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Author : M. M. Schiffer
Publisher :
ISBN 13 : 9780883856000
Total Pages : 207 pages
Book Rating : 4.8/5 (56 download)
Download or read book The Role of Mathematics in Science written by M. M. Schiffer and published by . This book was released on 1984 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Giovanni Boniolo
Publisher : Springer Science & Business Media
ISBN 13 : 1402031076
Total Pages : 244 pages
Book Rating : 4.4/5 (2 download)
Download or read book The Role of Mathematics in Physical Sciences written by Giovanni Boniolo and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Even though mathematics and physics have been related for centuries and this relation appears to be unproblematic, there are many questions still open: Is mathematics really necessary for physics, or could physics exist without mathematics? Should we think physically and then add the mathematics apt to formalise our physical intuition, or should we think mathematically and then interpret physically the obtained results? Do we get mathematical objects by abstraction from real objects, or vice versa? Why is mathematics effective into physics? These are all relevant questions, whose answers are necessary to fully understand the status of physics, particularly of contemporary physics. The aim of this book is to offer plausible answers to such questions through both historical analyses of relevant cases, and philosophical analyses of the relations between mathematics and physics.
Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309284570
Total Pages : 223 pages
Book Rating : 4.3/5 (92 download)
Download or read book The Mathematical Sciences in 2025 written by National Research Council and published by National Academies Press. This book was released on 2013-06-13 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : M. M. Schiffer
Publisher : MAA Press
ISBN 13 :
Total Pages : 228 pages
Book Rating : 4.3/5 (97 download)
Download or read book The Role of Mathematics in Science written by M. M. Schiffer and published by MAA Press. This book was released on 1984 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustrates the many ways in which mathematical methods have helped discovery in science. It is aimed at a group of readers who are interested in mathematics beyond the level of high school. The authors occasionally use some calculus and more intricate arguments. The book should appeal to college students and general readers with some background in mathematics.
Author : Francis Bailly
Publisher : World Scientific
ISBN 13 : 1908977795
Total Pages : 336 pages
Book Rating : 4.9/5 (89 download)
Download or read book Mathematics and the Natural Sciences written by Francis Bailly and published by World Scientific. This book was released on 2011-03-04 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:Mathematical Concepts and Physical ObjectsIncompleteness and Indetermination in Mathematics and PhysicsSpace and Time from Physics to BiologyInvariances, Symmetries, and Symmetry BreakingsCauses and Symmetries: The Continuum and the Discrete in Mathematical ModelingExtended Criticality: The Physical Singularity of Life PhenomenaRandomness and Determination in the Interplay between the Continuum and the DiscreteConclusion: Unification and Separation of Theories, or the Importance of Negative Results Readership: Graduate students and professionals in the fields of natural sciences, biology, computer science, mathematics, and physics. Keywords:Foundations of Mathematics and of Physics;Epistemology;Theoretical BiologyKey Features:This book is an epistemological reflection carried out by two working scientists, a physicist and a mathematician, who focus on biology. They first address a comparative analysis of the founding principles of their own disciplines. On the grounds of a three-fold blend, they then introduce a unique proposal, which does not passively transfer the paradigms of the first two theoretically well-established disciplines, to suggest a novel theoretical framework for the third discipline
Author : Christopher Pincock
Publisher : Oxford University Press
ISBN 13 : 0190208570
Total Pages : 352 pages
Book Rating : 4.1/5 (92 download)
Download or read book Mathematics and Scientific Representation written by Christopher Pincock and published by Oxford University Press. This book was released on 2012-01-13 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a scientific representation. Several different sorts of contributions from mathematics are then articulated. Pincock argues that each contribution can be understood as broadly epistemic, so that what mathematics ultimately contributes to science is best connected with our scientific knowledge. In the second part of the book, Pincock critically evaluates alternative approaches to the role of mathematics in science. These include the potential benefits for scientific discovery and scientific explanation. A major focus of this part of the book is the indispensability argument for mathematical platonism. Using the results of part one, Pincock argues that this argument can at best support a weak form of realism about the truth-value of the statements of mathematics. The book concludes with a chapter on pure mathematics and the remaining options for making sense of its interpretation and epistemology. Thoroughly grounded in case studies drawn from scientific practice, this book aims to bring together current debates in both the philosophy of mathematics and the philosophy of science and to demonstrate the philosophical importance of applications of mathematics.
