Author: Steve Nadis
Publisher:
ISBN: 9781541604292
Category :
Languages : en
Pages : 0
Book Description
One of the preeminent mathematicians of the past half century shows how physics and math were combined to give us the theory of gravity and the dizzying array of ideas and insights that has come from it In 1915, Albert Einstein published his field equations of general relativity, which transformed our conception of gravity. Rather than being a mysterious force that pulls objects together, gravity, Einstein proclaimed, is merely a consequence of the curvature of space and time. Gravity, in other words, springs from geometry itself. In The Gravity of Math, the writer Steve Nadis and mathematician Shing-Tung Yau show how Einstein formulated his revolutionary theory, building upon the prior work of Bernhard Riemann, with help from Marcel Grossmann, David Hilbert, Tullio Levi-Civita, and other mathematicians. The book explains how the implications of Einstein's theory have been, and continue to be, uncovered by mathematicians to help us understand phenomena like black holes, gravitational waves, and the Big Bang. The story of gravity also sheds light on one of the most profound questions of science: Why do our best descriptions of the physical world reduce to mathematical statements? Whatever the answer, one thing is clear: gravity shapes the universe on the largest scales with a reach that is seemingly boundless. So, too, is the reach of mathematics, which can carry us to the edge of infinity and back.
The Gravity of Math
Author: Steve Nadis
Publisher:
ISBN: 9781541604292
Category :
Languages : en
Pages : 0
Book Description
One of the preeminent mathematicians of the past half century shows how physics and math were combined to give us the theory of gravity and the dizzying array of ideas and insights that has come from it In 1915, Albert Einstein published his field equations of general relativity, which transformed our conception of gravity. Rather than being a mysterious force that pulls objects together, gravity, Einstein proclaimed, is merely a consequence of the curvature of space and time. Gravity, in other words, springs from geometry itself. In The Gravity of Math, the writer Steve Nadis and mathematician Shing-Tung Yau show how Einstein formulated his revolutionary theory, building upon the prior work of Bernhard Riemann, with help from Marcel Grossmann, David Hilbert, Tullio Levi-Civita, and other mathematicians. The book explains how the implications of Einstein's theory have been, and continue to be, uncovered by mathematicians to help us understand phenomena like black holes, gravitational waves, and the Big Bang. The story of gravity also sheds light on one of the most profound questions of science: Why do our best descriptions of the physical world reduce to mathematical statements? Whatever the answer, one thing is clear: gravity shapes the universe on the largest scales with a reach that is seemingly boundless. So, too, is the reach of mathematics, which can carry us to the edge of infinity and back.
Publisher:
ISBN: 9781541604292
Category :
Languages : en
Pages : 0
Book Description
One of the preeminent mathematicians of the past half century shows how physics and math were combined to give us the theory of gravity and the dizzying array of ideas and insights that has come from it In 1915, Albert Einstein published his field equations of general relativity, which transformed our conception of gravity. Rather than being a mysterious force that pulls objects together, gravity, Einstein proclaimed, is merely a consequence of the curvature of space and time. Gravity, in other words, springs from geometry itself. In The Gravity of Math, the writer Steve Nadis and mathematician Shing-Tung Yau show how Einstein formulated his revolutionary theory, building upon the prior work of Bernhard Riemann, with help from Marcel Grossmann, David Hilbert, Tullio Levi-Civita, and other mathematicians. The book explains how the implications of Einstein's theory have been, and continue to be, uncovered by mathematicians to help us understand phenomena like black holes, gravitational waves, and the Big Bang. The story of gravity also sheds light on one of the most profound questions of science: Why do our best descriptions of the physical world reduce to mathematical statements? Whatever the answer, one thing is clear: gravity shapes the universe on the largest scales with a reach that is seemingly boundless. So, too, is the reach of mathematics, which can carry us to the edge of infinity and back.
The Gravity of Math
Author: Steve Nadis
Publisher: Basic Books
ISBN: 154160430X
Category : Science
Languages : en
Pages : 211
Book Description
One of the preeminent mathematicians of the past half century shows how physics and math were combined to give us the theory of gravity and the dizzying array of ideas and insights that has come from it Mathematics is far more than just the language of science. It is a critical underpinning of nature. The famed physicist Albert Einstein demonstrated this in 1915 when he showed that gravity—long considered an attractive force between massive objects—was actually a manifestation of the curvature, or geometry, of space and time. But in making this towering intellectual leap, Einstein needed the help of several mathematicians, including Marcel Grossmann, who introduced him to the geometrical framework upon which his theory rest. In The Gravity of Math, Steve Nadis and Shing-Tung Yau consider how math can drive and sometimes even anticipate discoveries in physics. Examining phenomena like black holes, gravitational waves, and the Big Bang, Nadis and Yau ask: Why do mathematical statements, derived solely from logic, provide the best descriptions of our physical world? The Gravity of Math offers an insightful and compelling look into the power of mathematics—whose reach, like that of gravity, can extend to the edge of the universe.
