Before he died at the age of twenty, shot in a mysterious early-morning duel at the end of May 1832, Evariste Galois created mathematics that changed the direction of algebra. This book contains English translations of almost all the Galois material. The translations are presented alongside a new transcription of the original French and are enhanced by three levels of commentary. An introduction explains the context of Galois' work, the various publications in which it appears, and the vagaries of his manuscripts. Then there is a chapter in which the five mathematical articles published in his lifetime are reprinted. After that come the testamentary letter and the first memoir (in which Galois expounded on the ideas that led to Galois Theory), which are the most famous of the manuscripts. These are followed by the second memoir and other lesser known manuscripts. This book makes available to a wide mathematical and historical readership some of the most exciting mathematics of the first half of the nineteenth century, presented in its original form. The primary aim is to establish a text of what Galois wrote. The details of what he did, the proper evidence of his genius, deserve to be well understood and appreciated by mathematicians as well as historians of mathematics.

*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* This open access book is the product of ICMI Study 22 Task Design in Mathematics Education. The study offers a state-of-the-art summary of relevant research and goes beyond that to develop new insights and new areas of knowledge and study about task design. The authors represent a wide range of countries and cultures and are leading researchers, teachers and designers. In particular, the authors develop explicit understandings of the opportunities and difficulties involved in designing and implementing tasks and of the interfaces between the teaching, researching and designing roles – recognising that these might be undertaken by the same person or by completely separate teams. Tasks generate the activity through which learners meet mathematical concepts, ideas, strategies and learn to use and develop mathematical thinking and modes of enquiry. Teaching includes the selection, modification, design, sequencing, installation, observation and evaluation of tasks. The book illustrates how task design is core to effective teaching, whether the task is a complex, extended, investigation or a small part of a lesson; whether it is part of a curriculum system, such as a textbook, or promotes free standing activity; whether the task comes from published source or is devised by the teacher or the student.

The Violence of Modernity turns to Charles Baudelaire, one of the most canonical figures of literary modernism, in order to reclaim an aesthetic legacy for ethical inquiry and historical critique. Works of modern literature are commonly theorized as symptomatic responses to the trauma of history. In a climate that tends to privilege crisis over critique, Debarati Sanyal argues that it is urgent to rethink literary experience in terms that recall its contestatory potential. Examining Baudelaire's poems afresh, she shifts the focus of critical attention toward an account of modernism as an active engagement with violence, specifically the violence of history in nineteenth-century France. Sanyal analyzes a literary current that uses the traditional hallmarks of modernism—irony, intertextuality, self-reflexivity, and formalism—to challenge the historical violence of modernity. Baudelaire and the committed ironists writing in his wake teach us how to read and resist the violence of history, and thereby to challenge the melancholy tenor of our contemporary "wound culture." In a series of provocative readings, Sanyal presents Baudelaire's poetry as an aesthetic form that contests historical violence through rhetorical strategies of complicity, counterviolence, and critique. The book develops a new account of Baudelaire's significance as a modernist by dislodging him both from his traditional status as a practitioner of "art for art's sake" and from his more recent incarnation as the poet of trauma. Following her extended analysis of Baudelaire's poetry, Sanyal in later chapters considers a number of authors influenced by his strategies—including Rachilde, Virginie Despentes, Albert Camus, and Jean-Paul Sartre—to examine the relevance of their interventions for our current climate of trauma and terror. The result is a study that underscores how Baudelaire's legacy continues to energize literary engagements with the violence of modernity.

*THIS BOOK WILL SOON BECOME AVAILABLE AS OPEN ACCESS BOOK* This book examines multiple facets of language diversity and mathematics education. It features renowned authors from around the world and explores the learning and teaching of mathematics in contexts that include multilingual classrooms, indigenous education, teacher education, blind and deaf learners, new media and tertiary education. Each chapter draws on research from two or more countries to illustrate important research findings, theoretical developments and practical strategies. This open access book examines multiple facets of language diversity

Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

This book provides a comprehensive account of the intentionality of perceptual experience. With special emphasis on vision Searle explains how the raw phenomenology of perception sets the content and the conditions of satisfaction of experience. The central question concerns the relation between the subjective conscious perceptual field and the objective perceptual field. Everything in the objective field is either perceived or can be perceived. Nothing in the subjective field is perceived nor can be perceived precisely because the events in the subjective field consist of the perceivings, whether veridical or not, of the events in the objective field. Searle begins by criticizing the classical theories of perception and identifies a single fallacy, what he calls the Bad Argument, as the source of nearly all of the confusions in the history of the philosophy of perception. He next justifies the claim that perceptual experiences have presentational intentionality and shows how this justifies the direct realism of his account. In the central theoretical chapters, he shows how it is possible that the raw phenomenology must necessarily determine certain form of intentionality. Searle introduces, in detail, the distinction between different levels of perception from the basic level to the higher levels and shows the internal relation between the features of the experience and the states of affairs presented by the experience. The account applies not just to language possessing human beings but to infants and conscious animals. He also discusses how the account relates to certain traditional puzzles about spectrum inversion, color and size constancy and the brain-in-the-vat thought experiments. In the final chapters he explains and refutes Disjunctivist theories of perception, explains the role of unconscious perception, and concludes by discussing traditional problems of perception such as skepticism.