Explorations in Complex and Riemannian Geometry

A Volume Dedicated to Robert E. Greene

Author: Robert Everist Greene,John Bland,Kang-Tae Kim,Steven George Krantz

Publisher: American Mathematical Soc.

ISBN: 0821832735

Category: Mathematics

Page: 325

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This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.

Geometric Function Theory

Explorations in Complex Analysis

Author: Steven G. Krantz

Publisher: Springer Science & Business Media

ISBN: 0817644407

Category: Mathematics

Page: 314

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* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations


Synergetics 2

Further Explorations in the Geometry of Thinking

Author: R. Buckminster Fuller

Publisher: The Estate of R. Buckminster Fuller

ISBN: 0020926405

Category: Architecture

Page: 592

View: 4746

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Synergetics 2 contains a ninety-page index to both volumes. They comprise a single work with the sequence of paragraphs numbered to dovetail in a single integrated narrative. They should eventually be published as a single work eliminating the artificial division into two volumes resulting from the chronology of their composition. E. J. Applewhite, courtesy of the Estate of R. Buckminster Fuller


Explorations in Complex Analysis

Author: Michael A. Brilleslyper,Michael J. Dorff,Jane M. McDougall, James S. Rolf,Lisbeth E. Schaubroek,Richard L. Stankewitz,Kenneth Stephenson

Publisher: MAA

ISBN: 0883857782

Category: Mathematics

Page: 373

View: 8804

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This book is written for mathematics students who have encountered basic complex analysis and want to explore more advanced project and/or research topics. It could be used as (a) a supplement for a standard undergraduate complex analysis course, allowing students in groups or as individuals to explore advanced topics, (b) a project resource for a senior capstone course for mathematics majors, (c) a guide for an advanced student or a small group of students to independently choose and explore an undergraduate research topic, or (d) a portal for the mathematically curious, a hands-on introduction to the beauties of complex analysis. Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation. There are more than 15 Java applets that allow students to explore the research topics without the need for purchasing additional software.


Explorations in Mathematical Physics

The Concepts Behind an Elegant Language

Author: Don Koks

Publisher: Springer Science & Business Media

ISBN: 0387327932

Category: Science

Page: 539

View: 5253

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Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.

Explorations in Topology

Map Coloring, Surfaces and Knots

Author: David Gay

Publisher: Elsevier

ISBN: 0124166407

Category: Mathematics

Page: 332

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Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigations provide opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method," to make conjectures from which theorems emerge. The revised end-of-chapter notes provide historical background to the chapter's ideas, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of projects provides ideas for continued research. Explorations in Topology, Second Edition, enhances upper division courses and is a valuable reference for all levels of students and researchers working in topology. Students begin to solve substantial problems from the start Ideas unfold through the context of a storyline, and students become actively involved The text models the problem-solving process, presents the development of concepts in a natural way, and helps the reader engage with the material

Storytime Mathtime

Math Explorations in Children's Literature

Author: Patricia Satariano

Publisher: Dale Seymour Publication

ISBN: 9780866517324

Category: Education

Page: 166

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Lessons derived from 18 quality children's books -- including Caps for Sale, Millions of Cats, Curious George Rides a Bike, and Cherries and Cherry Pits -- how students how math appears in unexpected places. Through group discussion, cooperative learning, and hands-on experiences, students explore patterns, logic, numbers, geometry, measurement, mathematical language, and graphing.

Bringing the NCTM Standards to Life

Exemplary Practices for Middle School

Author: Yvelyne Germain- Mc Carthy

Publisher: Routledge

ISBN: 1317919793

Category: Education

Page: 208

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This book provides the practical information you need to make the transition from traditional "vocational" education programs to the new approaches to career and technical education. It shows you how to organize your schools around relevant career majors using a variety of evolving school formats such as Career Major programs, Tech Prep programs, Academies, and Magnet Schools.

Explorations in Autism

Author: John Bremner,Shirley Hoxter,Donald Meltzer,Doreen Weddell

Publisher: Karnac Books

ISBN: 178049422X

Category: Psychology

Page: 254

View: 4118

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Explorations in Autism is a turning point in both the understanding of and the clinical approach to autism. The clinical material gradually unveils the geography of the internal mother (which proved crucial for the development of Meltzer's claustrum theory) and allowed him to draft, for the first time in psychoanalysis, a theory of the dimensionality of mental life. The book is a moving journey through the dynamics of the transference- countertransference, revealing what Meltzer calls the essentials of humanity. It should be part of the training of every analyst and I believe it would be a revelation to many philosophers of the mind.


Einführung in die Komplexe Analysis

Elemente der Funktionentheorie

Author: Wolfgang Fischer,Ingo Lieb

Publisher: Springer-Verlag

ISBN: 3834893773

Category: Mathematics

Page: 214

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In den Bachelor-Studiengängen der Mathematik steht für die Komplexe Analysis (Funktionentheorie) oft nur eine einsemestrige 2-stündige Vorlesung zur Verfügung. Dieses Buch eignet sich als Grundlage für eine solche Vorlesung im 2. Studienjahr. Mit einer guten thematischen Auswahl, vielen Beispielen und ausführlichen Erläuterungen gibt dieses Buch eine Darstellung der Komplexen Analysis, die genau die Grundlagen und den wesentlichen Kernbestand dieses Gebietes enthält. Das Buch bietet über diese Grundausbildung hinaus weiteres Lehrmaterial als Ergänzung, sodass es auch für eine 3- oder 4 –stündige Vorlesung geeignet ist. Je nach Hörerkreis kann der Stoff unterschiedlich erweitert werden. So wurden für den „Bachelor Lehramt“ die geometrischen Aspekte der Komplexen Analysis besonders herausgearbeitet.

Geometry from Africa

Mathematical and Educational Explorations

Author: Paulus Gerdes

Publisher: MAA

ISBN: 0883857154

Category: Crafts & Hobbies

Page: 210

View: 4038

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Presents an introduction to the Pythagorean Theorem and other mathematical concepts through the study of Sub-Saharan African craft patterns.

Convex Integration Theory

Solutions to the H-Principle in Geometry and Topology

Author: David Spring

Publisher: Springer Science & Business Media

ISBN: 9783764358051

Category: Mathematics

Page: 212

View: 5359

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This book provides a comprehensive study of convex integration theory in immersion-theoretic topology. Convex integration theory, developed originally by M. Gromov, provides general topological methods for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDE theory and to optimal control theory. Though topological in nature, the theory is based on a precise analytical approximation result for higher order derivatives of functions, proved by M. Gromov. This book is the first to present an exacting record and exposition of all of the basic concepts and technical results of convex integration theory in higher order jet spaces, including the theory of iterated convex hull extensions and the theory of relative h-principles. A second feature of the book is its detailed presentation of applications of the general theory to topics in symplectic topology, divergence free vector fields on 3-manifolds, isometric immersions, totally real embeddings, underdetermined non-linear systems of PDEs, the relaxation theorem in optimal control theory, as well as applications to the traditional immersion-theoretical topics such as immersions, submersions, k-mersions and free maps. The book should prove useful to graduate students and to researchers in topology, PDE theory and optimal control theory who wish to understand the h-principle and how it can be applied to solve problems in their respective disciplines.