On The Relation Between Mathematics Natural Sciences And Scientific Inquiry
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On the Relation between Mathematics, Natural Sciences, And Scientific Inquiry by V. Christianto,Florentin Smarandache Pdf
In this article, we will shortly review a few old thoughts and recent thoughts on the relation between Mathematics and the Natural Sciences. Of course, the classic references to this open problem will include Wigner’s paper (1964); a more recent review article is Darvas (2008). But it appears that this issue is partly on the domain of natural philosophy and also philosophy of inquiry. Therefore we will begin with a review on some known thoughts of Kant, Bacon, Popper, etc.
On the Relation between Mathematics, Natural Sciences, And Scientific Inquiry by V. Christianto,Florentin Smarandache Pdf
In this article, we will shortly review a few old thoughts and recent thoughts on the relation between Mathematics and the Natural Sciences. Of course, the classic references to this open problem will include Wigner’s paper (1964); a more recent review article is Darvas (2008). But it appears that this issue is partly on the domain of natural philosophy and also philosophy of inquiry. Therefore we will begin with a review on some known thoughts of Kant, Bacon, Popper, etc.
Philosophy of Mathematics and Natural Science by Hermann Weyl Pdf
When mathematician Hermann Weyl decided to write a book on philosophy, he faced what he referred to as "conflicts of conscience"--the objective nature of science, he felt, did not mesh easily with the incredulous, uncertain nature of philosophy. Yet the two disciplines were already intertwined. In Philosophy of Mathematics and Natural Science, Weyl examines how advances in philosophy were led by scientific discoveries--the more humankind understood about the physical world, the more curious we became. The book is divided into two parts, one on mathematics and the other on the physical sciences. Drawing on work by Descartes, Galileo, Hume, Kant, Leibniz, and Newton, Weyl provides readers with a guide to understanding science through the lens of philosophy. This is a book that no one but Weyl could have written--and, indeed, no one has written anything quite like it since.
Mathematics and the Natural Sciences by Francis Bailly,Giuseppe Longo Pdf
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.
Scientific Inquiry and Nature of Science by Lawrence Flick,N.G. Lederman Pdf
This book synthesizes current literature and research on scientific inquiry and the nature of science in K-12 instruction. Its presentation of the distinctions and overlaps of inquiry and nature of science as instructional outcomes are unique in contemporary literature. Researchers and teachers will find the text interesting as it carefully explores the subtleties and challenges of designing curriculum and instruction for integrating inquiry and nature of science.
The Application of Mathematics to the Sciences of Nature by Claudio Pellegrini,Paola Cerrai,Paolo Freguglia Pdf
The historical and epistemological reflection on the applications of mathematical techniques to the Sciences of Nature - physics, biology, chemistry, and geology - today generates attention and interest because of the increasing use of mathematical models in all sciences and their high level of sophistication. The goal of the meeting and the papers collected in this proceedings volume is to give physicists, biologists, mathematicians, and historians of science the opportunity to share information on their work and reflect on the and mathematical models are used in the natural sciences today and in way mathematics the past. The program of the workshop combines the experience of those working on current scientific research in many different fields with the historical analysis of previous results. We hope that some novel interdisciplinary, philosophical, and epistemological considerations will follow from the two aspects of the workshop, the historical and the scientific· This proceedings includes papers presented at the meeting and some of the results of the discussions that took place during the workshop. We wish to express our gratitude to Sergio Monteiro for all his work, which has been essential for the successful publication of these proceedings. We also want to thank the editors of Kluwer AcademidPlenum Publishers for their patience and constant help, and in particular Beth Kuhne and Roberta Klarreich. Our thanks to the fallowing institutions: -Amministrazione Comunale di Arcidosso -Comunita Montana del Monte Amiata ·Center for the History of Physics, UCLA -Centre F.
Multispace & Multistructure. Neutrosophic Transdisciplinarity (100 Collected Papers of Science) by Florentin Smarandache Pdf
This is an eclectic tome of 100 papers in various fields of sciences, alphabetically listed, such as: astronomy, biology, calculus, chemistry, computer programming codification, economics and business and politics, education and administration, game theory, geometry, graph theory,information fusion, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, psychology, quantum physics, scientific research methods, and statistics ¿ containing 800 pages.It was my preoccupation and collaboration as author, co-author, translator, or co-translator, and editor with many scientists from around the world for long time. Many ideas from this book are to be developed and expanded in future explorations.
