Download or read book Understanding Physics Using Mathematical Reasoning written by Andrzej Sokolowski and published by Springer Nature. This book was released on 2021-08-20 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book speaks about physics discoveries that intertwine mathematical reasoning, modeling, and scientific inquiry. It offers ways of bringing together the structural domain of mathematics and the content of physics in one coherent inquiry. Teaching and learning physics is challenging because students lack the skills to merge these learning paradigms. The purpose of this book is not only to improve access to the understanding of natural phenomena but also to inspire new ways of delivering and understanding the complex concepts of physics. To sustain physics education in college classrooms, authentic training that would help develop high school students’ skills of transcending function modeling techniques to reason scientifically is needed and this book aspires to offer such training The book draws on current research in developing students’ mathematical reasoning. It identifies areas for advancements and proposes a conceptual framework that is tested in several case studies designed using that framework. Modeling Newton’s laws using limited case analysis, Modeling projectile motion using parametric equations and Enabling covariational reasoning in Einstein formula for the photoelectric effect represent some of these case studies. A wealth of conclusions that accompany these case studies, drawn from the realities of classroom teaching, is to help physics teachers and researchers adopt these ideas in practice.
Download or read book Physics for Mathematicians written by Michael Spivak and published by . This book was released on 2010 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Mathematical Thinking written by Keith J. Devlin and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.
Download or read book Understanding Physics written by Colm O'Sullivan and published by John Wiley & Sons. This book was released on 2012-05-18 with total page 1084 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding Physics – Second edition is a comprehensive, yet compact, introductory physics textbook aimed at physics undergraduates and also at engineers and other scientists taking a general physics course. Written with today's students in mind, this text covers the core material required by an introductory course in a clear and refreshing way. A second colour is used throughout to enhance learning and understanding. Each topic is introduced from first principles so that the text is suitable for students without a prior background in physics. At the same time the book is designed to enable students to proceed easily to subsequent courses in physics and may be used to support such courses. Mathematical methods (in particular, calculus and vector analysis) are introduced within the text as the need arises and are presented in the context of the physical problems which they are used to analyse. Particular aims of the book are to demonstrate to students that the easiest, most concise and least ambiguous way to express and describe phenomena in physics is by using the language of mathematics and that, at this level, the total amount of mathematics required is neither large nor particularly demanding. 'Modern physics' topics (relativity and quantum mechanics) are introduced at an earlier stage than is usually found in introductory textbooks and are integrated with the more 'classical' material from which they have evolved. This book encourages students to develop an intuition for relativistic and quantum concepts at as early a stage as is practicable. The text takes a reflective approach towards the scientific method at all stages and, in keeping with the title of the text, emphasis is placed on understanding of, and insight into, the material presented.
Download or read book An Introduction to Mathematical Reasoning written by Peter J. Eccles and published by Cambridge University Press. This book was released on 1997-12-11 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. Over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.
Download or read book The Road to Reality written by Roger Penrose and published by Vintage. This book was released on 2021-06-09 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt: **WINNER OF THE 2020 NOBEL PRIZE IN PHYSICS** The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book. Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. The Road to Reality is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit. 'Roger Penrose is the most important physicist to work in relativity theory except for Einstein. He is one of the very few people I've met in my life who, without reservation, I call a genius' Lee Smolin
Download or read book Understanding Physics written by David C. Cassidy and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough grounding in contemporary physics while placing the subject into its social and historical context. Based largely on the highly respected Project Physics Course developed by two of the authors, it also integrates the results of recent pedagogical research. The text thus teaches the basic phenomena in the physical world and the concepts developed to explain them; shows that science is a rational human endeavour with a long and continuing tradition, involving many different cultures and people; develops facility in critical thinking, reasoned argumentation, evaluation of evidence, mathematical modelling, and ethical values. The treatment emphasises not only what we know but also how we know it, why we believe it, and what effects this knowledge has.
Download or read book How to Fall Slower Than Gravity written by Paul J. Nahin and published by Princeton University Press. This book was released on 2021-11-23 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engaging collection of intriguing problems that shows you how to think like a mathematical physicist Paul Nahin is a master at explaining odd phenomena through straightforward mathematics. In this collection of twenty-six intriguing problems, he explores how mathematical physicists think. Always entertaining, the problems range from ancient catapult conundrums to the puzzling physics of a very peculiar material called NASTYGLASS—and from dodging trucks to why raindrops fall slower than the rate of gravity. The questions raised may seem impossible to answer at first and may require an unexpected twist in reasoning, but sometimes their solutions are surprisingly simple. Nahin’s goal, however, is always to guide readers—who will need only to have studied advanced high school math and physics—in expanding their mathematical thinking to make sense of the curiosities of the physical world. The problems are in the first part of the book and the solutions are in the second, so that readers may challenge themselves to solve the questions on their own before looking at the explanations. The problems show how mathematics—including algebra, trigonometry, geometry, and calculus—can be united with physical laws to solve both real and theoretical problems. Historical anecdotes woven throughout the book bring alive the circumstances and people involved in some amazing discoveries and achievements. More than a puzzle book, this work will immerse you in the delights of scientific history while honing your math skills.
