Mathematical Perspectives
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Mathematical Perspectives
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Author : Joseph W. Dauben
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Mathematical Perspectives written by Joseph W. Dauben and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Mathematical Perspectives: Essays on Mathematics and its Historical Development is a collection of 13 biographical essays on the historical advances of science. This collection is originally meant to comprise an issue of the journal Historia Mathematica in honor of Professor Kurt R. Biermann's 60th birthday. This 12-chapter text includes essays on studies and commentaries on the problem of "figures of equal perimeter by various authors in antiquity, including Zenodorus, Theon, and Pappus. Other essays explore the comparison of the areas of polygons with equal perimeter; the concept of function; history of mathematics; the development of mathematical physics in France; and the history of Logicism and Formalism. The remaining chapters deal with essays on an early version of Gauss' Disquisitiones Arithmeticae, ideal numbers, a mathematical-philosophilica theory of probability, and historical examples of problem of number sequence interpolation. This book will be of value to mathematicians, historians, and researchers.
Mathematical Perspectives On Theoretical Physics
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Author : Nirmala Prakash
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-09-02
Mathematical Perspectives On Theoretical Physics written by Nirmala Prakash and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-02 with Science categories.
This book presents the basics of mathematics that are needed for learning the physics of today. It describes briefly the theories of groups and operators, finite- and infinite-dimensional algebras, concepts of symmetry and supersymmetry, and then delineates their relations to theories of relativity and black holes, classical and quantum physics, electroweak fields and Yang-Mills. It concludes with a chapter on (the complex theory of) strings and superstrings and their link to black holes — an idea that fascinates both the physicist and the mathematician. Contents:Complex Functions, Riemann Surfaces and Two-Dimensional Conformal Field Theory (an Introduction)Elements of Group Theory and Group RepresentationsA Primer on OperatorsBasics of Algebras and Related ConceptsInfinite-Dimensional AlgebrasThe Role of Symmetry in Physics and MathematicsAll That's Super — An IntroductionGravitation, Relativity and Black HolesBasics of Quantum TheoryTheory of Yang–Mills and the Yang–Mills–Higgs MechanismStrings and Superstrings (Elementary Aspects) Readership: Upper level undergraduates, graduate students, lecturers and researchers in theoretical physics, mathematical physics, quantum physics and astrophysics as well as Yang-Mills and superstring theory.
Mathematical Perspectives On Neural Networks
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Author : Paul Smolensky
language : en
Publisher: Psychology Press
Release Date : 2013-05-13
Mathematical Perspectives On Neural Networks written by Paul Smolensky and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-13 with Psychology categories.
Recent years have seen an explosion of new mathematical results on learning and processing in neural networks. This body of results rests on a breadth of mathematical background which even few specialists possess. In a format intermediate between a textbook and a collection of research articles, this book has been assembled to present a sample of these results, and to fill in the necessary background, in such areas as computability theory, computational complexity theory, the theory of analog computation, stochastic processes, dynamical systems, control theory, time-series analysis, Bayesian analysis, regularization theory, information theory, computational learning theory, and mathematical statistics. Mathematical models of neural networks display an amazing richness and diversity. Neural networks can be formally modeled as computational systems, as physical or dynamical systems, and as statistical analyzers. Within each of these three broad perspectives, there are a number of particular approaches. For each of 16 particular mathematical perspectives on neural networks, the contributing authors provide introductions to the background mathematics, and address questions such as: * Exactly what mathematical systems are used to model neural networks from the given perspective? * What formal questions about neural networks can then be addressed? * What are typical results that can be obtained? and * What are the outstanding open problems? A distinctive feature of this volume is that for each perspective presented in one of the contributed chapters, the first editor has provided a moderately detailed summary of the formal results and the requisite mathematical concepts. These summaries are presented in four chapters that tie together the 16 contributed chapters: three develop a coherent view of the three general perspectives -- computational, dynamical, and statistical; the other assembles these three perspectives into a unified overview of the neural networks field.
Affect And Mathematics Education
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Author : Markku S. Hannula
language : en
Publisher: Springer
Release Date : 2019-06-03
Affect And Mathematics Education written by Markku S. Hannula and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-03 with Education categories.
This open access book, inspired by the ICME 13 topic study group “Affect, beliefs and identity in mathematics education”, presents the latest trends in research in the area. Following an introduction and a survey chapter providing a concise overview of the state-of-art in the field of mathematics-related affect, the book is divided into three main sections: motivation and values, engagement, and identity in mathematics education. Each section comprises several independent chapters based on original research, as well as a reflective commentary by an expert in the area. Collectively, the chapters present a rich methodological spectrum, from narrative analysis to structural equation modelling. In the final chapter, the editors look ahead to future directions in the area of mathematics-education-related affect. It is a timely resource for all those interested in the interaction between affect and mathematics education.
Mathematical Modelling Education And Sense Making
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Author : Gloria Ann Stillman
language : en
Publisher: Springer Nature
Release Date : 2020-05-14
Mathematical Modelling Education And Sense Making written by Gloria Ann Stillman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-14 with Education categories.
This volume documents on-going research and theorising in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in people’s everyday lives as well as sophisticated new problems for society at large. Mathematical modelling and real world applications are considered as having potential for cultivating sense making in classroom settings. This book focuses on the educational perspective, researching the complexities encountered in effective teaching and learning of real world modelling and applications for sense making is only beginning. All authors of this volume are members of the International Community of Teachers of Mathematical Modelling (ICTMA), the peak research body into researching the teaching and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace.
Viewpoints
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Author : Marc Frantz
language : en
Publisher: Princeton University Press
Release Date : 2011-07-05
Viewpoints written by Marc Frantz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-05 with Mathematics categories.
An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students. Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery. Classroom-tested activities and problem solving Accessible problems that move beyond regular art school curriculum Multiple solutions of varying difficulty and applicability Appropriate for students of all mathematics and art levels Original and exclusive essays by contemporary artists Forthcoming: Instructor's manual (available only to teachers)
New Perspectives On Mathematical Practices
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Author : Bart van Kerkhove
language : en
Publisher: World Scientific
Release Date : 2009
New Perspectives On Mathematical Practices written by Bart van Kerkhove and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.
Mathematical Commentaries In The Ancient World
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Author : Karine Chemla
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
Mathematical Commentaries In The Ancient World written by Karine Chemla and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with History categories.
Comparative analysis of the techniques and procedures of important mathematical commentaries in five ancient cultures from China to Greece.
Anomalous Transport Applications Mathematical Perspectives And Big Data
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Author : Ralf Metzler
language : en
Publisher: Frontiers Media SA
Release Date : 2021-01-08
Anomalous Transport Applications Mathematical Perspectives And Big Data written by Ralf Metzler and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-08 with Science categories.
Free Energy Computations
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Author : Tony Lelivre
language : en
Publisher: World Scientific
Release Date : 2010
Free Energy Computations written by Tony Lelivre and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.
This monograph provides a general introduction to advanced computational methods for free energy calculations, from the systematic and rigorous point of view of applied mathematics. Free energy calculations in molecular dynamics have become an outstanding and increasingly broad computational field in physics, chemistry and molecular biology within the past few years, by making possible the analysis of complex molecular systems. This work proposes a new, general and rigorous presentation, intended both for practitioners interested in a mathematical treatment, and for applied mathematicians interested in molecular dynamics.