Author : Richard Courant
Publisher : Oxford University Press, USA
ISBN 13 : 9780195105193
Total Pages : 596 pages
Book Rating : 4.1/5 (51 download)
Download or read book What is Mathematics? written by Richard Courant and published by Oxford University Press, USA. This book was released on 1996 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but not real understanding or greater intellectual independence. The new edition of this classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. "Lucid . . . easily understandable".--Albert Einstein. 301 linecuts.
Author : M. M. Schiffer
Publisher :
ISBN 13 : 9780883856000
Total Pages : 207 pages
Book Rating : 4.8/5 (56 download)
Download or read book The Role of Mathematics in Science written by M. M. Schiffer and published by . This book was released on 1984 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Salomon Bochner Trust
Publisher : Princeton University Press
ISBN 13 : 140085282X
Total Pages : 397 pages
Book Rating : 4.4/5 (8 download)
Download or read book Role of Mathematics in the Rise of Science written by Salomon Bochner Trust and published by Princeton University Press. This book was released on 2014-07-14 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of these essays is the nature and role of mathematics, its growth and spread, and its involvement with ever-wider areas of knowledge. The author attempts to determine the decisive and creative aspects of the abstractness" of mathematics which have made it the dominant intellectual force that it is. He frequently confronts the mathematics and physics of today with the mathematics and physics of the Greeks, which, however renowned, was not yet capable of this abstractness. Originally published in 1966. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Patrick M. Jenlink
Publisher :
ISBN 13 : 9781648027451
Total Pages : 266 pages
Book Rating : 4.0/5 (274 download)
Download or read book Mathematics as the Science of Patterns written by Patrick M. Jenlink and published by . This book was released on 2022 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics as the Science of Patterns: Making the Invisible Visible to Students through Teaching introduces the reader to a collection of thoughtful, research-based works by authors that represent current thinking about mathematics, mathematics education, and the preparation of mathematics teachers. Each chapter focuses on mathematics teaching and the preparation of teachers who will enter classrooms to instruct the next generation of students in mathematics. The value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond. Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep-seated cognitive patterns that both teachers and students bring to the classroom require change. Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Pólya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers' patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students' learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov's Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching.
Author : Barry Cipra
Publisher : American Mathematical Soc.
ISBN 13 : 9780821890431
Total Pages : 108 pages
Book Rating : 4.8/5 (94 download)
Download or read book What's Happening in the Mathematical Sciences written by Barry Cipra and published by American Mathematical Soc.. This book was released on with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.
Author : E. Batschelet
Publisher : Springer Science & Business Media
ISBN 13 : 364296270X
Total Pages : 657 pages
Book Rating : 4.6/5 (429 download)
Download or read book Introduction to Mathematics for Life Scientists written by E. Batschelet and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: A few decades ago mathematics played a modest role in life sciences. Today, however, a great variety of mathematical methods is applied in biology and medicine. Practically every mathematical procedure that is useful in physics, chemistry, engineering, and economics has also found an important application in the life sciences. The past and present training of life scientists does by no means reflect this development. However, the impact ofthe fast growing number of applications of mathematical methods makes it indispensable that students in the life sciences are offered a basic training in mathematics, both on the undergraduate and the graduate level. This book is primarily designed as a textbook for an introductory course. Life scientists may also use it as a reference to find mathematical methods suitable to their research problems. Moreover, the book should be appropriate for self-teaching. It will also be a guide for teachers. Numerous references are included to assist the reader in his search for the pertinent literature.
Author : Carl L. DeVito
Publisher : Berghahn Books
ISBN 13 : 1782380701
Total Pages : 220 pages
Book Rating : 4.7/5 (823 download)
Download or read book Science, Seti, and Mathematics written by Carl L. DeVito and published by Berghahn Books. This book was released on 2013-11-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is as much a part of our humanity as music and art. And it is our mathematics that might be understandable, even familiar, to a distant race and might provide the basis for mutual communication. This book discusses, in a conversational way, the role of mathematics in the search for extraterrestrial intelligence. The author explores the science behind that search, its history, and the many questions associated with it, including those regarding the nature of language and the philosophical/psychological motivation behind this search.
