THIS **BOOK IS AVAILABLE ON AMAZON** / By modeling pedagogical scenarios as directed geometrical graphs and proposing an associated modeling language, this book describes how rich learning activities, often designed for small classes, can be scaled up for use with thousands of participants. With the vertices of these graphs representing learning activities and the edges capturing the pedagogical relationship between activities, individual, team, and class-wide activities are integrated into a consistent whole. The workflow mechanisms modeled in the graphs enable the construction of scenarios that are richer than those currently implemented in MOOCs. The cognitive states of learners in two consecutive activities feed a transition matrix, which encapsulates the probability of succeeding in the second activity, based on success in the former. This transition matrix is summarized by a numerical value, which is used as the weight of the edge. This pedagogical framework is connected to stochastic models, with the goal of making learning analytics more appealing for data scientists. However, the proposed modeling language is not only useful in learning technologies, it also allows researchers in learning sciences to formally describe the structure of any lesson, from an elementary school lesson with 20 students to an online course with 20,000 participants.

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*Circles Disturbed* brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier--"Don't disturb my circles"--words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds--stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities.

A book unlike any other, *Circles Disturbed* delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more.

In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.

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The sign outside the conservative, white church in the small southern U.S. town announces that the church is part of the Episcopal Church--of Rwanda. In *Anglican Communion in Crisis*, Miranda Hassett tells the fascinating story of how a new alliance between conservative American Episcopalians and African Anglicans is transforming conflicts between American Episcopalians--especially over homosexuality--into global conflicts within the Anglican church.

In the mid-1990s, conservative American Episcopalians and Anglican leaders from Africa and other parts of the Southern Hemisphere began to forge ties in opposition to the American Episcopal Church's perceived liberalism and growing toleration of homosexuality. This resulted in dozens of American Episcopal churches submitting to the authority of African bishops.

Based on wide research, interviews with key participants and observers, and months Hassett spent in a southern U.S. parish of the Episcopal Church of Rwanda and in Anglican communities in Uganda, *Anglican Communion in Crisis* is the first anthropological examination of the coalition between American Episcopalians and African Anglicans. The book challenges common views--that the relationship between the Americans and Africans is merely one of convenience or even that the Americans bought the support of the Africans. Instead, Hassett argues that their partnership is a deliberate and committed movement that has tapped the power and language of globalization in an effort to move both the American Episcopal Church and the worldwide Anglican Communion to the right.

In *Reinventing Discovery*, Michael Nielsen argues that we are living at the dawn of the most dramatic change in science in more than 300 years. This change is being driven by powerful new cognitive tools, enabled by the internet, which are greatly accelerating scientific discovery. There are many books about how the internet is changing business or the workplace or government. But this is the first book about something much more fundamental: how the internet is transforming the nature of our collective intelligence and how we understand the world.

*Reinventing Discovery* tells the exciting story of an unprecedented new era of networked science. We learn, for example, how mathematicians in the Polymath Project are spontaneously coming together to collaborate online, tackling and rapidly demolishing previously unsolved problems. We learn how 250,000 amateur astronomers are working together in a project called Galaxy Zoo to understand the large-scale structure of the Universe, and how they are making astonishing discoveries, including an entirely new kind of galaxy. These efforts are just a small part of the larger story told in this book--the story of how scientists are using the internet to dramatically expand our problem-solving ability and increase our combined brainpower.

This is a book for anyone who wants to understand how the online world is revolutionizing scientific discovery today--and why the revolution is just beginning.

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The emigration of mathematicians from Europe during the Nazi era signaled an irrevocable and important historical shift for the international mathematics world. *Mathematicians Fleeing from Nazi Germany* is the first thoroughly documented account of this exodus. In this greatly expanded translation of the 1998 German edition, Reinhard Siegmund-Schultze describes the flight of more than 140 mathematicians, their reasons for leaving, the political and economic issues involved, the reception of these emigrants by various countries, and the emigrants' continuing contributions to mathematics. The influx of these brilliant thinkers to other nations profoundly reconfigured the mathematics world and vaulted the United States into a new leadership role in mathematics research.

