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Tarski's World
Revised and Expanded
David Barker-Plummer, Jon Barwise, and John Etchemendy
CSLI, 2004
Tarski’s World is an innovative and exciting method of introducing students to the language of first-order logic. Using the courseware package, students quickly master the meanings of connectives and qualifiers and soon become fluent in the symbolic language at the core of modern logic. The program allows students to build three-dimensional worlds and then describe them in first-order logic. The program, compatible with Macintosh and Windows formats, also contains a unique and effective corrective tool in the form of a game, which methodically leads students back through their errors if they wrongly evaluate the sentences in the constructed worlds.

A brand new feature in this revised and expanded edition is student access to Grade Grinder, an innovative Internet-based grading service that provides accurate and timely feedback to students whenever they need it. Students can submit solutions for the program’s more than 100 exercises to the Grade Grinder for assessment, and the results are returned quickly to the students and optionally to the teacher as well. A web-based interface also allows instructors to manage assignments and grades for their classes.

Intended as a supplement to a standard logic text, Tarski’s World is an essential tool for helping students learn the language of logic.
 
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The Tbilisi Symposium on Logic, Language and Computation
Selected Papers
Edited by Jonathan Ginzburg, Zurab Khasidashvili, Carl Vogel, Jean-Jacques Lévy,
CSLI, 1998
This volume brings together papers from linguists, logicians, and computer scientists from thirteen countries (Armenia, Denmark, France, Georgia, Germany, Israel, Italy, Japan, Poland, Spain, Sweden, UK, and USA). This collection aims to serve as a catalyst for new interdisciplinary developments in language, logic and computation and to introduce new ideas from the expanded European academic community. Spanning a wide range of disciplines, the papers cover such topics as formal semantics of natural language, dynamic semantics, channel theory, formal syntax of natural language, formal language theory, corpus-based methods in computational linguistics, computational semantics, syntactic and semantic aspects of l-calculus, non-classical logics, and a fundamental problem in predicate logic.
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Teaching the Quadrivium
A Guide for Instructors
Peter Ulrickson
Catholic University of America Press, 2023
Reviving an educational tradition involves a double task. A new generation of students must be taught, and at the same time the teachers themselves must learn. This book addresses the teachers who seek to hand on the quadrivium-the four mathematical liberal arts of arithmetic, geometry, music, and astronomy-at the same time as they acquire it. Two components run in parallel throughout the book. The first component is practical. Weekly overviews and daily lesson plans explain how to complete the study of A Brief Quadrivium in the course of a single school year, and suggestions for weekly assessments make it easy to plan tests and monitor student progress. The second component is directed to the continuing education of the teacher. Short essays explore the history, philosophy, and practice of mathematics. The themes of these essays are coordinated with the simultaneous mathematical work being done by students, allowing the teacher to instruct more reflectively. Some users of this book are confident in their grasp of mathematics and natural science. For them, the essays will clarify the unity of mathematical activity over time and reveal the old roots of new developments. Other users of this book, including some parents who school their children at home, find mathematics intimidating. The clear structure of the lesson plans, and the support of the companion essays, give them the confidence to lead students through a demanding but doable course of study. The British mathematician John Edensor Littlewood remarked that one finds in the ancient mathematicians not “clever schoolboys” but rather “Fellows of another College.” This guide invites all teachers of the quadrivium to join the enduring mathematical culture of Littlewood and his predecessors, and to witness for themselves the significance and vitality of a tradition as old as Pythagoras.
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The Theology of Arithmetic
Number Symbolism in Platonism and Early Christianity
Joel Kalvesmaki
Harvard University Press, 2013
In the second century, Valentinians and other gnosticizing Christians used numerical structures and symbols to describe God, interpret the Bible, and frame the universe. In this study of the controversy that resulted, Joel Kalvesmaki shows how earlier neo-Pythagorean and Platonist number symbolism provided the impetus for this theology of arithmetic, and describes the ways in which gnosticizing groups attempted to engage both the Platonist and Christian traditions. He explores the rich variety of number symbolism then in use, among both gnosticizing groups and their orthodox critics, demonstrating how those critics developed an alternative approach to number symbolism that would set the pattern for centuries to come. Arguing that the early dispute influenced the very tradition that inspired it, Kalvesmaki explains how, in the late third and early fourth centuries, numbers became increasingly important to Platonists, who engaged in arithmological constructions and disputes that mirrored the earlier Christian ones.
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Thinking Through Statistics
John Levi Martin
University of Chicago Press, 2018
Simply put, Thinking Through Statistics is a primer on how to maintain rigorous data standards in social science work, and one that makes a strong case for revising the way that we try to use statistics to support our theories. But don’t let that daunt you. With clever examples and witty takeaways, John Levi Martin proves himself to be a most affable tour guide through these scholarly waters.