Publisher: Basic Books
ISBN: 154160430X
Category : Science
Languages : en
Pages : 211
Book Description
One of the preeminent mathematicians of the past half century shows how physics and math were combined to give us the theory of gravity and the dizzying array of ideas and insights that has come from it Mathematics is far more than just the language of science. It is a critical underpinning of nature. The famed physicist Albert Einstein demonstrated this in 1915 when he showed that gravity—long considered an attractive force between massive objects—was actually a manifestation of the curvature, or geometry, of space and time. But in making this towering intellectual leap, Einstein needed the help of several mathematicians, including Marcel Grossmann, who introduced him to the geometrical framework upon which his theory rest. In The Gravity of Math, Steve Nadis and Shing-Tung Yau consider how math can drive and sometimes even anticipate discoveries in physics. Examining phenomena like black holes, gravitational waves, and the Big Bang, Nadis and Yau ask: Why do mathematical statements, derived solely from logic, provide the best descriptions of our physical world? The Gravity of Math offers an insightful and compelling look into the power of mathematics—whose reach, like that of gravity, can extend to the edge of the universe.
The Shape of Inner Space
Author: Shing-Tung Yau
Publisher: Il Saggiatore
ISBN: 0465020232
Category : Mathematics
Languages : en
Pages : 398
Book Description
The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
Publisher: Il Saggiatore
ISBN: 0465020232
Category : Mathematics
Languages : en
Pages : 398
Book Description
The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
The Shape of a Life
Author: Shing-Tung Yau
Publisher: Yale University Press
ISBN: 0300245521
Category : Science
Languages : en
Pages : 449
Book Description
A Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe. Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics. “The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe “Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist
Publisher: Yale University Press
ISBN: 0300245521
Category : Science
Languages : en
Pages : 449
Book Description
A Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe. Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics. “The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe “Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist
How to Fall Slower Than Gravity
Author: Paul Nahin
Publisher: Princeton University Press
ISBN: 0691185026
Category : Mathematics
Languages : en
Pages : 319
Book Description
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.
Publisher: Princeton University Press
ISBN: 0691185026
Category : Mathematics
Languages : en
Pages : 319
Book Description
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.
A History in Sum
Author: Steve Nadis
Publisher: Harvard University Press
ISBN: 0674727894
Category : Mathematics
Languages : en
Pages : 272
Book Description
In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard’s mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics—in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose. The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics—an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce’s successors—William Fogg Osgood and Maxime Bôcher—undertook the task of transforming the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Birkhoff produced a dazzling body of work, while training a generation of innovators—students like Marston Morse and Hassler Whitney, who forged novel pathways in topology and other areas. Influential figures from around the world soon flocked to Harvard, some overcoming great challenges to pursue their elected calling. A History in Sum elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.
Publisher: Harvard University Press
ISBN: 0674727894
Category : Mathematics
Languages : en
Pages : 272
Book Description
In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard’s mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics—in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose. The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics—an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce’s successors—William Fogg Osgood and Maxime Bôcher—undertook the task of transforming the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Birkhoff produced a dazzling body of work, while training a generation of innovators—students like Marston Morse and Hassler Whitney, who forged novel pathways in topology and other areas. Influential figures from around the world soon flocked to Harvard, some overcoming great challenges to pursue their elected calling. A History in Sum elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.
Mathematics of Wave Phenomena
Author: Willy Dörfler
Publisher: Springer Nature
ISBN: 3030471748
Category : Mathematics
Languages : en
Pages : 330
Book Description
Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.
Publisher: Springer Nature
ISBN: 3030471748
Category : Mathematics
Languages : en
Pages : 330
Book Description
Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.
Do the Math!
Author: John K. White
Publisher: SAGE Publications
ISBN: 1452281068
Category : Social Science
Languages : en
Pages : 393
Book Description
Our world has become more complicated, and the notion of growth at any cost has led to constant economic uncertainty, a permanently stressed-out workforce, and everyday stories of government and corporate corruption. John K. White argues that a better knowledge of basic systems is needed to understand the world we live in, and one place to start is with counting and mathematics. Without an understanding of mathematics, we make poor personal financial choices, and we can't make the important decisions about government bailouts, oil supplies, or global warming. Do the Math! uses creative examples—borrowing liberally from the anecdotal and the academic, from literature and the newspaper, and from the stock market and the casino—to provide a thought-provoking guide to better understanding the world around us.
