Mathematics As A Science Of Patterns
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Mathematics As The Science Of Patterns
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Author : Patrick M. Jenlink
language : en
Publisher: Information Age Publishing
Release Date : 2022-02-11
Mathematics As The Science Of Patterns written by Patrick M. Jenlink and has been published by Information Age Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-11 with Education categories.
This book explores the role of patterns in teaching mathematics, emphasizing their importance in helping students understand and enjoy math. It highlights the need for teacher development to improve student learning and discusses how recognizing patterns aids in generalization and abstraction, essential skills in mathematics education.
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.
Discovering Patterns In Mathematics And Poetry
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Author : Marcia Birken
language : en
Publisher: Rodopi
Release Date : 2008
Discovering Patterns In Mathematics And Poetry written by Marcia Birken and has been published by Rodopi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Art categories.
You are invited to join a fascinating journey of discovery, as Marcia Birken and Anne C. Coon explore the intersecting patterns of mathematics and poetry -- bringing the two fields together in a new way. Setting the tone with humor and illustrating each chapter with countless examples, Birken and Coon begin with patterns we can see, hear, and feel and then move to more complex patterns. Number systems and nursery rhymes lead to the Golden Mean and sestinas. Simple patterns of shape introduce tessellations and concrete poetry. Fractal geometry makes fractal poetry possible. Ultimately, patterns for the mind lead to questions: How do mathematicians and poets conceive of proof, paradox, and infinity? What role does analogy play in mathematical discovery and poetic expression? The book will be of special interest to readers who enjoy looking for connections across traditional disciplinary boundaries. Discovering Patterns in Mathematics and Poetry features centuries of creative work by mathematicians, poets, and artists, including Fibonacci, Albrecht Dürer, M. C. Escher, David Hilbert, Benoit Mandelbrot, William Shakespeare, Edna St. Vincent Millay, Langston Hughes, E.E. Cummings, and many contemporary experimental poets. Original illustrations include digital photographs, mathematical and poetic models, and fractal imagery.
Patterns Of Change
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Author : Ladislav Kvasz
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-28
Patterns Of Change written by Ladislav Kvasz 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 2008-10-28 with Mathematics categories.
Kvasz’s book is a contribution to the history and philosophy of mat- matics, or, as one might say, the historical approach to the philosophy of mathematics. This approach is for mathematics what the history and philosophy of science is for science. Yet the historical approach to the philosophy of science appeared much earlier than the historical approach to the philosophy of mathematics. The ?rst signi?cant work in the history and philosophy of science is perhaps William Whewell’s Philosophy of the Inductive Sciences, founded upon their History. This was originally published in 1840, a second, enlarged edition appeared in 1847, and the third edition appeared as three separate works p- lished between 1858 and 1860. Ernst Mach’s The Science of Mech- ics: A Critical and Historical Account of Its Development is certainly a work of history and philosophy of science. It ?rst appeared in 1883, and had six further editions in Mach’s lifetime (1888, 1897, 1901, 1904, 1908, and 1912). Duhem’s Aim and Structure of Physical Theory appeared in 1906 and had a second enlarged edition in 1914. So we can say that history and philosophy of science was a well-established ?eld th th by the end of the 19 and the beginning of the 20 century. By contrast the ?rst signi?cant work in the history and philosophy of mathematics is Lakatos’s Proofs and Refutations, which was p- lished as a series of papers in the years 1963 and 1964.
Mathematics
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Author : Keith Devlin
language : en
Publisher: Macmillan
Release Date : 1996-12-15
Mathematics written by Keith Devlin and has been published by Macmillan this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-15 with Mathematics categories.
To most people, mathematics means working with numbers. But as Keith Devlin shows in Mathematics: The Science of Patterns, this definition has been out of date for nearly 2,500 years. Mathematicians now see their work as the study of patterns—real or imagined, visual or mental, arising from the natural world or from within the human mind. Using this basic definition as his central theme, Devlin explores the patterns of counting, measuring, reasoning, motion, shape, position, and prediction, revealing the powerful influence mathematics has over our perception of reality. Interweaving historical highlights and current developments, and using a minimum of formulas, Devlin celebrates the precision, purity, and elegance of mathematics.
Mathematics As The Science Of Patterns
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Author : Patrick M. Jenlink
language : en
Publisher: IAP
Release Date : 2022-02-01
Mathematics As The Science Of Patterns written by Patrick M. Jenlink and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-01 with Education categories.
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 Po lya 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.
Pattern Theory
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Author : David Mumford
language : en
Publisher: CRC Press
Release Date : 2010-08-09
Pattern Theory written by David Mumford and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-09 with Computers categories.
Pattern theory is a distinctive approach to the analysis of all forms of real-world signals. At its core is the design of a large variety of probabilistic models whose samples reproduce the look and feel of the real signals, their patterns, and their variability. Bayesian statistical inference then allows you to apply these models in the analysis of new signals. This book treats the mathematical tools, the models themselves, and the computational algorithms for applying statistics to analyze six representative classes of signals of increasing complexity. The book covers patterns in text, sound, and images. Discussions of images include recognizing characters, textures, nature scenes, and human faces. The text includes onlineaccess to thematerials (data, code, etc.) needed for the exercises.
The Beauty Of Numbers In Nature
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Author : Ian Stewart
language : en
Publisher:
Release Date : 2017-03-29
The Beauty Of Numbers In Nature written by Ian Stewart and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-29 with categories.
Think of a zebra's stripes, the complexities of a spider's web, the uniformity of desert dunes, or the spirals in a sunflower head ... think of a snowflake. The Beauty of Numbers in Nature shows how life on Earth forms the principles of mathematics. Starting with the simplest patterns, each chapter looks at a different kind of patterning system and the mathematics that underlies it. In doing so the book also uncovers some universal patterns, both in nature and man-made, from the basic geometry of ancient Greece to the visually startling fractals that we are familiar with today. Elegantly illustrated, The Beauty of Numbers in Nature is an illuminating and engaging vision of how the apparently cold laws of mathematics find expression in the beauty of nature.
Pattern Formation
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Author : Rebecca Hoyle
language : en
Publisher: Cambridge University Press
Release Date : 2006
Pattern Formation written by Rebecca Hoyle and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
From the stripes of a zebra and the spots on a leopard's back to the ripples on a sandy beach or desert dune, regular patterns arise everywhere in nature. The appearance and evolution of these phenomena have been a focus of recent research activity across several disciplines. This book provides an introduction to the range of mathematical theory and methods used to analyze and explain these often intricate and beautiful patterns. Bringing together several different approaches, from group theoretic methods to envelope equations and theory of patterns in large-aspect ratio-systems, the book also provides insight behind the selection of one pattern over another.
Mathematics As A Science Of Patterns
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Author : Michael D. Resnik
language : en
Publisher: Oxford University Press
Release Date : 1997
Mathematics As A Science Of Patterns written by Michael D. Resnik and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defence of realism about the metaphysics of mathematics--the view that mathematics is about things that really exist. Resnik's distinctive philosophy of mathematics is here presented in an accessible and systematic form: it will be of value not only to specialists in this area, but to philosophers, mathematicians, and logicians interested in the relationship between these three disciplines, or in truth, realism, and epistemology.