National Research Council,Division on Engineering and Physical Sciences,Board on Mathematical Sciences and Their Applications,Committee on the Mathematical Sciences in 2025
Author : National Research Council,Division on Engineering and Physical Sciences,Board on Mathematical Sciences and Their Applications,Committee on the Mathematical Sciences in 2025 Publisher : National Academies Press Page : 223 pages File Size : 46,8 Mb Release : 2013-06-13 Category : Mathematics ISBN : 9780309284578
The Mathematical Sciences in 2025 by National Research Council,Division on Engineering and Physical Sciences,Board on Mathematical Sciences and Their Applications,Committee on the Mathematical Sciences in 2025 Pdf
The mathematical sciences are part of nearly all aspects of everyday life-the discipline has underpinned such beneficial modern capabilities as Internet search, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. The Mathematical Sciences in 2025 examines the current state of the mathematical sciences and explores the changes needed for the discipline to be in a strong position and able to maximize its contribution to the nation in 2025. It finds the vitality of the discipline excellent and that it contributes in expanding ways to most areas of science and engineering, as well as to the nation as a whole, and recommends that training for future generations of mathematical scientists should be re-assessed in light of the increasingly cross-disciplinary nature of the mathematical sciences. In addition, because of the valuable interplay between ideas and people from all parts of the mathematical sciences, the report emphasizes that universities and the government need to continue to invest in the full spectrum of the mathematical sciences in order for the whole enterprise to continue to flourish long-term.
National Research Council,Commission on Physical Sciences, Mathematics, and Applications,Committee on Strengthening the Linkages Between the Sciences and the Mathematical Sciences
Author : National Research Council,Commission on Physical Sciences, Mathematics, and Applications,Committee on Strengthening the Linkages Between the Sciences and the Mathematical Sciences Publisher : National Academies Press Page : 134 pages File Size : 44,7 Mb Release : 2000-04-05 Category : Mathematics ISBN : 9780309183628
Strengthening the Linkages Between the Sciences and the Mathematical Sciences by National Research Council,Commission on Physical Sciences, Mathematics, and Applications,Committee on Strengthening the Linkages Between the Sciences and the Mathematical Sciences Pdf
Over three hundred years ago, Galileo is reported to have said, "The laws of nature are written in the language of mathematics." Often mathematics and science go hand in hand, with one helping develop and improve the other. Discoveries in science, for example, open up new advances in statistics, computer science, operations research, and pure and applied mathematics which in turn enabled new practical technologies and advanced entirely new frontiers of science. Despite the interdependency that exists between these two disciplines, cooperation and collaboration between mathematical scientists and scientists have only occurred by chance. To encourage new collaboration between the mathematical sciences and other fields and to sustain present collaboration, the National Research Council (NRC) formed a committee representing a broad cross-section of scientists from academia, federal government laboratories, and industry. The goal of the committee was to examine the mechanisms for strengthening interdisciplinary research between mathematical sciences and the sciences, with a strong focus on suggesting the most effective mechanisms of collaboration. Strengthening the Linkages Between the Sciences and the Mathematical Sciences provides the findings and recommendations of the committee as well as case studies of cross-discipline collaboration, the workshop agenda, and federal agencies that provide funding for such collaboration.
