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Mathematics as a Science of Patterns

Mathematics as a Science of Patterns Author Michael D. Resnik
ISBN-10 0198236085
Release 1997
Pages 285
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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.


Mathematics Author Keith Devlin
ISBN-10 0805073442
Release 1996-12-15
Pages 224
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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 But as Keith Devlin shows in Mathematics: The Science of Patterns, this definition has been out of date for nearly 2,500 years.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 in Nature

Mathematics in Nature Author John A. Adam
ISBN-10 9781400841011
Release 2011-10-02
Pages 392
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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.

The Mathematics of Love

The Mathematics of Love Author Hannah Fry
ISBN-10 9781476784892
Release 2015-02-03
Pages 128
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In this must-have for anyone who wants to better understand their love life, a mathematician pulls back the curtain and reveals the hidden patterns—from dating sites to divorce, sex to marriage—behind the rituals of love. The roller coaster of romance is hard to quantify; defining how lovers might feel from a set of simple equations is impossible. But that doesn’t mean that mathematics isn’t a crucial tool for understanding love. Love, like most things in life, is full of patterns. And mathematics is ultimately the study of patterns—from predicting the weather to the fluctuations of the stock market, the movement of planets or the growth of cities. These patterns twist and turn and warp and evolve just as the rituals of love do. In The Mathematics of Love, Dr. Hannah Fry takes the reader on a fascinating journey through the patterns that define our love lives, applying mathematical formulas to the most common yet complex questions pertaining to love: What’s the chance of finding love? What’s the probability that it will last? How do online dating algorithms work, exactly? Can game theory help us decide who to approach in a bar? At what point in your dating life should you settle down? From evaluating the best strategies for online dating to defining the nebulous concept of beauty, Dr. Fry proves—with great insight, wit, and fun—that math is a surprisingly useful tool to negotiate the complicated, often baffling, sometimes infuriating, always interesting, mysteries of love.

Patterns of the Universe

Patterns of the Universe Author Alex Bellos
ISBN-10 9781615193233
Release 2015
Pages 144
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"A coloring book that reveals math's hidden beauty and contemplative power as never before with 78 coloring designs and games that explore symmetry, fractals, tessellations, randomness, and more."--

Philosophy of Mathematics

Philosophy of Mathematics Author Stewart Shapiro
ISBN-10 0198025459
Release 1997-08-07
Pages 296
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Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.

The Beauty of Numbers in Nature

The Beauty of Numbers in Nature Author Ian Stewart
ISBN-10 1782404716
Release 2017-03-29
Pages 224
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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.

Symmetry in Chaos

Symmetry in Chaos Author Michael Field
ISBN-10 0898717701
Release 2009
Pages 199
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Symmetry suggests order and regularity whilst chaos suggests disorder and randomness. 'Symmetry in Chaos' is an exploration of how combining seemingly contradictory principles can lead to the construction of striking and beautiful images. This book is an engaging look at the interplay of art and mathematics.

Discovering Patterns in Mathematics and Poetry

Discovering Patterns in Mathematics and Poetry Author Marcia Birken
ISBN-10 9789042023703
Release 2008-01
Pages 213
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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.

Mathematics as a Cultural System

Mathematics as a Cultural System Author Raymond L. Wilder
ISBN-10 9781483100616
Release 2014-05-20
Pages 194
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Mathematics as a Cultural System discusses the relationship between mathematics and culture. The book is comprised of eight chapters discussing topics that support the concept of mathematics as a cultural system. Chapter I deals with the nature of culture and cultural systems, while Chapter 2 provides examples of cultural patterns observable in the evolution of mechanics. Chapter III treats historical episodes as a laboratory for the illustration of patterns and forces that have been operative in cultural change. Chapter IV covers hereditary stress, and Chapter V discusses consolidation as a force and process. Chapter VI talks about the singularities in the evolution of mechanics, while Chapter 7 deals with the laws governing the evolution of mathematics. Chapter VIII tackles the role and future of mathematics. The book will be of great interest to readers who are curious about how mathematics relates to culture.

Pattern Theory

Pattern Theory Author David Mumford
ISBN-10 9781439865569
Release 2010-08-09
Pages 375
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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 online access to the materials (data, code, etc.) needed for the exercises.

