Mathematics And The Natural Sciences

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Mathematics And The Natural Sciences

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Author : Francis Bailly
language : en
Publisher: World Scientific
Release Date : 2011

Mathematics And The Natural Sciences written by Francis Bailly and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.

The book aims at the identification of the organising concepts of some physical and biological phenomena, by means of an analysis of the foundations of mathematics and of physics. This is done in the perspective of unifying phenomena, of bringing different conceptual universes into dialog. The analysis of the role of “order” and of symmetries in the foundations of mathematics is linked to the main invariants and principles, among which the geodesic principle (a consequence of symmetries), which govern and confer unity to the various physical theories. Moreover, we attempt to understand causal structures, a central element of physical intelligibility, in terms of symmetries and their breakings. The importance of the mathematical tool is also highlighted, enabling us to grasp the differences in the models for physics and biology which are proposed by continuous and discrete mathematics, such as computational simulations. A distinction between principles of (conceptual) construction and principles of proofs, both in physics and in mathematics, guides this part of the work.As for biology, being particularly difficult and not as thoroughly examined at a theoretical level, we propose a “unification by concepts”, an attempt which should always precede mathematisation. This constitutes an outline for unification also basing itself upon the highlighting of conceptual differences, of complex points of passage, of technical irreducibilities of one field to another. Indeed, a monist point of view such as ours should not make us blind: we, the living objects, are surely just big bags of molecules or, at least, this is our main metaphysical assumption. The point though is: which theory can help us to better understand these bags of molecules, as they are, indeed, rather “singular”, from the physical point of view. Technically, this singularity is expressed by the notion of “extended criticality”, a notion that logically extends the pointwise critical transitions in physics.

Mathematics For Natural Scientists

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Author : Lev Kantorovich
language : en
Publisher: Springer
Release Date : 2015-10-08

Mathematics For Natural Scientists written by Lev Kantorovich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-08 with Science categories.

This book covers a course of mathematics designed primarily for physics and engineering students. It includes all the essential material on mathematical methods, presented in a form accessible to physics students, avoiding precise mathematical jargon and proofs which are comprehensible only to mathematicians. Instead, all proofs are given in a form that is clear and convincing enough for a physicist. Examples, where appropriate, are given from physics contexts. Both solved and unsolved problems are provided in each section of the book. Mathematics for Natural Scientists: Fundamentals and Basics is the first of two volumes. Advanced topics and their applications in physics are covered in the second volume.

Mathematics And The Natural Sciences The Physical Singularity Of Life

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Author : Giuseppe Longo
language : en
Publisher: World Scientific
Release Date : 2011-03-04

Mathematics And The Natural Sciences The Physical Singularity Of Life written by Giuseppe Longo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-04 with Science categories.

This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics. Our aim is to propose a dialog between different conceptual universes and thus to provide a unification of phenomena. The role of “order” and symmetries in the foundations of mathematics is linked to the main invariants and principles, among them the geodesic principle (a consequence of symmetries), which govern and confer unity to various physical theories. Moreover, an attempt is made to understand causal structures, a central element of physical intelligibility, in terms of both symmetries and symmetry breakings. A distinction between the principles of (conceptual) construction and of proofs, both in physics and in mathematics, guides most of the work.The importance of mathematical tools is also highlighted to clarify differences in the models for physics and biology that are proposed by continuous and discrete mathematics, such as computational simulations.Since biology is particularly complex and not as well understood at a theoretical level, we propose a “unification by concepts” which in any case should precede mathematization. This constitutes an outline for unification also based on highlighting conceptual differences, complex points of passage and technical irreducibilities of one field to another. Indeed, we suppose here a very common monist point of view, namely the view that living objects are “big bags of molecules”. The main question though is to understand which “theory” can help better understand these bags of molecules. They are, indeed, rather “singular”, from the physical point of view. Technically, we express this singularity through the concept of “extended criticality”, which provides a logical extension of the critical transitions that are known in physics. The presentation is mostly kept at an informal and conceptual level./a

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.

Mathematics And Science

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Author : Ronald E Mickens
language : en
Publisher: World Scientific
Release Date : 1990-08-23

Mathematics And Science written by Ronald E Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-08-23 with Mathematics categories.

The purpose of this review volume is to present the opinions of a number of distinguished individuals who have given careful thought as to why mathematics is so “unreasonably effective” when applied to the analysis of the natural sciences.

Philosophy Of Mathematics And Natural Science

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Author : Hermann Weyl
language : en
Publisher: Princeton University Press
Release Date : 2009-05-17

Philosophy Of Mathematics And Natural Science written by Hermann Weyl 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 2009-05-17 with Mathematics categories.

History of mathematics.

Historical Encyclopedia Of Natural And Mathematical Sciences

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Author : Ari Ben-Menahem
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-06

Historical Encyclopedia Of Natural And Mathematical Sciences written by Ari Ben-Menahem 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 2009-03-06 with Biography & Autobiography categories.

The 5800-page Encyclopedia surveys 100 generations of great thinkers, offering 2070 detailed biographies of scientists, engineers, explorers and inventors, who left their mark on the history of science and technology. This six-volume masterwork also includes 380 articles summarizing the time-line of ideas in the leading fields of science, technology, mathematics and philosophy, plus useful tables, figures and photos, and 20 ‘Science Progress Reports’ detailing scientific setbacks. Interspersed throughout are quotations, gathered from the wit and wisdom of sages, savants and scholars throughout the ages from antiquity to modern times. The Encyclopedia represents 20 years’ work by the sole author, Ari Ben-Menahem, of Israel’s Weizmann Institute of Science

Mathematics In Nature

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Author : John Adam
language : en
Publisher: Princeton University Press
Release Date : 2011-10-02

Mathematics In Nature written by John Adam 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 2011-10-02 with Mathematics categories.

From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks. Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.

Mathematical Analysis Of Problems In The Natural Sciences

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Author : Vladimir Zorich
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-11

Mathematical Analysis Of Problems In The Natural Sciences written by Vladimir Zorich 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 2010-10-11 with Mathematics categories.

Based on a two-semester course aimed at illustrating various interactions of "pure mathematics" with other sciences, such as hydrodynamics, thermodynamics, statistical physics and information theory, this text unifies three general topics of analysis and physics, which are as follows: the dimensional analysis of physical quantities, which contains various applications including Kolmogorov's model for turbulence; functions of very large number of variables and the principle of concentration along with the non-linear law of large numbers, the geometric meaning of the Gauss and Maxwell distributions, and the Kotelnikov-Shannon theorem; and, finally, classical thermodynamics and contact geometry, which covers two main principles of thermodynamics in the language of differential forms, contact distributions, the Frobenius theorem and the Carnot-Caratheodory metric. It includes problems, historical remarks, and Zorich's popular article, "Mathematics as language and method."

Evolutionary Equations With Applications In Natural Sciences

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Author : Jacek Banasiak
language : en
Publisher: Springer
Release Date : 2014-11-07

Evolutionary Equations With Applications In Natural Sciences written by Jacek Banasiak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-07 with Mathematics categories.

With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. Truly unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering.