Understanding Physics Using Mathematical Reasoning

Author : Andrzej Sokolowski
Publisher : Springer Nature
Page : 208 pages
File Size : 40,5 Mb
Release : 2021-08-20
Category : Education
ISBN : 9783030802059

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Understanding Physics Using Mathematical Reasoning by Andrzej Sokolowski Pdf

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.

Author : Colm O'Sullivan,Michael Mansfield
Publisher : John Wiley & Sons
Page : 1084 pages
File Size : 42,5 Mb
Release : 2012-05-18
Category : Science
ISBN : 9781118437827

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Understanding Physics by Colm O'Sullivan,Michael Mansfield Pdf

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.

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 318 pages
File Size : 48,5 Mb
Release : 2021-11-23
Category : Crafts & Hobbies
ISBN : 9780691229171

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How to Fall Slower Than Gravity by Paul J. Nahin Pdf

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.

Author : Gesche Pospiech,Marisa Michelini,Bat-Sheva Eylon
Publisher : Springer
Page : 385 pages
File Size : 49,9 Mb
Release : 2019-07-02
Category : Science
ISBN : 9783030046279

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Mathematics in Physics Education by Gesche Pospiech,Marisa Michelini,Bat-Sheva Eylon Pdf

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.

Author : Michael Spivak
Publisher : Unknown
Page : 733 pages
File Size : 52,8 Mb
Release : 2010
Category : Mechanics
ISBN : 0914098322

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Physics for Mathematicians by Michael Spivak Pdf

Author : Keith J. Devlin
Publisher : Unknown
Page : 0 pages
File Size : 40,7 Mb
Release : 2012
Category : Mathematics
ISBN : 0615653634

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Introduction to Mathematical Thinking by Keith J. Devlin Pdf

"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.

Author : Nicolò Barbero,Matteo Delfino,Carlo Palmisano,Gianfranco Zosi
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 46,8 Mb
Release : 2013-11-19
Category : Science
ISBN : 9788847052208

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Pathways Through Applied and Computational Physics by Nicolò Barbero,Matteo Delfino,Carlo Palmisano,Gianfranco Zosi Pdf

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.

Author : Ronald E Mickens
Publisher : World Scientific
Page : 354 pages
File Size : 54,5 Mb
Release : 1990-08-23
Category : Mathematics
ISBN : 9789814531924

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Mathematics And Science by Ronald E Mickens Pdf

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.

Author : Mark Levi
Publisher : Princeton University Press
Page : 201 pages
File Size : 44,6 Mb
Release : 2023-01-24
Category : Mathematics
ISBN : 9780691244174

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The Mathematical Mechanic by Mark Levi Pdf

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.

Author : Sabine Hossenfelder
Publisher : Basic Books
Page : 277 pages
File Size : 45,6 Mb
Release : 2018-06-12
Category : Science
ISBN : 9780465094264

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Lost in Math by Sabine Hossenfelder Pdf

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.

Author : Roger Penrose
Publisher : Vintage
Page : 1136 pages
File Size : 42,6 Mb
Release : 2021-06-09
Category : Science
ISBN : 9780593315309

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The Road to Reality by Roger Penrose Pdf

**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

Author : Jude W. Shavlik
Publisher : Morgan Kaufmann
Page : 236 pages
File Size : 41,6 Mb
Release : 2014-07-10
Category : Computers
ISBN : 9781483258911

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Extending Explanation-Based Learning by Generalizing the Structure of Explanations by Jude W. Shavlik Pdf

Extending Explanation-Based Learning by Generalizing the Structure of Explanations presents several fully-implemented computer systems that reflect theories of how to extend an interesting subfield of machine learning called explanation-based learning. This book discusses the need for generalizing explanation structures, relevance to research areas outside machine learning, and schema-based problem solving. The result of standard explanation-based learning, BAGGER generalization algorithm, and empirical analysis of explanation-based learning are also elaborated. This text likewise covers the effect of increased problem complexity, rule access strategies, empirical study of BAGGER2, and related work in similarity-based learning. This publication is suitable for readers interested in machine learning, especially explanation-based learning.

Author : The Open University
Publisher : The Open University
Page : 128 pages
File Size : 53,7 Mb
Release : 2024-06-05
Category : Electronic
ISBN : 8210379456XXX

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The restless Universe by The Open University Pdf

This 12-hour free course introduced major achievements and figures in the history of physics.

Author : Nicos Papadouris,Angela Hadjigeorgiou,Constantinos P. Constantinou
Publisher : Springer
Page : 313 pages
File Size : 51,7 Mb
Release : 2015-11-02
Category : Science
ISBN : 9783319200743

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Insights from Research in Science Teaching and Learning by Nicos Papadouris,Angela Hadjigeorgiou,Constantinos P. Constantinou Pdf

This book includes studies that represent the state of the art in science education research and convey a sense of the variation in educational traditions around the world. The papers are organized into six main sections: science teaching processes, conceptual understanding, reasoning strategies, early years science education, and affective and social aspects of science teaching and learning. The volume features 18 papers, selected from the most outstanding papers presented during the 10th European Science Education Research Association (ESERA) Conference, held in Nicosia, Cyprus, in September 2013. The theme of the conference was “Science Education Research for Evidence-based Teaching and Coherence in Learning”. The studies presented underline aspects of great relevance in contemporary science education: the need to reflect on different approaches to enhance our knowledge of learning processes and the role of context, designed or circumstantial, formal or non-formal, in learning and instruction. These studies are innovative in the issues they explore, the methods they use, or the ways in which emergent knowledge in the field is represented. The book is of interest to science educators and science education researchers with a commitment to evidence informed teaching and learning.

Author : Gila Hanna,Hans Niels Jahnke,Helmut Pulte
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 55,7 Mb
Release : 2009-12-04
Category : Education
ISBN : 9781441905765

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Explanation and Proof in Mathematics by Gila Hanna,Hans Niels Jahnke,Helmut Pulte Pdf

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.