Based on archival sources that have never been examined before, the book discusses the preeminent emigrant mathematicians of the period, including Emmy Noether, John von Neumann, Hermann Weyl, and many others. The author explores the mechanisms of the expulsion of mathematicians from Germany, the emigrants' acculturation to their new host countries, and the fates of those mathematicians forced to stay behind. The book reveals the alienation and solidarity of the emigrants, and investigates the global development of mathematics as a consequence of their radical migration.

An in-depth yet accessible look at mathematics both as a scientific enterprise and human endeavor, *Mathematicians Fleeing from Nazi Germany* provides a vivid picture of a critical chapter in the history of international science.

Based on extensive research in Sanskrit sources, *Mathematics in India* chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic scientific traditions. Plofker shows that Indian mathematics appears not as a disconnected set of discoveries, but as a lively, diverse, yet strongly unified discipline, intimately linked to other Indian forms of learning.

Far more than in other areas of the history of mathematics, the literature on Indian mathematics reveals huge discrepancies between what researchers generally agree on and what general readers pick up from popular ideas. This book explains with candor the chief controversies causing these discrepancies--both the flaws in many popular claims, and the uncertainties underlying many scholarly conclusions. Supplementing the main narrative are biographical resources for dozens of Indian mathematicians; a guide to key features of Sanskrit for the non-Indologist; and illustrations of manuscripts, inscriptions, and artifacts. *Mathematics in India* provides a rich and complex understanding of the Indian mathematical tradition.

**Author's note: The concept of "computational positivism" in Indian mathematical science, mentioned on p. 120, is due to Prof. Roddam Narasimha and is explored in more detail in some of his works, including "The Indian half of Needham's question: some thoughts on axioms, models, algorithms, and computational positivism" (*Interdisciplinary Science Reviews* 28, 2003, 1-13).

Although political and legal institutions are essential to any nation's economic development, the forces that have shaped these institutions are poorly understood. Drawing on rich evidence about the development of the American states from the mid-nineteenth to the late twentieth century, this book documents the mechanisms through which geographical and historical conditions--such as climate, access to water transportation, and early legal systems--impacted political and judicial institutions and economic growth.

The book shows how a state's geography and climate influenced whether elites based their wealth in agriculture or trade. States with more occupationally diverse elites in 1860 had greater levels of political competition in their legislature from 1866 to 2000. The book also examines the effects of early legal systems. Because of their colonial history, thirteen states had an operational civil-law legal system prior to statehood. All of these states except Louisiana would later adopt common law. By the late eighteenth century, the two legal systems differed in their balances of power. In civil-law systems, judiciaries were subordinate to legislatures, whereas in common-law systems, the two were more equal. Former civil-law states and common-law states exhibit persistent differences in the structure of their courts, the retention of judges, and judicial budgets. Moreover, changes in court structures, retention procedures, and budgets occur under very different conditions in civil-law and common-law states.

*The Evolution of a Nation* illustrates how initial geographical and historical conditions can determine the evolution of political and legal institutions and long-run growth.

In today's unpredictable and chaotic world, we look to science to provide certainty and answers--and often blame it when things go wrong. *The Blind Spot* reveals why our faith in scientific certainty is a dangerous illusion, and how only by embracing science's inherent ambiguities and paradoxes can we truly appreciate its beauty and harness its potential.

Crackling with insights into our most perplexing contemporary dilemmas, from climate change to the global financial meltdown, this book challenges our most sacredly held beliefs about science, technology, and progress. At the same time, it shows how the secret to better science can be found where we least expect it--in the uncertain, the ambiguous, and the inevitably unpredictable. William Byers explains why the subjective element in scientific inquiry is in fact what makes it so dynamic, and deftly balances the need for certainty and rigor in science with the equally important need for creativity, freedom, and downright wonder. Drawing on an array of fascinating examples--from Wall Street's overreliance on algorithms to provide certainty in uncertain markets, to undecidable problems in mathematics and computer science, to Georg Cantor's paradoxical but true assertion about infinity--Byers demonstrates how we can and must learn from the existence of blind spots in our scientific and mathematical understanding.