National Research Council,Center for Science, Mathematics, and Engineering Education,Committee on Development of an Addendum to the National Science Education Standards on Scientific Inquiry
Author : National Research Council,Center for Science, Mathematics, and Engineering Education,Committee on Development of an Addendum to the National Science Education Standards on Scientific Inquiry Publisher : National Academies Press Page : 223 pages File Size : 42,6 Mb Release : 2000-05-03 Category : Education ISBN : 9780309064767
Inquiry and the National Science Education Standards by National Research Council,Center for Science, Mathematics, and Engineering Education,Committee on Development of an Addendum to the National Science Education Standards on Scientific Inquiry Pdf
Humans, especially children, are naturally curious. Yet, people often balk at the thought of learning scienceâ€"the "eyes glazed over" syndrome. Teachers may find teaching science a major challenge in an era when science ranges from the hardly imaginable quark to the distant, blazing quasar. Inquiry and the National Science Education Standards is the book that educators have been waiting forâ€"a practical guide to teaching inquiry and teaching through inquiry, as recommended by the National Science Education Standards. This will be an important resource for educators who must help school boards, parents, and teachers understand "why we can't teach the way we used to." "Inquiry" refers to the diverse ways in which scientists study the natural world and in which students grasp science knowledge and the methods by which that knowledge is produced. This book explains and illustrates how inquiry helps students learn science content, master how to do science, and understand the nature of science. This book explores the dimensions of teaching and learning science as inquiry for K-12 students across a range of science topics. Detailed examples help clarify when teachers should use the inquiry-based approach and how much structure, guidance, and coaching they should provide. The book dispels myths that may have discouraged educators from the inquiry-based approach and illuminates the subtle interplay between concepts, processes, and science as it is experienced in the classroom. Inquiry and the National Science Education Standards shows how to bring the standards to life, with features such as classroom vignettes exploring different kinds of inquiries for elementary, middle, and high school and Frequently Asked Questions for teachers, responding to common concerns such as obtaining teaching supplies. Turning to assessment, the committee discusses why assessment is important, looks at existing schemes and formats, and addresses how to involve students in assessing their own learning achievements. In addition, this book discusses administrative assistance, communication with parents, appropriate teacher evaluation, and other avenues to promoting and supporting this new teaching paradigm.
Scientific Research in Information Systems by Jan Recker Pdf
This book introduces higher-degree research students and early career academics to scientific research as occurring in the field of information systems and adjacent fields, such as computer science, management science, organization science, and software engineering. Instead of focusing primarily on research methods as many other textbooks do, it covers the entire research process, from start to finish, placing particular emphasis on understanding the cognitive and behavioural aspects of research, such as motivation, modes of inquiry, theorising, planning for research, planning for publication, and ethical challenges in research. Comprehensive but also succinct and compact, the book guides beginning researchers in their quest to do scholarly work and to assist them in developing their own answers and strategies over the course of their work. Jan Recker explains in this book the fundamental concepts that govern scientific research and then moves on to introduce the basic steps every researcher undertakes: choosing research questions, developing theory, building a research design, employing research methods, and finally writing academic papers. He also covers essentials of ethical conduct of scientific research. This second edition contains major updates on all these elements plus significant expansions on relevant research methods such as design research and computational methods, a rewritten and extended chapter on theory development, and expansions to the chapters on research methods, scientific publishing, and research ethics. A companion website provides pedagogical materials and instructions for using this book in teaching.
National Academies of Sciences, Engineering, and Medicine,Policy and Global Affairs,Committee on Science, Engineering, Medicine, and Public Policy,Board on Research Data and Information,Division on Engineering and Physical Sciences,Committee on Applied and Theoretical Statistics,Board on Mathematical Sciences and Analytics,Division on Earth and Life Studies,Nuclear and Radiation Studies Board,Division of Behavioral and Social Sciences and Education,Committee on National Statistics,Board on Behavioral, Cognitive, and Sensory Sciences,Committee on Reproducibility and Replicability in Science
Author : National Academies of Sciences, Engineering, and Medicine,Policy and Global Affairs,Committee on Science, Engineering, Medicine, and Public Policy,Board on Research Data and Information,Division on Engineering and Physical Sciences,Committee on Applied and Theoretical Statistics,Board on Mathematical Sciences and Analytics,Division on Earth and Life Studies,Nuclear and Radiation Studies Board,Division of Behavioral and Social Sciences and Education,Committee on National Statistics,Board on Behavioral, Cognitive, and Sensory Sciences,Committee on Reproducibility and Replicability in Science Publisher : National Academies Press Page : 257 pages File Size : 46,8 Mb Release : 2019-10-20 Category : Science ISBN : 9780309486163