Publisher: SAGE Publications
ISBN: 1452281068
Category : Social Science
Languages : en
Pages : 393
Book Description
Our world has become more complicated, and the notion of growth at any cost has led to constant economic uncertainty, a permanently stressed-out workforce, and everyday stories of government and corporate corruption. John K. White argues that a better knowledge of basic systems is needed to understand the world we live in, and one place to start is with counting and mathematics. Without an understanding of mathematics, we make poor personal financial choices, and we can't make the important decisions about government bailouts, oil supplies, or global warming. Do the Math! uses creative examples—borrowing liberally from the anecdotal and the academic, from literature and the newspaper, and from the stock market and the casino—to provide a thought-provoking guide to better understanding the world around us.
Math for Programmers
Author: Paul Orland
Publisher: Manning
ISBN: 1617295353
Category : Computers
Languages : en
Pages : 686
Book Description
Explore important mathematical concepts through hands-on coding. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. To score a job in data science, machine learning, computer graphics, and cryptography, you need to bring strong math skills to the party. Math for Programmers teaches the math you need for these hot careers, concentrating on what you need to know as a developer. Filled with lots of helpful graphics and more than 200 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest programming fields. About the technology Skip the mathematical jargon: This one-of-a-kind book uses Python to teach the math you need to build games, simulations, 3D graphics, and machine learning algorithms. Discover how algebra and calculus come alive when you see them in code! About the book In Math for Programmers you’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. What's inside Vector geometry for computer graphics Matrices and linear transformations Core concepts from calculus Simulation and optimization Image and audio processing Machine learning algorithms for regression and classification About the reader For programmers with basic skills in algebra. About the author Paul Orland is a programmer, software entrepreneur, and math enthusiast. He is co-founder of Tachyus, a start-up building predictive analytics software for the energy industry. You can find him online at www.paulor.land. Table of Contents 1 Learning math with code PART I - VECTORS AND GRAPHICS 2 Drawing with 2D vectors 3 Ascending to the 3D world 4 Transforming vectors and graphics 5 Computing transformations with matrices 6 Generalizing to higher dimensions 7 Solving systems of linear equations PART 2 - CALCULUS AND PHYSICAL SIMULATION 8 Understanding rates of change 9 Simulating moving objects 10 Working with symbolic expressions 11 Simulating force fields 12 Optimizing a physical system 13 Analyzing sound waves with a Fourier series PART 3 - MACHINE LEARNING APPLICATIONS 14 Fitting functions to data 15 Classifying data with logistic regression 16 Training neural networks
Publisher: Manning
ISBN: 1617295353
Category : Computers
Languages : en
Pages : 686
Book Description
Explore important mathematical concepts through hands-on coding. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. To score a job in data science, machine learning, computer graphics, and cryptography, you need to bring strong math skills to the party. Math for Programmers teaches the math you need for these hot careers, concentrating on what you need to know as a developer. Filled with lots of helpful graphics and more than 200 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest programming fields. About the technology Skip the mathematical jargon: This one-of-a-kind book uses Python to teach the math you need to build games, simulations, 3D graphics, and machine learning algorithms. Discover how algebra and calculus come alive when you see them in code! About the book In Math for Programmers you’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. What's inside Vector geometry for computer graphics Matrices and linear transformations Core concepts from calculus Simulation and optimization Image and audio processing Machine learning algorithms for regression and classification About the reader For programmers with basic skills in algebra. About the author Paul Orland is a programmer, software entrepreneur, and math enthusiast. He is co-founder of Tachyus, a start-up building predictive analytics software for the energy industry. You can find him online at www.paulor.land. Table of Contents 1 Learning math with code PART I - VECTORS AND GRAPHICS 2 Drawing with 2D vectors 3 Ascending to the 3D world 4 Transforming vectors and graphics 5 Computing transformations with matrices 6 Generalizing to higher dimensions 7 Solving systems of linear equations PART 2 - CALCULUS AND PHYSICAL SIMULATION 8 Understanding rates of change 9 Simulating moving objects 10 Working with symbolic expressions 11 Simulating force fields 12 Optimizing a physical system 13 Analyzing sound waves with a Fourier series PART 3 - MACHINE LEARNING APPLICATIONS 14 Fitting functions to data 15 Classifying data with logistic regression 16 Training neural networks
A Mathematical and Philosophical Dictionary
Author: Charles Hutton
Publisher:
ISBN:
Category : Handbooks, vade-mecums, etc
Languages : en
Pages : 712
Book Description
Publisher:
ISBN:
Category : Handbooks, vade-mecums, etc
Languages : en
Pages : 712
Book Description