—difference equations, probability, matrix models, likelihood statistics, and other numerical methods—the book introduces basic concepts, starting with exponential and logistic growth, and helps readers to understand the field’s more advanced subjects, such as bootstrapping, stochastic optimization, and cellular automata. Complete with online solutions to all numerical problems, Kitzes’s Handbook of Quantitative Ecology is an ideal coursebook for both undergraduate and graduate students of ecology, as well as a useful and necessary resource for mathematically out-of-practice scientists.
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Haphazard Reality
Half a Century of Science
H.B.G. Casimir
Amsterdam University Press, 2010

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Harmonic Analysis and Partial Differential Equations
Essays in Honor of Alberto P. Calderon
Edited by Michael Christ, Carlos E. Kenig, and Cora Sadosky
University of Chicago Press, 1999
Alberto P. Calderón (1920-1998) was one of this century's leading mathematical analysts. His contributions, characterized by great originality and depth, have changed the way researchers approach and think about everything from harmonic analysis to partial differential equations and from signal processing to tomography. In addition, he helped define the "Chicago school" of analysis, which remains influential to this day.

In 1996, more than 300 mathematicians from around the world gathered in Chicago for a conference on harmonic analysis and partial differential equations held in Calderón's honor. This volume originated in papers given there and presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest scholars working in these areas. An important addition to the literature, this book is essential reading for researchers in these and other related fields.
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Hexaflexagons and Other Mathematical Diversions
The First Scientific American Book of Puzzles and Games
Martin Gardner
University of Chicago Press, 1988
These clearly and cleverly presented mathematical recreations of paradoxes and paperfolding, Moebius variations and mnemonics both ancient and modern delight and perplex while demonstating principles of logic, probability, geometry, and other mathematical fields.

"A classic."—Andrew Rothery, Times Education Supplement

"Martin Gardner has turned a trick as neat as any in the book itself. He has selected a group of diversions which are not only entertaining but mathematically meaningful as well. The result is a work which is rewarding on almost every level of mathematical achievement."—Miriam Hecht, Iscripta Mathematica
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The Hidden Game of Baseball
A Revolutionary Approach to Baseball and Its Statistics
John Thorn, Pete Palmer, with David Reuther
University of Chicago Press, 2015
Long before Moneyball became a sensation or Nate Silver turned the knowledge he’d honed on baseball into electoral gold, John Thorn and Pete Palmer were using statistics to shake the foundations of the game. First published in 1984, The Hidden Game of Baseball ushered in the sabermetric revolution by demonstrating that we were thinking about baseball stats—and thus the game itself—all wrong. Instead of praising sluggers for gaudy RBI totals or pitchers for wins, Thorn and Palmer argued in favor of more subtle measurements that correlated much more closely to the ultimate goal: winning baseball games.
            The new gospel promulgated by Thorn and Palmer opened the door for a flood of new questions, such as how a ballpark’s layout helps or hinders offense or whether a strikeout really is worse than another kind of out. Taking questions like these seriously—and backing up the answers with data—launched a new era, showing fans, journalists, scouts, executives, and even players themselves a new, better way to look at the game.
            This brand-new edition retains the body of the original, with its rich, accessible analysis rooted in a deep love of baseball, while adding a new introduction by the authors tracing the book’s influence over the years. A foreword by ESPN’s lead baseball analyst, Keith Law, details The Hidden Game’s central role in the transformation of baseball coverage and team management and shows how teams continue to reap the benefits of Thorn and Palmer’s insights today. Thirty years after its original publication, The Hidden Game is still bringing the high heat—a true classic of baseball literature.
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The Hidden Game of Football
A Revolutionary Approach to the Game and Its Statistics
Bob Carroll, Pete Palmer, and John Thorn
University of Chicago Press, 2023
The 1988 cult classic behind football’s data analytics revolution, now back in print with a new foreword and preface.

Data analytics have revolutionized football. With play sheets informed by advanced statistical analysis, today’s coaches pass more, kick less, and go for more two-point or fourth-down conversions than ever before. In 1988, sportswriters Bob Carroll, Pete Palmer, and John Thorn proposed just this style of play in The Hidden Game of Football, but at the time baffled readers scoffed at such a heartless approach to the game. Football was the ultimate team sport and unlike baseball could not be reduced to pure probabilities. Nevertheless, the book developed a cult following among analysts who, inspired by its unorthodox methods, went on to develop the core metrics of football analytics used today: win probability, expected points, QBR, and more. With a new preface by Thorn and Palmer and a new foreword by Football Outsiders’s Aaron Schatz, The Hidden Game of Football remains an essential resource for armchair coaches, fantasy managers, and fans of all stripes.
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Higher-Order Techniques in Computational Electromagnetics
Roberto D. Graglia
The Institution of Engineering and Technology, 2016
Improvements in the accuracy, computational cost, and reliability of computational techniques for high-frequency electromagnetics (including antennas, microwave devices and radar scattering applications) can be achieved through the use of 'high-order' techniques. This book outlines these techniques by presenting high-order basis functions, explaining their use, and illustrating their performance. The specific basis functions under consideration were developed by the authors, and include scalar and vector functions for use with equations such as the vector Helmholtz equation and the electric field integral equation.
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History and Philosophy of Modern Mathematics
Volume XI
William Aspray and Philip Kitcher, Editors
University of Minnesota Press, 1988

History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions.

