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Author: Fernando Zalamea Publisher: National Geographic Books ISBN: 0956775012 Category : Philosophy Languages : en Pages : 0
Book Description
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830–1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the “real mathematics” of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the “making of mathematics.” In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.
Author: Fernando Zalamea Publisher: National Geographic Books ISBN: 0956775012 Category : Philosophy Languages : en Pages : 0
Book Description
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830–1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the “real mathematics” of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the “making of mathematics.” In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.
Author: Ignacio Bello Publisher: Houghton Mifflin ISBN: 9780618347520 Category : Mathematics Languages : en Pages : 0
Book Description
Topics in Contemporary Mathematics, 8/e, is uniquely designed to help students see math at work in the contemporary world by presenting problem solving in purposeful and meaningful contexts.
Author: Tony Brown Publisher: Springer Nature ISBN: 3030551008 Category : Education Languages : en Pages : 165
Book Description
This book by-passes both psychology and sociology to present an original social theory centered on seeing mathematical learning by everyone as an intrinsic dimension of how mathematics develops as a field in support of human activity. Here, mathematics is defined by how we collectively talk about it. Drawing on psychoanalytic theory, the student is seen as participating in the renewal of mathematics through their contributions to our collective gaze on mathematics as the field responds to ever new demands. As such learning takes a critical stance on the standard initiations into current practices often promoted by formal education. In the field of mathematics education, researchers have moved from psychology where individual students were seen as following natural paths of development through existing mathematical knowledge, to socio-cultural models predicated on students being initiated into the human world and understood through the reflective gazes this world has of itself, such as those found in comparisons of student learning in different countries. This book addresses the domain, purpose and functioning of contemporary research in mathematics education and is an original contribution to this theme. The book is aimed at a mathematics education research audience. It continues a dialogue with existing publications, seen widely as a cutting edge and will also be of interest to students and practitioners in the fields of qualitative research, social theory and psychology.
Author: Alexey Stakhov Publisher: World Scientific ISBN: 9812775838 Category : Mathematics Languages : en Pages : 745
Book Description
Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."
Author: Robert Brechner Publisher: Cengage Learning ISBN: 9780357026441 Category : Business & Economics Languages : en Pages : 0
Book Description
Gain a strong understand of today's key mathematical concepts and learn how to use math for success in business today with Brechner/Bergeman's CONTEMPORARY MATHEMATICS FOR BUSINESS AND CONSUMERS, 9E. This reader-friendly approach helps you overcome any math anxiety and confidently master mathematical concepts. A proven step-by-step instructional model allows you to progress through one topic at a time without being intimidated or overwhelmed. Learning features connect the topics you're learning to the latest business news and even provide helpful personal money tips. You can immediately practice concepts and hone essential skills with more than 2,000 exercises. To model solution strategies, Jump Start problems introduce new topics and provide worked-out solutions to help you begin on your own assignments with confidence. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Author: Ignacio Bello Publisher: Cengage Learning ISBN: 9780538737791 Category : Mathematics Languages : en Pages : 1056
Book Description
Written for the Math for Liberal Arts course, TOPICS IN CONTEMPORARY MATHEMATICS helps students see math at work in the world by presenting problem solving in purposeful and meaningful contexts. Many of the problems in the text demonstrate how math relates to subjects -- such as sociology, psychology, business, and technology -- that generally interest students. This Enhanced Edition includes instant access to WebAssign, the most widely-used and reliable homework system. WebAssign presents over 500 problems, as well as links to relevant textbook sections, that help students grasp the concepts needed to succeed in this course. As an added bonus, the Start Smart Guide has been bound into this text. This guide contains instructions to help students learn the basics of WebAssign quickly. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Author: Samuel J. Lomonaco Publisher: American Mathematical Soc. ISBN: 0821821407 Category : Computers Languages : en Pages : 322
Book Description
This book is a collection of papers given by invited speakers at the first AMS Special Session on Quantum Computation and Information held at the January 2000 Annual Meeting of the AMS in Washington, DC. The papers in this volume give readers a broad introduction to the many mathematical research challenges posed by the new and emerging field of quantum computation and quantum information. Of particular interest is a long paper by Lomonaco and Kauffman discussing mathematical and computational aspects of the so-called hidden subgroup algorithm. This book is intended to help readers recognize that, as a result of this new field of quantum information science, mathematical research opportunities abound in such diverse mathematical fields as algebraic coding theory, algebraic geometry, algebraic topology, communication theory, control theory, cryptography, differential geometry, differential topology, dynamical systems, game theory, group theory, information theory, number theory, operator theory, robotics, theory of computation, mathematical logic, mathematical physics, and more. It is hoped that this book will act as a catalyst to encourage members of the mathematical community to take advantage of the many mathematical research opportunities arising from the ``grand challenge'' of Quantum Information Science. This book is the companion volume to Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium, PSAPM/58, Volume 58 in the Proceedings of Symposia in Applied Mathematics series.
Author: Jürgen Jost Publisher: Springer Science & Business Media ISBN: 3662034468 Category : Mathematics Languages : en Pages : 304
Book Description
This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.
Author: Fernando Zalamea
Author: Fernando Zalamea
Author: 
Author: Ignacio Bello
Author: Tony Brown
Author: Lizhen Ji
Author: Alexey Stakhov
Author: Robert Brechner
Author: Ignacio Bello
Author: Samuel J. Lomonaco
Author: Jürgen Jost