Martin argues that the task of social statistics isn't to estimate parameters, but to reject false theory. He illustrates common pitfalls that can keep researchers from doing just that using a combination of visualizations, re-analyses, and simulations. Thinking Through Statistics gives social science practitioners accessible insight into troves of wisdom that would normally have to be earned through arduous trial and error, and it does so with a lighthearted approach that ensures this field guide is anything but stodgy.
 
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Timaeus. Critias. Cleitophon. Menexenus. Epistles
Plato
Harvard University Press

On the creation of the world, and the destruction of Atlantis.

Plato, the great philosopher of Athens, was born in 427 BC. In early manhood an admirer of Socrates, he later founded the famous school of philosophy in the grove Academus. Much else recorded of his life is uncertain; that he left Athens for a time after Socrates’ execution is probable; that later he went to Cyrene, Egypt, and Sicily is possible; that he was wealthy is likely; that he was critical of “advanced” democracy is obvious. He lived to be 80 years old. Linguistic tests including those of computer science still try to establish the order of his extant philosophical dialogues, written in splendid prose and revealing Socrates’ mind fused with Plato’s thought.

In Laches, Charmides, and Lysis, Socrates and others discuss separate ethical conceptions. Protagoras, Ion, and Meno discuss whether righteousness can be taught. In Gorgias, Socrates is estranged from his city’s thought, and his fate is impending. The Apology (not a dialogue), Crito, Euthyphro, and the unforgettable Phaedo relate the trial and death of Socrates and propound the immortality of the soul. In the famous Symposium and Phaedrus, written when Socrates was still alive, we find the origin and meaning of love. Cratylus discusses the nature of language. The great masterpiece in ten books, the Republic, concerns righteousness (and involves education, equality of the sexes, the structure of society, and abolition of slavery). Of the six so-called dialectical dialogues Euthydemus deals with philosophy; metaphysical Parmenides is about general concepts and absolute being; Theaetetus reasons about the theory of knowledge. Of its sequels, Sophist deals with not-being; Politicus with good and bad statesmanship and governments; Philebus with what is good. The Timaeus seeks the origin of the visible universe out of abstract geometrical elements. The unfinished Critias treats of lost Atlantis. Unfinished also is Plato’s last work, Laws, a critical discussion of principles of law which Plato thought the Greeks might accept.

The Loeb Classical Library edition of Plato is in twelve volumes.

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Time Warps, String Edits, and Macromolecules
The Theory and Practice of Sequence Comparision
David Sankoff and Joseph Kruskal
CSLI, 1983
Time Warps, String Edits and Macromolecules is a young classic in computational science. The computational perspective is that of sequence processing, in particular the problem of recognizing related sequences. The book is the first, and still best compilation of papers explaining how to measure distance between sequences, and how to compute that measure effectively. This is called string distance, Levenshtein distance, or edit distance. The book contains lucid explanations of the basic techniques; well-annotated examples of applications; mathematical analysis of its computational (algorithmic) complexity; and extensive discussion of the variants needed for weighted measures, timed sequences (songs), applications to continuous data, comparison of multiple sequences and extensions to tree-structures. This theory finds applications in molecular biology, speech recognition, analysis of bird song and error correcting in computer software.
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Topics in Analytic Number Theory
Edited by Sidney W. Graham and Jeffrey D. Vaaler
University of Texas Press, 1985
This collection of research papers, originally published in 1985, brings together twelve articles by distinguished contributors.
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Topics in Geometric Group Theory
Pierre de la Harpe
University of Chicago Press, 2000
In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples.

The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.
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Topics in the Foundations of General Relativity and Newtonian Gravitation Theory
David B. Malament
University of Chicago Press, 2012
In Topics in the Foundations of General Relativity and Newtonian Gravitation Theory, David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and Gödel spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there is no criterion of orbital rotation in general relativity that fully answers to our classical intuitions. Topics is intended for both students and researchers in mathematical physics and philosophy of science.
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The Topological Classification of Stratified Spaces
Shmuel Weinberger
University of Chicago Press, 1994
This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results.

Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III.

This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.
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The Topological Imagination
Spheres, Edges, and Islands
Angus Fletcher
Harvard University Press, 2016

Boldly original and boundary defining, The Topological Imagination clears a space for an intellectual encounter with the shape of human imagining. Joining two commonly opposed domains, literature and mathematics, Angus Fletcher maps the imagination’s ever-ramifying contours and dimensions, and along the way compels us to re-envision our human existence on the most unusual sphere ever imagined, Earth.

