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The essays in this book explore the ancient affinity between the mathematical and the aesthetic, focusing on the fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine the ways in which the aesthetic is ever present in mathematical thinking and contributes to the growth and value of mathematical knowledge. This book includes the following essays: • A Historical Gaze at the Mathematical Aesthetic, by Nathalie Sinclair and David Pimm • Aesthetics for the Working Mathematician, by Jonathan M. Borwein • Beauty and Truth in Mathematics, by Doris Schattschneider • Experiencing Meanings in Geometry, by David W. Henderson and Daina Taimina • The Aesthetic Sensibilities of Mathematicians, by Nathalie Sinclair • The Meaning of Pattern, by Martin Schiralli • Mathematics, Aesthetics and Being Human, by William Higginson • Mechanism and Magic in the Psychology of Dynamic Geometry, by R. Nicholas Jackiw • Drawing on the Image in Mathematics and Art, by David Pimm • Sensible Objects, by Dick Tahta • Aesthetics and the ‘Mathematical Mind’, by David Pimm and Nathalie Sinclair.
7.01 --- 72.01 --- Mathematics. --- Aesthetics. --- 51 --- Beautiful, The --- Beauty --- Esthetics --- Taste (Aesthetics) --- Philosophy --- Art --- Criticism --- Literature --- Proportion --- Symmetry --- Math --- Science --- Kunst (esthetica) --- Kunstesthetica --- Architectuur (esthetica) --- Architectuuresthetica --- Mathematica --- Wiskunde --- Psychology --- Aesthetics --- Mathematics --- Radio broadcasting Aesthetics
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Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.
Banach spaces. --- Electronic books. -- local. --- Functional analysis. --- Banach spaces --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematics. --- Topology. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functions of complex variables --- Generalized spaces --- Topology --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear
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Bioceramics: Properties, Characterizations, and Applications is a general introduction to the uses of ceramics and glasses in the human body for the purposes of aiding, healing, correcting deformities, and restoring lost function. With over 35 years experience, the author developed the text as an outgrowth of a course for senior and beginning graduate students in biomedical engineering and will emphasize the fundamentals and applications in modern implant fabrication, and will also deal with tissue engineering scaffolds made of ceramics. Organized as a textbook for the student needing to acquire the core competencies, it will meet the demands of advanced undergraduate or graduate coursework in bioceramics, biomaterials, biomedical engineering, and biophysics. Key Features: Detailed illustrations Example problems to provide the student with hands-on experience with concepts Extensive appendices and tutorial materials on new developments including expanded treatment of ceramic materials and implants Tissue engineering and regenerative medicine Detailed references for further reading About the Author: Joon Park is a Professor in the Biomedical Engineering Department at the College of Engineering at the University of Iowa.
Engineering. --- Biomedical Engineering. --- Biomaterials. --- Biophysics/Biomedical Physics. --- Ceramics, Glass, Composites, Natural Methods. --- Surfaces and Interfaces, Thin Films. --- Biomedical engineering. --- Surfaces (Physics). --- Ingénierie --- Génie biomédical --- Surfaces (Physique) --- Biomedical materials. --- Ceramics in medicine. --- Ceramics in medicine --- Biomedical materials --- Health & Biological Sciences --- Biomedical Engineering --- Biocompatible materials --- Biomaterials --- Medical materials --- Medicine --- Materials --- Biophysics. --- Biological physics. --- Industrial engineering. --- Production engineering. --- Thin films. --- Industrial and Production Engineering. --- Biophysics and Biological Physics. --- Surfaces. --- Films, Thin --- Solid film --- Solid state electronics --- Solids --- Surfaces (Technology) --- Coatings --- Thick films --- Surface phenomena --- Friction --- Surfaces (Physics) --- Tribology --- Biomedical engineering --- Biocompatibility --- Prosthesis --- Clinical engineering --- Medical engineering --- Bioengineering --- Biophysics --- Engineering --- Manufacturing engineering --- Process engineering --- Industrial engineering --- Mechanical engineering --- Management engineering --- Simplification in industry --- Value analysis (Cost control) --- Biological physics --- Biology --- Medical sciences --- Physics --- Construction --- Industrial arts --- Technology --- Surfaces --- Algebraic topology --- Congresses. --- Congresses --- Topologie algébrique --- Congrès --- Biomedical Engineering and Bioengineering. --- Biological and Medical Physics, Biophysics. --- Ceramics, Glass, Composites, Natural Materials. --- Surface chemistry --- Ceramics. --- Glass. --- Composites (Materials). --- Composite materials. --- Materials—Surfaces. --- Bioartificial materials --- Hemocompatible materials --- Composites (Materials) --- Multiphase materials --- Reinforced solids --- Solids, Reinforced --- Two phase materials --- Amorphous substances --- Ceramics --- Glazing --- Ceramic technology --- Industrial ceramics --- Keramics --- Building materials --- Chemistry, Technical --- Clay --- Biomaterials (Biomedical materials) --- Topologie algébrique
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