Maker of Patterns An Autobiography Through Letters

Maker of Patterns  An Autobiography Through Letters Author Freeman Dyson
ISBN-10 9780871403872
Release 2018-04-10
Pages 320
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Both recalling his life story and recounting many of the major advances in twentieth-century science, a renowned physicist shares his autobiography through letters. Having penned hundreds of letters to his family over four decades, Freeman Dyson has framed them with the reflections made by a man now in his nineties. While maintaining that “the letters record the daily life of an ordinary scientist doing ordinary work,” Dyson nonetheless has worked with many of the twentieth century’s most renowned physicists, mathematicians, and intellectuals, so that Maker of Patterns presents not only his personal story but chronicles through firsthand accounts an exciting era of twentieth-century science. Though begun in the dark year of 1941 when Hitler’s armies had already conquered much of Europe, Dyson’s letters to his parents, written at Trinity College, Cambridge, often burst with the curiosity of a precocious seventeen-year-old. Pursuing mathematics and physics with a cast of legendary professors, Dyson thrived in Cambridge’s intellectual ferment, working on, for example, the theory of partitions or reading about Kurt Gödel’s hypotheses, while still finding time for billiards and mountain climbing. After graduating and serving with the Royal Air Force’s Bomber Command operational research section, whose job it was “to demolish German cities and kill as many German civilians as possible,” Dyson visited a war-torn Germany, hoping through his experience to create a “tolerably peaceful world.” Juxtaposing descriptions of scientific breakthroughs with concerns for mankind’s future, Dyson’s postwar letters reflect the quandaries faced by an entire scientific generation that was dealing with the aftereffects of nuclear detonations and concentration camp killings. Arriving in America in 1947 to study with Cornell’s Hans Bethe, Dyson continued to send weekly missives to England that were never technical but written with grace and candor, creating a portrait of a generation that was eager, as Einstein once stated, to solve “deep mysteries that Nature intend[ed] to keep for herself.” We meet, among others, scientists like Richard Feynman, who took Dyson across country on Route 66, Robert Oppenheimer, Eugene Wigner, Niels Bohr, James Watson, and a young Stephen Hawking; and we encounter intellectuals and leaders, among them Reinhold Niebuhr, George Kennan, Arthur C. Clarke, as well as Martin Luther King, Jr. The “patterns of comparable beauty in the dance of electrons jumping around atoms” invariably replicate themselves in this autobiography told through letters, one that combines accounts of wanton arms development with the not-inconsiderable demands of raising six children. As we once again attempt to guide society toward a more hopeful future, these letters, with their reenactment of what, at first, seems like a distant past, reveal invaluable truths about human nature.

Patterns in Nature

Patterns in Nature Author Philip Ball
ISBN-10 9780226332567
Release 2016-04-05
Pages 288
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Though at first glance the natural world may appear overwhelming in its diversity and complexity, there are regularities running through it, from the hexagons of a honeycomb to the spirals of a seashell and the branching veins of a leaf. Revealing the order at the foundation of the seemingly chaotic natural world, Patterns in Nature explores not only the math and science but also the beauty and artistry behind nature’s awe-inspiring designs. Unlike the patterns we create in technology, architecture, and art, natural patterns are formed spontaneously from the forces that act in the physical world. Very often the same types of pattern and form – spirals, stripes, branches, and fractals, say—recur in places that seem to have nothing in common, as when the markings of a zebra mimic the ripples in windblown sand. That’s because, as Patterns in Nature shows, at the most basic level these patterns can often be described using the same mathematical and physical principles: there is a surprising underlying unity in the kaleidoscope of the natural world. Richly illustrated with 250 color photographs and anchored by accessible and insightful chapters by esteemed science writer Philip Ball, Patterns in Nature reveals the organization at work in vast and ancient forests, powerful rivers, massing clouds, and coastlines carved out by the sea. By exploring similarities such as those between a snail shell and the swirling stars of a galaxy, or the branches of a tree and those of a river network, this spectacular visual tour conveys the wonder, beauty, and richness of natural pattern formation.

Creating Symmetry

Creating Symmetry Author Frank A. Farris
ISBN-10 9781400865673
Release 2015-06-02
Pages 248
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This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks—a sort of potato-stamp method—Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics. Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own. Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.

Nature s Numbers

Nature s Numbers Author Ian Stewart
ISBN-10 9780786723928
Release 2008-08-04
Pages 176
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States that the mental construct of mathematics can provide humankind with a key tool to understanding the world, and discusses the implications of basic math concepts

The Pattern Book

The Pattern Book Author Clifford A. Pickover
ISBN-10 981021426X
Release 1995
Pages 427
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Although the patterns are computer-generated, the book is informal and emphasis is on the fun that the true pattern lover finds in doing rather than in reading about the doing.

The Language of Mathematics

The Language of Mathematics Author Keith Devlin
ISBN-10 0805072543
Release 2000-03-13
Pages 352
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"The great book of nature," said Galileo, "can be read only by those who know the language in which it was written. And this language is mathematics." In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life—patterns that exist in the physical, biological, and social worlds without, and the realm of ideas and thoughts within. Taking the reader on a wondrous journey through the invisible universe that surrounds us—a universe made visible by mathematics—Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, allows us to predict the weather, the behavior of the stock market, and the outcome of elections. Microwave ovens, telephone cables, children's toys, pacemakers, automobiles, and computers—all operate on mathematical principles. Far from a dry and esoteric subject, mathematics is a rich and living part of our culture. An exploration of an often woefully misunderstood subject, The Language of Mathematics celebrates the simplicity, the precision, the purity, and the elegance of mathematics.