Harvard University Press

Mathematics

The Applicability of Mathematics as a Philosophical Problem: Mark Steiner; This book analyzes the different ways in which mathematics is applicable to the physical sciences. Mark Steiner distinguishes among the semantic problems that arise from the use of mathematics in logical deduction; the metaphysical problems that arise from the alleged gap between mathematical objects and the physical world; the descriptive problems that arise from the use of mathematics to describe nature; and the epistemological problems that arise from the use of mathematics to discover those very descriptions.

Bigger than Chaos: Understanding Complexity through Probability; Michael Strevens; Many complex systems--from immensely complicated ecosystems to minute assemblages of molecules--surprise us with their simple behavior. Consider, for instance, the snowflake, in which a great number of water molecules arrange themselves in patterns with six-way symmetry. How is it that molecules moving seemingly at random become organized according to the simple, six-fold rule? How do the comings, goings, meetings, and eatings of individual animals add up to the simple dynamics of ecosystem populations? More generally, how does complex and seemingly capricious microbehavior generate stable, predictable macrobehavior? In this book, Michael Strevens aims to explain how simplicity can coexist with, indeed be caused by, the tangled interconnections between a complex system's many parts.

A Course in Econometrics: Arthur S. Goldberger; This book is an excellent choice for first year graduate econometrics courses because it provides a solid foundation in statistical reasoning in a manner that is both clear and concise. It addresses a number of issues that are of central importance to developing practitioners and theorists alike and achieves this in a fairly nontechnical manner...The topics addressed here are rarely given such a thorough treatment in econometrics textbooks. For example, in discussions of bivariate distributions, Goldberger points out that two uncorrelated normal random variables may not be independent, since a nonnormal bivariate distribution can generate normal marginal distributions. Other texts typically leave readers with the impression that two uncorrelated normal random variables are independent without reference to their joint distribution...A Course in Econometrics is rigorous, it makes students think hard about important issues, and it avoids a cookbook approach. For these reasons, I strongly recommend it as a basic text for all first year graduate econometrics courses.
--Douglas G. Steigerwald, Econometric Theory

The Equations: Icons of Knowledge; Sander Bais; In this beautifully designed book, the equations that govern our world unfold in all their formal grace--and their deeper meaning as core symbols of our civilization. The renowned Dutch physicist Sander Bais has produced a book that delves into the details of seventeen equations that form the very basis of what we know of the universe today.

Frege's Philosophy of Mathematics: Edited and with an Introduction by William Demopoulos; This collection of essays addresses three main developments in recent work on Frege's philosophy of mathematics: the emerging interest in the intellectual background to his logicism; the rediscovery of Frege's theorem; and the reevaluation of the mathematical content of The Basic Laws of Arithmetic.

Game Theory: Analysis of Conflict; Roger B. Myerson; Eminently suited to classroom use as well as individual study, Roger Myerson's introductory text provides a clear and thorough examination of the models, solution concepts, results, and methodological principles of noncooperative and cooperative game theory. Myerson introduces, clarifies, and synthesizes the extraordinary advances made in the subject over the past fifteen years, presents an overview of decision theory, and comprehensively reviews the development of the fundamental models.

Game Theory and the Law: Douglas Baird
Robert Gertner
Randal Picker; The most comprehensive and encompassing treatment of this approach...[This] is the first nontechnical, modern introduction to how (noncooperative) game theory can be applied specifically to legal analysis...Game Theory and the Law is a user-friendly analysis of concrete, numerical examples, rather than a theoretical presentation of abstract concepts. The authors introduce and explain, with actual legal cases or hypotheticals, the salient issues of modern game theory. This breadth of coverage is remarkable. This is not just a textbook; it is also something of a research monograph, introducing many new models attributable to the authors alone.
--Peter H. Huang, Jurimetrics Journal

The History of Statistics: The Measurement of Uncertainty before 1900; Stephen M. Stigler; An exceptionally searching, almost loving, study of the relevant inspirations and aberrations of its principal characters James Bernoulli, de Moivre, Bayes, Laplace, Gauss, Quetelet, Lexis, Galton, Edgeworth, and Pearson, not neglecting a grand supporting cast...The definitive record of an intellectual Golden Age, an overoptimistic climb to a height not to be maintained.
--M. Stone, Science

Introductory Econometrics: Arthur S. Goldberger; Arthur Goldberger, an outstanding researcher and teacher of econometrics, views the subject as a tool of empirical inquiry rather than as a collection of arcane procedures. This is his textbook for the standard undergraduate econometrics course, with prerequisites of a semester course in statistics and one in differential calculus.

Knots: Mathematics with a Twist; Alexei Sossinsky
Giselle Weiss, Translator; Ornaments and icons, symbols of complexity or evil, aesthetically appealing and endlessly useful in everyday ways, knots are also the object of mathematical theory, used to unravel ideas about the topological nature of space. In recent years knot theory has been brought to bear on the study of equations describing weather systems, mathematical models used in physics, and even, with the realization that DNA sometimes is knotted, molecular biology.

Logic, Logic, and Logic: George Boolos
Introduction and Afterword by Richard Jeffrey
John P. Burgess, Volume editor; George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems.

The Politics of Large Numbers: A History of Statistical Reasoning; Alain Desrosières
Camille Naish, Translator; In this sophisticated study of the history of statistics, which begins with probability theory in the seventeenth century, Alain Desrosières shows how the evolution of modern statistics has been inextricably bound up with the knowledge and power of governments. He traces the complex reciprocity between modern governments and the mathematical artifacts that both dictate the duties of the state and measure its successes.

Randomness: Deborah J. Bennett; From the ancients' first readings of the innards of birds to your neighbor's last bout with the state lottery, humankind has put itself into the hands of chance. This book is aimed at the trouble with trying to learn about probability. A story of the misconceptions and difficulties civilization overcame in progressing toward probabilistic thinking, Randomness is also a skillful account of what makes the science of probability so daunting in our own day.

Statistics on the Table: The History of Statistical Concepts and Methods; Stephen M. Stigler; This lively collection of essays examines statistical ideas with an ironic eye for their essence and what their history can tell us for current disputes. The topics range from seventeenth-century medicine and the circulation of blood, to the cause of the Great Depression and the effect of the California gold discoveries of 1848 upon price levels, to the determinations of the shape of the Earth and the speed of light, to the meter of Virgil's poetry and the prediction of the Second Coming of Christ.

Understanding the Infinite: Shaughan Lavine; How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge.