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Sam Gillespie's The Mathematics of Novelty presents a new account of Alain Badiou and Gilles Deleuze, identifying conceptual impasses in their philosophical projects and proposing a way through by recourse to the psychoanalysis of Jacques Lacan.
Novelty, Information and Surprise by Günther Palm Pdf
This revised edition offers an approach to information theory that is more general than the classical approach of Shannon. Classically, information is defined for an alphabet of symbols or for a set of mutually exclusive propositions (a partition of the probability space Ω) with corresponding probabilities adding up to 1. The new definition is given for an arbitrary cover of Ω, i.e. for a set of possibly overlapping propositions. The generalized information concept is called novelty and it is accompanied by two concepts derived from it, designated as information and surprise, which describe "opposite" versions of novelty, information being related more to classical information theory and surprise being related more to the classical concept of statistical significance. In the discussion of these three concepts and their interrelations several properties or classes of covers are defined, which turn out to be lattices. The book also presents applications of these concepts, mostly in statistics and in neuroscience.
Author : Michael North Publisher : University of Chicago Press Page : 265 pages File Size : 51,8 Mb Release : 2013-10-18 Category : Literary Criticism ISBN : 9780226077901
If art and science have one thing in common, it’s a hunger for the new—new ideas and innovations, new ways of seeing and depicting the world. But that desire for novelty carries with it a fundamental philosophical problem: If everything has to come from something, how can anything truly new emerge? Is novelty even possible? In Novelty, Michael North takes us on a dazzling tour of more than two millennia of thinking about the problem of the new, from the puzzles of the pre-Socratics all the way up to the art world of the 1960s and ’70s. The terms of the debate, North shows, were established before Plato, and have changed very little since: novelty, philosophers argued, could only arise from either recurrence or recombination. The former, found in nature’s cycles of renewal, and the latter, seen most clearly in the workings of language, between them have accounted for nearly all the ways in which novelty has been conceived in Western history, taking in reformation, renaissance, invention, revolution, and even evolution. As he pursues this idea through centuries and across disciplines, North exhibits astonishing range, drawing on figures as diverse as Charles Darwin and Robert Smithson, Thomas Kuhn and Ezra Pound, Norbert Wiener and Andy Warhol, all of whom offer different ways of grappling with the idea of originality. Novelty, North demonstrates, remains a central problem of contemporary science and literature—an ever-receding target that, in its complexity and evasiveness, continues to inspire and propel the modern. A heady, ambitious intellectual feast, Novelty is rich with insight, a masterpiece of perceptive synthesis.
How the Brain Learns Mathematics by David A. Sousa Pdf
Learn how the brain processes mathematical concepts and why some students develop math anxiety! David A. Sousa discusses the cognitive mechanisms for learning mathematics and the environmental and developmental factors that contribute to mathematics difficulties. This award-winning text examines: Children’s innate number sense and how the brain develops an understanding of number relationships Rationales for modifying lessons to meet the developmental learning stages of young children, preadolescents, and adolescents How to plan lessons in PreK–12 mathematics Implications of current research for planning mathematics lessons, including discoveries about memory systems and lesson timing Methods to help elementary and secondary school teachers detect mathematics difficulties Clear connections to the NCTM standards and curriculum focal points
Transforming Mathematics Instruction by Yeping Li,Edward A. Silver,Shiqi Li Pdf
This book surveys and examines different approaches and practices that contribute to the changes in mathematics instruction, including (1) innovative approaches that bring direct changes in classroom instructional practices, (2) curriculum reforms that introduce changes in content and requirements in classroom instruction, and (3) approaches in mathematics teacher education that aim to improve teachers’ expertise and practices. It also surveys relevant theory and methodology development in studying and assessing mathematics instruction. Classroom instruction is commonly seen as one of the key factors contributing to students’ learning of mathematics, but much remains to be understood about teachers’ instructional practices that lead to the development and enactment of effective classroom instruction, and approaches and practices developed and used to transform classroom instruction in different education systems. Transforming Mathematics Instruction is organized to help readers learn not only from reading individual chapters, but also from reading across chapters and sections to explore broader themes, including: - Identifying what is important in mathematics for teaching and learning emphasized in different approaches; - Exploring how students’ learning is considered and facilitated through different approaches and practices; - Understanding the nature of various approaches that are valued in different systems and cultural contexts; - Probing culturally valued approaches in identifying and evaluating effective instructional practices. The book brings new research and insights into multiple approaches and practices for transforming mathematics instruction to the international community of mathematics education, with 25 chapters and four section prefaces contributed by 56 scholars from 10 different education systems. This rich collection is indispensable reading for mathematics educators, researchers, teacher educators, curriculum developers, and graduate students interested in learning about different instructional practices, approaches for instructional transformation, and research in different education systems. It will help readers to reflect on approaches and practices that are useful for instructional changes in their own education systems, and also inspire them to identify and further explore new areas of research and program development in improving mathematics teaching and learning.