Reproducibility and Replicability in Science by National Academies of Sciences, Engineering, and Medicine,Policy and Global Affairs,Committee on Science, Engineering, Medicine, and Public Policy,Board on Research Data and Information,Division on Engineering and Physical Sciences,Committee on Applied and Theoretical Statistics,Board on Mathematical Sciences and Analytics,Division on Earth and Life Studies,Nuclear and Radiation Studies Board,Division of Behavioral and Social Sciences and Education,Committee on National Statistics,Board on Behavioral, Cognitive, and Sensory Sciences,Committee on Reproducibility and Replicability in Science Pdf
One of the pathways by which the scientific community confirms the validity of a new scientific discovery is by repeating the research that produced it. When a scientific effort fails to independently confirm the computations or results of a previous study, some fear that it may be a symptom of a lack of rigor in science, while others argue that such an observed inconsistency can be an important precursor to new discovery. Concerns about reproducibility and replicability have been expressed in both scientific and popular media. As these concerns came to light, Congress requested that the National Academies of Sciences, Engineering, and Medicine conduct a study to assess the extent of issues related to reproducibility and replicability and to offer recommendations for improving rigor and transparency in scientific research. Reproducibility and Replicability in Science defines reproducibility and replicability and examines the factors that may lead to non-reproducibility and non-replicability in research. Unlike the typical expectation of reproducibility between two computations, expectations about replicability are more nuanced, and in some cases a lack of replicability can aid the process of scientific discovery. This report provides recommendations to researchers, academic institutions, journals, and funders on steps they can take to improve reproducibility and replicability in science.
Scientific Inquiry in Mathematics - Theory and Practice by Andrzej Sokolowski Pdf
This valuable resource provides an overview of recent research and strategies in developing and applying modelling to promote practice-based research in STEM education. In doing so, it bridges barriers across academic disciplines by suggesting activities that promote integration of qualitative science concepts with the tools of mathematics and engineering. The volume’s three parts offer a comprehensive review, by 1) Presenting a conceptual background of how scientific inquiry can be induced in mathematics classes considering recommendations of prior research, 2) Collecting case studies that were designed using scientific inquiry process designed for math classes, and 3) Exploring future possibilities and directions for the research included within. Among the topics discussed: · STEM education: A platform for multidisciplinary learning. · Teaching and learning representations in STEM. · Formulating conceptual framework for multidisciplinary STEM modeling. · Exploring function continuity in context. · Exploring function transformations using a dynamic system. Scientific Inquiry in Mathematics - Theory and Practice delivers hands-on and concrete strategies for effective STEM teaching in practice to educators within the fields of mathematics, science, and technology. It will be of interest to practicing and future mathematics teachers at all levels, as well as teacher educators, mathematics education researchers, and undergraduate and graduate mathematics students interested in research based methods for integrating inquiry-based learning into STEM classrooms.
Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram and Neutrosophic Degree of Paradoxicity by Florentin Smarandache Pdf
This book is a collection of articles, notes, reviews, blogs and abstracts on Physics. Some are published for the first time here, some were previously published in journals, and revised here. We approach a novel form of plasma, Unmatter Plasma. The electron-positron beam plasma was generated in the laboratory in the beginning of 2015. This experimental fact shows that unmatter, a new form of matter that is formed by matter and antimatter bind together (mathematically predicted a decade ago) really exists. Further, we generalize the Lorentz Contraction Factor for the case when the lengths are moving at an oblique angle with respect to the motion direction, and show that the angles of the moving relativistic objects are distorted. Then, using the Oblique-Length Contraction Factor, we show several trigonometric relations between distorted and original angles of moving object lengths in the Special Theory of Relativity. We also discuss some paradoxes which we call “neutrosophic” since they are based on indeterminacy (or neutrality, i.e. neither true nor false), which is the third component in neutrosophic logic. We generalize the Venn diagram to a Neutrosophic Diagram, which deals with vague, inexact, ambiguous, ill-defined ideas, statements, notions, entities with unclear borders. We define the neutrosophic truth table, then we introduce two neutrosophic operators (neuterization and antonymization operators), and give many classes of neutrosophic paradoxes. Other topics addressed in this book are: neutrosophic physics as a new field of research, neutrosophic numbers in physics, neutrosophic degree of paradoxicity, unparticle and unmatter, multispace and multistructure, nucleon clusters, and others.