The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective.

The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.

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A History in Sum
150 Years of Mathematics at Harvard (1825–1975)
Steve Nadis and Shing-Tung Yau
Harvard University Press, 2013

In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard’s mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics—in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose.

The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics—an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce’s successors—William Fogg Osgood and Maxime Bôcher—undertook the task of transforming the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Birkhoff produced a dazzling body of work, while training a generation of innovators—students like Marston Morse and Hassler Whitney, who forged novel pathways in topology and other areas. Influential figures from around the world soon flocked to Harvard, some overcoming great challenges to pursue their elected calling.

A History in Sum elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.

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The History of Statistics
The Measurement of Uncertainty before 1900
Stephen M. Stigler
Harvard University Press, 1986

This magnificent book is the first comprehensive history of statistics from its beginnings around 1700 to its emergence as a distinct and mature discipline around 1900. Stephen M. Stigler shows how statistics arose from the interplay of mathematical concepts and the needs of several applied sciences including astronomy, geodesy, experimental psychology, genetics, and sociology. He addresses many intriguing questions: How did scientists learn to combine measurements made under different conditions? And how were they led to use probability theory to measure the accuracy of the result? Why were statistical methods used successfully in astronomy long before they began to play a significant role in the social sciences? How could the introduction of least squares predate the discovery of regression by more than eighty years? On what grounds can the major works of men such as Bernoulli, De Moivre, Bayes, Quetelet, and Lexis be considered partial failures, while those of Laplace, Galton, Edgeworth, Pearson, and Yule are counted as successes? How did Galton’s probability machine (the quincunx) provide him with the key to the major advance of the last half of the nineteenth century?

Stigler’s emphasis is upon how, when, and where the methods of probability theory were developed for measuring uncertainty in experimental and observational science, for reducing uncertainty, and as a conceptual framework for quantitative studies in the social sciences. He describes with care the scientific context in which the different methods evolved and identifies the problems (conceptual or mathematical) that retarded the growth of mathematical statistics and the conceptual developments that permitted major breakthroughs.

Statisticians, historians of science, and social and behavioral scientists will gain from this book a deeper understanding of the use of statistical methods and a better grasp of the promise and limitations of such techniques. The product of ten years of research, The History of Statistics will appeal to all who are interested in the humanistic study of science.

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A History of the Circle
Mathematical Reasoning and the Physical Universe
Zebrowski, Ernest
Rutgers University Press, 2000

The concept of the circle is ubiquitous. It can be described mathematically, represented physically, and employed technologically. The circle is an elegant, abstract form that has been transformed by humans into tangible, practical forms to make our lives easier.

And yet no one has ever discovered a true mathematical circle. Rainbows are fuzzy; car tires are flat on the bottom, and even the most precise roller bearings have measurable irregularities. Ernest Zebrowski, Jr., discusses why investigations of the circle have contributed enormously to our current knowledge of the physical universe. Beginning with the ancient mathematicians and culminating in twentieth-century theories of space and time, the mathematics of the circle has pointed many investigators in fruitful directions in their quests to unravel nature’s secrets. Johannes Kepler, for example, triggered a scientific revolution in 1609 when he challenged the conception of the earth’s circular motion around the sun. Arab and European builders instigated the golden age of mosque and cathedral building when they questioned the Roman structural arches that were limited to geometrical semicircles.

Throughout his book, Zebrowski emphasizes the concepts underlying these mathematicians’ calculations, and how these concepts are linked to real-life examples. Substantiated by easy-to-follow mathematical reasoning and clear illustrations, this accessible book presents a novel and interesting discussion of the circle in technology, culture, history, and science.

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How Our Days Became Numbered
Risk and the Rise of the Statistical Individual
Dan Bouk
University of Chicago Press, 2015
Long before the age of "Big Data" or the rise of today's "self-quantifiers," American capitalism embraced "risk"--and proceeded to number our days. Life insurers led the way, developing numerical practices for measuring individuals and groups, predicting their fates, and intervening in their futures. Emanating from the gilded boardrooms of Lower Manhattan and making their way into drawing rooms and tenement apartments across the nation, these practices soon came to change the futures they purported to divine.

How Our Days Became Numbered tells a story of corporate culture remaking American culture--a story of intellectuals and professionals in and around insurance companies who reimagined Americans' lives through numbers and taught ordinary Americans to do the same. Making individuals statistical did not happen easily. Legislative battles raged over the propriety of discriminating by race or of smoothing away the effects of capitalism's fluctuations on individuals. Meanwhile, debates within companies set doctors against actuaries and agents, resulting in elaborate, secretive systems of surveillance and calculation.

Dan Bouk reveals how, in a little over half a century, insurers laid the groundwork for the much-quantified, risk-infused world that we live in today. To understand how the financial world shapes modern bodies, how risk assessments can perpetuate inequalities of race or sex, and how the quantification and claims of risk on each of us continue to grow, we must take seriously the history of those who view our lives as a series of probabilities to be managed.
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