The Mathematics Playbook by John Almarode,Kateri Thunder,Michelle Shin,Douglas Fisher,Nancy Frey Pdf
Your Guide to Engaging and Effective Math Instruction With the latest research on what works best in teaching and learning, The Mathematics Playbook is your comprehensive guide to enhancing mathematics teaching and learning. With a focus on fostering equity and maximizing student learning, the authors provide practical modules that integrate the latest research on effective teaching practices, and answer four critical questions: How do we foster, nurture, and sustain mathematics learning? How do we ensure all learners have equity of access and opportunity? What are the non-negotiables in a high-quality mathematics task? How do we know if learners really "get it"? Through real-life examples and an emphasis on self-assessment and reflection, this playbook empowers you to create engaging and impactful learning experiences in mathematics.
The Joy of Mathematics by Alfred S. Posamentier,Robert Geretschläger,Charles Li,Christian Spreitzer Pdf
Wouldn't it be great if all school teachers (from kindergarten through high school) would share the joy of mathematics with their students, rather than focus only on the prescribed curriculum that will subsequently be tested? This book reveals some of the wonders of mathematics that are often missing from classrooms. Here's your chance to catch up with the math gems you may have missed. Using jargon-free language and many illustrations, the authors--all veteran math educators--explore five areas--arithmetic, algebra, geometry, probability, and the ways in which mathematics can reinforce common sense. Among other things, you'll learn "the rule of 72," which enables you to quickly determine how long it will take your bank account to double its value at a specific interest rate. Other handy techniques include an automatic algorithm for multiplying numbers mentally and a clever application that will allow you to convert from miles to kilometers (or the reverse) mentally. A delightful presentation of geometric novelties reveals relationships that could have made your study of geometry more fun and enlightening. In the area of probability there is a host of interesting examples: from the famous Monty-Hall problem to the counterintuitive probability of two people having the same birthday in a crowded room. Finally, the authors demonstrate how math will make you a better thinker by improving your organizing abilities and providing useful and surprising solutions to common mathematics problems. You'll come away with an appreciation for math you never thought possible and a true appreciation for this "queen of the sciences."
Alain Badiou and the Book of Revelation by Bruce Worthington Pdf
Using many key philosophical concepts based on the work of Alain Badiou, this book outlines the relationship between an event and the emergence of a “truth,” which serves as a helpful organizing principle from which to study the origins of Christianity. Alain Badiou and the Book of Revelation argues that despite what postmodern philosophy says, truths still appear, and their immanent character can be known in the world through a militant subject, one who is willing to declare the consequences of an event that has happened. The second half of the book applies Badiou’s theory of the event to the book of Revelation, a book that draws out radical, even terrifying, consequences from an event “the victory of the Lamb,” particularly in the logic of a new world, and a political body that is to come. Based on several new insights following the completion of Badiou’s “The Immanence of Truths,” the book is a full-length treatment of Badiou’s philosophy to the study of Christian origins and the book of Revelation.
"To mark the English translation of Etre et l'événement as Being and event, ... a special issue on the work of the philosopher Alain Badiou ... [encouraging] contributors to take up the challenge Badiou raises in Being and event ... and deploy his categories in thinking a particular situation - be it political, artistic, scientific or amorous."--Ch. 1.