Words and numbers are the twin powers that create value in our world. Poetry and other forms of creative literature stretch our ability to evaluate through the use of metaphors. In this sense, the literary imagination aligns with topology, the branch of mathematics that studies shape and space. Topology grasps the quality of geometries rather than their quantifiable measurements. It envisions how shapes can be bent, twisted, or stretched without losing contact with their original forms—one of the discoveries of the eighteenth-century mathematician Leonhard Euler, whose Polyhedron Theorem demonstrated how shapes preserve “permanence in change,” like an aging though familiar face.

The mysterious dimensionality of our existence, Fletcher says, is connected to our inhabiting a world that also inhabits us. Theories of cyclical history reflect circulatory biological patterns; the day-night cycle shapes our adaptive, emergent patterns of thought; the topology of islands shapes the evolution of evolutionary theory. Connecting literature, philosophy, mathematics, and science, The Topological Imagination is an urgent and transformative work, and a profound invitation to thought.

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Torsion-Free Modules
Eben Matlis
University of Chicago Press, 1973
The subject of torsion-free modules over an arbitrary integral domain arises naturally as a generalization of torsion-free abelian groups. In this volume, Eben Matlis brings together his research on torsion-free modules that has appeared in a number of mathematical journals. Professor Matlis has reworked many of the proofs so that only an elementary knowledge of homological algebra and commutative ring theory is necessary for an understanding of the theory.

The first eight chapters of the book are a general introduction to the theory of torsion-free modules. This part of the book is suitable for a self-contained basic course on the subject. More specialized problems of finding all integrally closed D-rings are examined in the last seven chapters, where material covered in the first eight chapters is applied.

An integral domain is said to be a D-ring if every torsion-free module of finite rank decomposes into a direct sum of modules of rank 1. After much investigation, Professor Matlis found that an integrally closed domain is a D-ring if, and only if, it is the intersection of at most two maximal valuation rings.
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The Total Survey Error Approach
A Guide to the New Science of Survey Research
Herbert F. Weisberg
University of Chicago Press, 2005
In 1939, George Gallup's American Institute of Public Opinion published a pamphlet optimistically titled The New Science of Public Opinion Measurement. At the time, though, survey research was in its infancy, and only now, six decades later, can public opinion measurement be appropriately called a science, based in part on the development of the total survey error approach.

Herbert F. Weisberg's handbook presents a unified method for conducting good survey research centered on the various types of errors that can occur in surveys—from measurement and nonresponse error to coverage and sampling error. Each chapter is built on theoretical elements drawn from specific disciplines, such as social psychology and statistics, and follows through with detailed treatments of the specific types of error and their potential solutions. Throughout, Weisberg is attentive to survey constraints, including time and ethical considerations, as well as controversies within the field and the effects of new technology on the survey process—from Internet surveys to those completed by phone, by mail, and in person. Practitioners and students will find this comprehensive guide particularly useful now that survey research has assumed a primary place in both public and academic circles.
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Toward a History of Game Theory, Volume 24
E. Roy Weintraub, ed.
Duke University Press
During the 1940s "game theory" emerged from the fields of mathematics and economics to provide a revolutionary new method of analysis. Today game theory provides a language for discussing conflict and cooperation not only for economists, but also for business analysts, sociologists, war planners, international relations theorists, and evolutionary biologists. Toward a History of Game Theory offers the first history of the development, reception, and dissemination of this crucial theory.

Drawing on interviews with original members of the game theory community and on the Morgenstern diaries, the first section of the book examines early work in game theory. It focuses on the groundbreaking role of the von Neumann-Morgenstern collaborative work, The Theory of Games and Economic Behavior (1944). The second section recounts the reception of this new theory, revealing just how game theory made its way into the literatures of the time and thus became known among relevant communities of scholars. The contributors explore how game theory became a wedge in opening up the social sciences to mathematical tools and use the personal recollections of scholars who taught at Michigan and Princeton in the late 1940s to show why the theory captivated those practitioners now considered to be "giants" in the field. The final section traces the flow of the ideas of game theory into political science, operations research, and experimental economics.

Contributors. Mary Ann Dimand, Robert W. Dimand, Robert J. Leonard, Philip Mirowski, Angela M. O'Rand, Howard Raiffa, Urs Rellstab, Robin E. Rider, William H. Riker, Andrew Schotter, Martin Shubik, Vernon L. Smith

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