Download or read book Lost in Math written by Sabine Hossenfelder and published by Basic Books. This book was released on 2018-06-12 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this "provocative" book (New York Times), a contrarian physicist argues that her field's modern obsession with beauty has given us wonderful math but bad science. Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.
Download or read book Mathematics in Physics Education written by Gesche Pospiech and published by Springer. This book was released on 2019-07-02 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about mathematics in physics education, the difficulties students have in learning physics, and the way in which mathematization can help to improve physics teaching and learning. The book brings together different teaching and learning perspectives, and addresses both fundamental considerations and practical aspects. Divided into four parts, the book starts out with theoretical viewpoints that enlighten the interplay of physics and mathematics also including historical developments. The second part delves into the learners’ perspective. It addresses aspects of the learning by secondary school students as well as by students just entering university, or teacher students. Topics discussed range from problem solving over the role of graphs to integrated mathematics and physics learning. The third part includes a broad range of subjects from teachers’ views and knowledge, the analysis of classroom discourse and an evaluated teaching proposal. The last part describes approaches that take up mathematization in a broader interpretation, and includes the presentation of a model for physics teachers’ pedagogical content knowledge (PCK) specific to the role of mathematics in physics.
Download or read book Mathematics And Science written by Ronald E Mickens and published by World Scientific. This book was released on 1990-08-23 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Reasoning written by Theodore A. Sundstrom and published by Prentice Hall. This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom
Download or read book The Mathematical Mechanic written by Mark Levi and published by Princeton University Press. This book was released on 2023-01-24 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles. The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.
Download or read book Pathways Through Applied and Computational Physics written by Nicolò Barbero and published by Springer Science & Business Media. This book was released on 2013-11-19 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for undergraduates and young researchers who wish to understand the role that different branches of physics and mathematics play in the execution of actual experiments. The unique feature of the book is that all the subjects addressed are strictly interconnected within the context of the execution of a single experiment with very high accuracy, namely the redetermination of the Avogadro constant NA, one of the fundamental physical constants. The authors illustrate how the basic laws of physics are applied to describe the behavior of the quantities involved in the measurement of NA and explain the mathematical reasoning and computational tools that have been exploited. It is emphasized that all these quantities, although pertaining to a specific experiment, are of wide and general interest. The book is organized into chapters covering the interaction of electromagnetic radiation with single crystals, linear elasticity and anisotropy, propagation of thermal energy, anti-vibration mounting systems, and data analysis and B-spline interpolation. An essential feature is the focus on the role of Mathematica, an invaluable, fully integrated software environment for handling diverse scientific and technical computations.
Download or read book An Essay on the Mathematical Principles of Physics written by James Challis and published by . This book was released on 1873 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Explanation and Proof in Mathematics written by Gila Hanna and published by Springer Science & Business Media. This book was released on 2009-12-04 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece. Proof as bearers of mathematical knowledge. Bridging knowing and proving in mathematical reasoning. The role of mathematics in long-term cognitive development of reasoning. Proof as experiment in the work of Wittgenstein. Relationships between mathematical proof, problem-solving, and explanation. Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
Download or read book Applying Cognitive Science to Education written by Frederick Reif and published by MIT Press. This book was released on 2008 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to some of the cognitive issues important for thinking and learning in scientific or other complex domains (such as mathematics, physics, chemistry, engineering, or expository writing), with practical educational applications and implementation methods. Many students find it difficult to learn the kind of knowledge and thinking required by college or high school courses in mathematics, science, or other complex domains. Thus they often emerge with significant misconceptions, fragmented knowledge, and inadequate problem-solving skills. Most instructors or textbook authors approach their teaching efforts with a good knowledge of their field of expertise but little awareness of the underlying thought processes and kinds of knowledge required for learning in scientific domains. In this book, Frederick Reif presents an accessible coherent introduction to some of the cognitive issues important for thinking and learning in scientific or other complex domains (such as mathematics, science, physics, chemistry, biology, engineering, or expository writing). Reif, whose experience teaching physics at the University of California led him to explore the relevance of cognitive science to education, examines with some care the kinds of knowledge and thought processes needed for good performance; discusses the difficulties faced by students trying to deal with unfamiliar scientific domains; describes some explicit teaching methods that can help students learn the requisite knowledge and thinking skills; and indicates how such methods can be implemented by instructors or textbook authors. Writing from a practically applied rather than predominantly theoretical perspective, Reif shows how findings from recent research in cognitive science can be applied to education. He discusses cognitive issues related to the kind of knowledge and thinking skills that are needed for science or mathematics courses in high school or colleges and that are essential prerequisites for more advanced intellectual performance. In particular, he argues that a better understanding of the underlying cognitive mechanisms should help to achieve a more scientific approach to science education.