*The Blind Spot* offers an entirely new way of thinking about science, one that highlights its strengths and limitations, its unrealized promise, and, above all, its unavoidable ambiguity. It also points to a more sophisticated approach to the most intractable problems of our time.

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.

*Reproducing Athens* examines the role of romantic comedy, particularly the plays of Menander, in defending democratic culture and transnational polis culture against various threats during the initial and most fraught period of the Hellenistic Era.

Menander's romantic comedies--which focus on ordinary citizens who marry for love--are most often thought of as entertainments devoid of political content. Against the view, Susan Lape argues that Menander's comedies are explicitly political. His nationalistic comedies regularly conclude by performing the laws of democratic citizen marriage, thereby promising the generation of new citizens. His transnational comedies, on the other hand, defend polis life against the impinging Hellenistic kingdoms, either by transforming their representatives into proper citizen-husbands or by rendering them ridiculous, romantic losers who pose no real threat to citizen or city.

In elaborating the political work of romantic comedy, this book also demonstrates the importance of gender, kinship, and sexuality to the making of democratic civic ideology. Paradoxically, by championing democratic culture against various Hellenistic outsiders, comedy often resists the internal status and gender boundaries on which democratic culture was based. Comedy's ability to reproduce democratic culture in scandalous fashion exposes the logic of civic inclusion produced by the contradictions in Athens's desperately politicized gender system.

Combining careful textual analysis with an understanding of the context in which Menander wrote, *Reproducing Athens* profoundly changes the way we read his plays and deepens our understanding of Athenian democratic culture.

In 1969, Princeton physicist Gerard O'Neill began looking outward to space colonies as the new frontier for humanity's expansion. A decade later, Eric Drexler, an MIT-trained engineer, turned his attention to the molecular world as the place where society's future needs could be met using self-replicating nanoscale machines. These modern utopians predicted that their technologies could transform society as humans mastered the ability to create new worlds, undertook atomic-scale engineering, and, if truly successful, overcame their own biological limits. *The Visioneers* tells the story of how these scientists and the communities they fostered imagined, designed, and popularized speculative technologies such as space colonies and nanotechnologies.

Patrick McCray traces how these visioneers blended countercultural ideals with hard science, entrepreneurship, libertarianism, and unbridled optimism about the future. He shows how they built networks that communicated their ideas to writers, politicians, and corporate leaders. But the visioneers were not immune to failure--or to the lures of profit, celebrity, and hype. O'Neill and Drexler faced difficulty funding their work and overcoming colleagues' skepticism, and saw their ideas co-opted and transformed by Timothy Leary, the scriptwriters of *Star Trek*, and many others. Ultimately, both men struggled to overcome stigma and ostracism as they tried to unshackle their visioneering from pejorative labels like "fringe" and "pseudoscience."

*The Visioneers* provides a balanced look at the successes and pitfalls they encountered. The book exposes the dangers of promotion--oversimplification, misuse, and misunderstanding--that can plague exploratory science. But above all, it highlights the importance of radical new ideas that inspire us to support cutting-edge research into tomorrow's technologies.

Some images inside the book are unavailable due to digital copyright restrictions.

]]>Modern warfare is almost always multilateral to one degree or another, requiring countries to cooperate as allies or coalition partners. Yet as the war in Afghanistan has made abundantly clear, multilateral cooperation is neither straightforward nor guaranteed. Countries differ significantly in what they are willing to do and how and where they are willing to do it. Some refuse to participate in dangerous or offensive missions. Others change tactical objectives with each new commander. Some countries defer to their commanders while others hold them to strict account.

*NATO in Afghanistan* explores how government structures and party politics in NATO countries shape how battles are waged in the field. Drawing on more than 250 interviews with senior officials from around the world, David Auerswald and Stephen Saideman find that domestic constraints in presidential and single-party parliamentary systems--in countries such as the United States and Britain respectively--differ from those in countries with coalition governments, such as Germany and the Netherlands. As a result, different countries craft different guidelines for their forces overseas, most notably in the form of military caveats, the often-controversial limits placed on deployed troops.