Author : Bob Anderssen
Publisher : Springer
ISBN 13 : 9811009627
Total Pages : 176 pages
Book Rating : 4.8/5 (11 download)
Download or read book The Role and Importance of Mathematics in Innovation written by Bob Anderssen and published by Springer. This book was released on 2016-08-09 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers presented at the “Forum Math-for-Industry 2015” for which the unifying theme was “The Role and Importance of Mathematics in Innovation”, held at the Institute of Mathematics for Industry, Kyushu University, October 26–30, 2015. The theme highlights two key roles that mathematics plays in supporting innovation in science, technology, and daily life, namely, needs-based and idea-based. For the former, mathematics assists with sorting through the possibilities and putting matters on a more rigorous foundation, and for the latter, mathematical models of the possible implementations play a key role. The book gives excellent examples of how mathematics assists with stimulating innovation and, thereby, highlights the importance and relevance of the concept Mathematics_FOR_Industry. The contents of this volume address productive and successful interaction between industry and mathematicians, as well as the cross-fertilization and collaboration that result when mathematics is involved with the advancement of science and technology.
Author : Stacy A. Costa
Publisher : Springer Nature
ISBN 13 : 3030591778
Total Pages : 231 pages
Book Rating : 4.0/5 (35 download)
Download or read book Mathematics (Education) in the Information Age written by Stacy A. Costa and published by Springer Nature. This book was released on 2020-12-10 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together ideas from experts in cognitive science, mathematics, and mathematics education to discuss these issues and to present research on how mathematics and its learning and teaching are evolving in the Information Age. Given the ever-broadening trends in Artificial Intelligence and the processing of information generally, the aim is to assess their implications for how math is evolving and how math should now be taught to a generation that has been reared in the Information Age. It will also look at the ever-spreading assumption that human intelligence may not be unique—an idea that dovetails with current philosophies of mind such as posthumanism and transhumanism. The role of technology in human evolution has become critical in the contemporary world. Therefore, a subgoal of this book is to illuminate how humans now use their sophisticated technologies to chart cognitive and social progress. Given the interdisciplinary nature of the chapters, this will be of interest to all kinds of readers, from mathematicians themselves working increasingly with computer scientists, to cognitive scientists who carry out research on mathematics cognition and teachers of mathematics in a classroom.
Author : Ann Renninger
Publisher :
ISBN 13 : 0935302425
Total Pages : 428 pages
Book Rating : 4.9/5 (353 download)
Download or read book Interest in Mathematics and Science Learning written by Ann Renninger and published by . This book was released on 2015-04-19 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in Mathematics and Science Learning, edited by K. Ann Renninger, Martin Nieswandt, and Suzanne Hidi, is the first volume to assemble findings on the role of interest in mathematics and science learning. As the contributors illuminate across the volume's 22 chapters, interest provides a critical bridge between cognition and affect in learning and development. This volume will be useful to educators, researchers, and policy makers, especially those whose focus is mathematics, science, and technology education.
Author : Johannes Lenhard
Publisher : Springer
ISBN 13 : 3319544691
Total Pages : 285 pages
Book Rating : 4.3/5 (195 download)
Download or read book Mathematics as a Tool written by Johannes Lenhard and published by Springer. This book was released on 2017-04-04 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book puts forward a new role for mathematics in the natural sciences. In the traditional understanding, a strong viewpoint is advocated, on the one hand, according to which mathematics is used for truthfully expressing laws of nature and thus for rendering the rational structure of the world. In a weaker understanding, many deny that these fundamental laws are of an essentially mathematical character, and suggest that mathematics is merely a convenient tool for systematizing observational knowledge. The position developed in this volume combines features of both the strong and the weak viewpoint. In accordance with the former, mathematics is assigned an active and even shaping role in the sciences, but at the same time, employing mathematics as a tool is taken to be independent from the possible mathematical structure of the objects under consideration. Hence the tool perspective is contextual rather than ontological. Furthermore, tool-use has to respect conditions like suitability, efficacy, optimality, and others. There is a spectrum of means that will normally differ in how well they serve particular purposes. The tool perspective underlines the inevitably provisional validity of mathematics: any tool can be adjusted, improved, or lose its adequacy upon changing practical conditions.
