Extending The Frontiers Of Mathematics
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Extending The Frontiers Of Mathematics
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Author : Edward B. Burger
language : en
Publisher:
Release Date : 2014-12-24
Extending The Frontiers Of Mathematics written by Edward B. Burger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-24 with categories.
Theories Of Mathematics Education
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Author : Bharath Sriraman
language : en
Publisher: Springer
Release Date : 2009-10-14
Theories Of Mathematics Education written by Bharath Sriraman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-14 with categories.
This volume highlights theories that influence mathematical education theory building. It also includes newer developments in areas within mathematics education such as complexity theory, neurosciences, modeling, critical theory and networking theories.
Extending The Frontiers Of Mathematics
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Author : Edward B. Burger
language : en
Publisher: Key College Publishing
Release Date : 2007-03-28
Extending The Frontiers Of Mathematics written by Edward B. Burger and has been published by Key College Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-28 with Computers categories.
This book leads students to develop a mature process that will serve them throughout their professional careers, whether inside or outside of mathematics. Its inquiry-based approach to the foundations of mathematics promotes exploration of proofs and other advanced mathematical ideas. The book uses puzzles and patterns, teaches the "prove and extend or disprove and salvage" approach to problems and proofs, and builds mathematical challenge on challenge to boost skills.
Solving Problems In Multiply Connected Domains
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Author : Darren Crowdy
language : en
Publisher: SIAM
Release Date : 2020-04-20
Solving Problems In Multiply Connected Domains written by Darren Crowdy and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-20 with Mathematics categories.
Whenever two or more objects or entities—be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid—interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected. This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author. This monograph is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in applications. The book contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time. Solving Problems in Multiply Connected Domains is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists; the framework it describes finds application in a diverse array of contexts. The book provides a rich source of project material for undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.
Infinity
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Author : Michael Heller
language : en
Publisher: Cambridge University Press
Release Date : 2014-01-02
Infinity written by Michael Heller 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 2014-01-02 with Mathematics categories.
"The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite." - David Hilbert This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world‐renowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than displaying a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: Can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity.
Extending The Frontiers Of Mathematics Instructor Resources
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Author : Edward B. Burger
language : en
Publisher:
Release Date : 2008-07-15
Extending The Frontiers Of Mathematics Instructor Resources written by Edward B. Burger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-15 with categories.
Mathematicians do not know in advance if their assertions are true, so they need to verify assertions with rigorous proofs or produce counterexamples, then attempt to salvage the assertions by transforming them into theorems. Extending the Frontiers of Mathematics: Inquiries into Proof and Argumentation invites readers to experience this progression of mathematical discovery. Burger's informal, humorous writing style and intriguing puzzles engage readers throughout the learning process. The innovative text offers a discovery-based approach that is ideal.
Introduction To The Mathematics Of Medical Imaging
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Author : Charles L. Epstein
language : en
Publisher: SIAM
Release Date : 2008-01-01
Introduction To The Mathematics Of Medical Imaging written by Charles L. Epstein and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most of these modalities. The text uses X-ray computed tomography (X-ray CT) as a 'pedagogical machine' to illustrate important ideas and its extensive discussion of background material makes the more advanced mathematical topics accessible to people with a less formal mathematical education. This new edition contains a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, an improved description of the gridding method, and new sections on both Grangreat's formula and noise analysis in MR-imaging. Mathematical concepts are illuminated with over 200 illustrations and numerous exercises.
Branching Processes
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Author : Krishna B. Athreya
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Branching Processes written by Krishna B. Athreya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The purpose of this book is to give a unified treatment of the limit theory of branching processes. Since the publication of the important book of T E. Harris (Theory of Branching Processes, Springer, 1963) the subject has developed and matured significantly. Many of the classical limit laws are now known in their sharpest form, and there are new proofs that give insight into the results. Our work deals primarily with this decade, and thus has very little overlap with that of Harris. Only enough material is repeated to make the treatment essentially self-contained. For example, certain foundational questions on the construction of processes, to which we have nothing new to add, are not developed. There is a natural classification of branching processes according to their criticality condition, their time parameter, the single or multi-type particle cases, the Markovian or non-Markovian character of the pro cess, etc. We have tried to avoid the rather uneconomical and un enlightening approach of treating these categories independently, and by a series of similar but increasingly complicated techniques. The basic Galton-Watson process is developed in great detail in Chapters I and II.
Mathematics Applied To Deterministic Problems In The Natural Sciences
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Author : C. C. Lin
language : en
Publisher: SIAM
Release Date : 1988-12-01
Mathematics Applied To Deterministic Problems In The Natural Sciences written by C. C. Lin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-12-01 with Mathematics categories.
This book addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences, with exercises that reinforce, test and extend the reader's understanding. It may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers.
Numerical Continuation Methods
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Author : Eugene L. Allgower
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Continuation Methods written by Eugene L. Allgower and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.