Providing critical insights into the realities of alliance and coalition warfare, *NATO in Afghanistan* also looks at non-NATO partners such as Australia, and assesses NATO's performance in the 2011 Libyan campaign to show how these domestic political dynamics are by no means unique to Afghanistan.

9/11 and its aftermath have shown that our ideas about what constitutes sovereign power lag dangerously behind the burgeoning claims to rights and recognition within and across national boundaries. New configurations of sovereignty are at the heart of political and cultural transformations globally. *Sovereign Bodies* shifts the debate on sovereign power away from territoriality and external recognition of state power, toward the shaping of sovereign power through the exercise of violence over human bodies and populations. In this volume, sovereign power, whether exercised by a nation-state or by a local despotic power or community, is understood and scrutinized as something tentative and unstable whose efficacy depends less on formal rules than on repeated acts of violence.

Following the editors' introduction are fourteen essays by leading scholars from around the globe that analyze cultural meanings of sovereign power and violence, as well as practices of citizenship and belonging--in South Africa, Peru, India, Mexico, Cyprus, Norway, and also among transnational Chinese and Indian populations. Sovereign Bodies enriches our understanding of power and sovereignty in the postcolonial world and in "the West" while opening new conceptual fields in the anthropology of politics. The contributors are Ana María Alonso, Lars Buur, Partha Chatterjee, Jean Comaroff and John L. Comaroff, Oivind Fuglerud, Thomas Blom Hansen, Barry Hindess, Steffen Jensen, Achille Mbembe, Aihwa Ong, Finn Stepputat, Simon Turner, Peter van der Veer, and Yael Navaro-Yashin.

]]>Combining literary and philosophical analysis, this study defends an utterly innovative reading of the early history of poetics. It is the first to argue that there is a distinctively Socratic view of poetry and the first to connect the Socratic view of poetry with earlier literary tradition.

Literary theory is usually said to begin with Plato's famous critique of poetry in the Republic. Grace Ledbetter challenges this entrenched assumption by arguing that Plato's earlier dialogues Ion, Protagoras, and Apology introduce a distinctively Socratic theory of poetry that responds polemically to traditional poets as rival theorists. Ledbetter tracks the sources of this Socratic response by introducing separate readings of the poetics implicit in the poetry of Homer, Hesiod, and Pindar. Examining these poets' theories from a new angle that uncovers their literary, rhetorical, and political aims, she demonstrates their decisive influence on Socratic thinking about poetry.

The Socratic poetics Ledbetter elucidates focuses not on censorship, but on the interpretation of poetry as a source of moral wisdom. This philosophical approach to interpreting poetry stands at odds with the poets' own theories--and with the Sophists' treatment of poetry. Unlike the Republic's focus on exposing and banishing poetry's irrational and unavoidably corrupting influence, Socrates' theory includes poetry as subject matter for philosophical inquiry within an examined life.

Reaching back into what has too long been considered literary theory's prehistory, Ledbetter advances arguments that will redefine how classicists, philosophers, and literary theorists think about Plato's poetics.

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Since the very birth of democracy in ancient Greece, the simple act of voting has given rise to mathematical paradoxes that have puzzled some of the greatest philosophers, statesmen, and mathematicians. *Numbers Rule* traces the epic quest by these thinkers to create a more perfect democracy and adapt to the ever-changing demands that each new generation places on our democratic institutions.

In a sweeping narrative that combines history, biography, and mathematics, George Szpiro details the fascinating lives and big ideas of great minds such as Plato, Pliny the Younger, Ramon Llull, Pierre Simon Laplace, Thomas Jefferson, Alexander Hamilton, John von Neumann, and Kenneth Arrow, among many others. Each chapter in this riveting book tells the story of one or more of these visionaries and the problem they sought to overcome, like the Marquis de Condorcet, the eighteenth-century French nobleman who demonstrated that a majority vote in an election might not necessarily result in a clear winner. Szpiro takes readers from ancient Greece and Rome to medieval Europe, from the founding of the American republic and the French Revolution to today's high-stakes elective politics. He explains how mathematical paradoxes and enigmas can crop up in virtually any voting arena, from electing a class president, a pope, or prime minister to the apportionment of seats in Congress.