Educating Prospective Secondary Mathematics Teachers by Marilyn E. Strutchens,Rongjin Huang,Despina Potari,Leticia Losano Pdf
This book highlights innovative approaches to preparing secondary mathematics teachers. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for preparing secondary mathematics teachers, and discusses issues related to their professional and personal growth, such as identity, content knowledge, and pedagogical content knowledge which also includes knowledge of integrating technology into teaching and learning mathematics. Divided into four parts, the book focuses on field experiences, technologies, tools and resources, teacher knowledge, and teacher professional identities. Some of the main threads running through the book are: the importance of university and school partners working together to ensure preservice secondary mathematics teacher’ success in developing pedagogical strategies that lead toward students’ mathematical engagement and achievement; the critical need for preservice secondary mathematics teachers to develop strong content knowledge and pedagogical content knowledge; and the importance of providing opportunities, during pre-service education, for developing prospective teachers ́professional identities.
Historiography of the History of Science in Islamicate Societies by Sonja Brentjes Pdf
This book presents eight papers about important historiographical issues as debated in the history of science in Islamicate societies, the history of science and philosophy of medieval Latin Europe and the history of mathematics as an academic discipline. Six papers deal with themes about the sciences in Islamicate societies from the ninth to the seventeenth centuries, among them novelty, context and decline. Two other papers discuss the historiographical practices of historians of mathematics and other disciplines in the nineteenth and twentieth centuries. The central argument of the collected papers is that in addition and beyond the study of scientific texts and instruments historians of science in Islamicate societies need to pay attention to cultural, material and social aspects that shaped the scientific activities of the authors and makers of such texts and instruments. It is pointed out that the diachronic, de-contextualized comparison between methods and results of scholars from different centuries, regions and cultures often leads to serious distortions of the historical record and is responsible for the long-term neglect of scholarly activities after the so-called "Golden Age". The book will appeal in particular to teachers of history of science in Islamicate societies, to graduate students interested in issues of methodology and to historians of science grappling with the unresolved problems of how think and write about the sciences in concrete societies of the past instead of subsuming all extant texts, instruments, maps and other objects related to the sciences under macro-level concepts like Islam or Latin Europe. (CS 1114).
Deleuze and the History of Mathematics by Simon Duffy Pdf
Gilles Deleuze's engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges provide an opportunity to reconfigure particular philosophical problems - for example, the problem of individuation - and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze's philosophy, as well as addressing the undervalued and often neglected question of the mathematical thinkers who influenced his work. In the wake of Alain Badiou's recent and seemingly devastating attack on the way the relation between mathematics and philosophy is configured in Deleuze's work, Simon B.Duffy offers a robust defence of the structure of Deleuze's philosophy and, in particular, the adequacy of the mathematical problems used in its construction. By reconciling Badiou and Deleuze's seemingly incompatible engagements with mathematics, Duffy succeeds in presenting a solid foundation for Deleuze's philosophy, rebuffing the recent challenges against it.
Creativity in Mathematics and the Education of Gifted Students by Roza Leikin,Abraham Berman,Boris Koichu Pdf
This book breaks through in the field of mathematical creativity and giftedness. It suggests directions for closing the gap between research in the field of mathematics education and research in the field of creativity and giftedness. It also outlines a research agenda for further research and development in the field.
In the context of life sciences, we are constantly confronted with information that possesses precise semantic values and appears essentially immersed in a specific evolutionary trend. In such a framework, Nature appears, in Monod’s words, as a tinkerer characterized by the presence of precise principles of self-organization. However, while Monod was obliged to incorporate his brilliant intuitions into the framework of first-order cybernetics and a theory of information with an exclusively syntactic character such as that defined by Shannon, research advances in recent decades have led not only to the definition of a second-order cybernetics but also to an exploration of the boundaries of semantic information. As H. Atlan states, on a biological level "the function self-organizes together with its meaning". Hence the need to refer to a conceptual theory of complexity and to a theory of self-organization characterized in an intentional sense. There is also a need to introduce, at the genetic level, a distinction between coder and ruler as well as the opportunity to define a real software space for natural evolution. The recourse to non-standard model theory, the opening to a new general semantics, and the innovative definition of the relationship between coder and ruler can be considered, today, among the most powerful theoretical tools at our disposal in order to correctly define the contours of that new conceptual revolution increasingly referred to as metabiology. This book focuses on identifying and investigating the role played by these particular theoretical tools in the development of this new scientific paradigm. Nature "speaks" by means of mathematical forms: we can observe these forms, but they are, at the same time, inside us as they populate our organs of cognition. In this context, the volume highlights how metabiology appears primarily to refer to the growth itself of our instruments of participatory knowledge of the world.