*Numbers Rule* describes the trials and triumphs of the thinkers down through the ages who have dared the odds in pursuit of a just and equitable democracy.

Löwenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theory--that is, the part of logic that concerns the relationship between formal theories and their models. However, while the original proofs of other, comparably significant theorems are well understood, this is not the case with Löwenheim's theorem. For example, the very result that scholars attribute to Löwenheim today is not the one that Skolem--a logician raised in the algebraic tradition, like Löwenheim--appears to have attributed to him. In *The Birth of Model Theory*, Calixto Badesa provides both the first sustained, book-length analysis of Löwenheim's proof and a detailed description of the theoretical framework--and, in particular, of the algebraic tradition--that made the theorem possible.

Badesa's three main conclusions amount to a completely new interpretation of the proof, one that sharply contradicts the core of modern scholarship on the topic. First, Löwenheim did not use an infinitary language to prove his theorem; second, the functional interpretation of Löwenheim's normal form is anachronistic, and inappropriate for reconstructing the proof; and third, Löwenheim did not aim to prove the theorem's weakest version but the stronger version Skolem attributed to him. This book will be of considerable interest to historians of logic, logicians, philosophers of logic, and philosophers of mathematics.

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Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. *Spin Glasses and Complexity* offers the most concise, engaging, and accessible introduction to the subject, fully explaining what spin glasses are, why they are important, and how they are opening up new ways of thinking about complexity.

This one-of-a-kind guide to spin glasses begins by explaining the fundamentals of order and symmetry in condensed matter physics and how spin glasses fit into--and modify--this framework. It then explores how spin-glass concepts and ideas have found applications in areas as diverse as computational complexity, biological and artificial neural networks, protein folding, immune response maturation, combinatorial optimization, and social network modeling.

Providing an essential overview of the history, science, and growing significance of this exciting field, S*pin Glasses and Complexity* also features a forward-looking discussion of what spin glasses may teach us in the future about complex systems. This is a must-have book for students and practitioners in the natural and social sciences, with new material even for the experts.

Roughly half the world's population speaks languages derived from a shared linguistic source known as Proto-Indo-European. But who were the early speakers of this ancient mother tongue, and how did they manage to spread it around the globe? Until now their identity has remained a tantalizing mystery to linguists, archaeologists, and even Nazis seeking the roots of the Aryan race. *The Horse, the Wheel, and Language* lifts the veil that has long shrouded these original Indo-European speakers, and reveals how their domestication of horses and use of the wheel spread language and transformed civilization.

Linking prehistoric archaeological remains with the development of language, David Anthony identifies the prehistoric peoples of central Eurasia's steppe grasslands as the original speakers of Proto-Indo-European, and shows how their innovative use of the ox wagon, horseback riding, and the warrior's chariot turned the Eurasian steppes into a thriving transcontinental corridor of communication, commerce, and cultural exchange. He explains how they spread their traditions and gave rise to important advances in copper mining, warfare, and patron-client political institutions, thereby ushering in an era of vibrant social change. Anthony also describes his fascinating discovery of how the wear from bits on ancient horse teeth reveals the origins of horseback riding.

*The Horse, the Wheel, and Language* solves a puzzle that has vexed scholars for two centuries--the source of the Indo-European languages and English--and recovers a magnificent and influential civilization from the past.

Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics.

These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished.

The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation.

]]>Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity.

The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time.

Aimed at upper-level undergraduates of moderate analytical background, *Three Views of Logic* will be useful in a variety of classroom settings.

- Gives an exceptionally broad view of logic
- Treats traditional logic in a modern format
- Presents relevance logic with applications
- Provides an ideal text for a variety of one-semester upper-level undergraduate courses