Download and read online Beyond Infinity in PDF and EPUB Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.
Download and read online Beyond Infinity in PDF and EPUB The hilarious and charming Eugenia Cheng leads us in search of what's bigger than infinity, and smaller than its opposite Imagine something small enough to fit in your head but too large to fit in the world-or even the universe. What would you call it? And what would it be? How about...infinity? In Beyond Infinity, musician, chef, and mathematician Eugenia Cheng answers this question by taking readers on a startling journey from math at its most elemental to its loftiest abstractions. Beginning with the classic thought experiment of Hilbert's hotel-the place where you can (almost) always find a room, if you don't mind being moved from room to room over the course of the night-she explores the wild and woolly world of the infinitely large and the infinitely small. Along the way she considers weighty questions like why some numbers are uncountable or why infinity plus one is not the same as one plus infinity. She finds insight in some unlikely examples: planning a dinner party for 7 billion people using a chessboard, making a chicken-sandwich sandwich, and creating infinite cookies from a finite ball of dough all tell you more about math than you could have imagined. An irresistible book on the universe's biggest possible topic, Beyond Infinity will beguile and bewitch you, and show all of us how one little symbol can hold the biggest idea of all.
Download and read online Beyond Infinity in PDF and EPUB Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity.What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough?Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.
Download and read online The Great Unknown in PDF and EPUB “Brilliant and fascinating. No one is better at making the recondite accessible and exciting.” —Bill Bryson A captivating journey to the outer reaches of human knowledge Ever since the dawn of civilization we have been driven by a desire to know. But are there limits to human knowledge? Are some things beyond the predictive powers of science and the capacities of the human brain? Or are those challenges the next big discovery waiting to happen? In The Great Unknown, one of the world’s most brilliant mathematicians takes us into the minds of science’s greatest innovators as he probes the many mysteries we have yet to solve. From the very large to the very small, from the distant future to the deep past, from the complexities of the human brain to the infinities of mathematics, Marcus du Sautoy invites us to join him on a journey to the seven frontiers of knowledge, the outer edges where scientists are actively grappling with the unknown. Can we locate consciousness in the brain? What is dark energy made of? Can we speak of time before the Big Bang? Is it possible to predict the future? At once exhilarating and mind bending, The Great Unknown will challenge you to think in new ways about every aspect of the known world. Du Sautoy reminds us that major breakthroughs were often ridiculed at the time of their discovery and invites us to consider big questions—about who we are and the nature of God—that even the most creative scientists have yet to answer definitively.
Download and read online The Mathematics Lover s Companion in PDF and EPUB Twenty-three mathematical masterpieces for exploration and enlightenment
Download and read online How to Bake Pi in PDF and EPUB What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? InHow to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen. We learn how the béchamel in a lasagna can be a lot like the number five, and why making a good custard proves that math is easy but life is hard. At the heart of it all is Cheng’s work on category theory, a cutting-edge "mathematics of mathematics,” that is about figuring out how math works. Combined with her infectious enthusiasm for cooking and true zest for life, Cheng’s perspective on math is a funny journey through a vast territory no popular book on math has explored before. So, what is math? Let’s look for the answer in the kitchen.
Download and read online Infinity a Very Short Introduction in PDF and EPUB Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) isintimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas ofmathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectualexercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.
Download and read online Calculating the Cosmos in PDF and EPUB Ian Stewart's up-to-the-minute guide to the cosmos moves from the formation of the Earth and its Moon to the planets and asteroids of the solar system and from there out into the galaxy and the universe. He describes the architecture of space and time, dark matter and dark energy, how galaxies form, why stars implode, how everything began, and how it will end. He considers parallel universes, what forms extra-terrestrial life might take, and the likelihood of Earth being hit by an asteroid. Mathematics, Professor Stewart shows, has been the driving force in astronomy and cosmology since the ancient Babylonians. He describes how Kepler's work on planetary orbits led Newton to formulate his theory of gravity, and how two centuries later irregularities in the motion of Mars inspired Einstein's theory of general relativity. In crystal-clear terms he explains the fundamentals of gravity, spacetime, relativity and quantum theory, and shows how they all relate to each other. Eighty years ago the discovery that the universe is expanding led to the Big Bang theory of its origins. This in turn led cosmologists to posit features such as dark matter and dark energy. But does dark matter exist? Could another scientific revolution be on the way to challenge current scientific orthodoxy? These are among the questions Ian Stewart raises in his quest through the realms of astronomy and cosmology.
Download and read online The Calculus of Happiness in PDF and EPUB How math holds the keys to improving one's health, wealth, and love life What's the best diet for overall health and weight management? How can we change our finances to retire earlier? How can we maximize our chances of finding our soul mate? In The Calculus of Happiness, Oscar Fernandez shows us that math yields powerful insights into health, wealth, and love. Using only high-school-level math (precalculus with a dash of calculus), Fernandez guides us through several of the surprising results, including an easy rule of thumb for choosing foods that lower our risk for developing diabetes (and that help us lose weight too), simple "all-weather" investment portfolios with great returns, and math-backed strategies for achieving financial independence and searching for our soul mate. Moreover, the important formulas are linked to a dozen free online interactive calculators on the book’s website, allowing one to personalize the equations. Fernandez uses everyday experiences—such as visiting a coffee shop—to provide context for his mathematical insights, making the math discussed more accessible, real-world, and relevant to our daily lives. Every chapter ends with a summary of essential lessons and takeaways, and for advanced math fans, Fernandez includes the mathematical derivations in the appendices. A nutrition, personal finance, and relationship how-to guide all in one, The Calculus of Happiness invites you to discover how empowering mathematics can be.
Download and read online Philosophy of Mathematics in PDF and EPUB A sophisticated, original introduction to the philosophy of mathematics from one of its leading contemporary scholars Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Written by Øystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, David Hilbert, Kurt Gödel, W. V. Quine, Paul Benacerraf, and Hartry H. Field. Sophisticated but clear and approachable, this is an essential introduction for all students and teachers of philosophy, as well as mathematicians and others who want to understand the foundations of mathematics.
Download and read online A Brief History of Mathematical Thought in PDF and EPUB Emblazoned on many advertisements for the wildly popular game of Sudoku are the reassuring words, "no mathematical knowledge required." Anxiety about math plagues many of us, and school memories can still summon intense loathing. In A Brief History of Mathematical Thought, Luke Heaton shows that much of what many think-and fear-about mathematics is misplaced, and to overcome our insecurities we need to understand its history. To help, he offers a lively guide into and through the world of mathematics and mathematicians, one in which patterns and arguments are traced through logic in a language grounded in concrete experience. Heaton reveals how Greek and Roman mathematicians like Pythagoras, Euclid, and Archimedes helped shaped the early logic of mathematics; how the Fibonacci sequence, the rise of algebra, and the invention of calculus are connected; how clocks, coordinates, and logical padlocks work mathematically; and how, in the twentieth century, Alan Turing's revolutionary work on the concept of computation laid the groundwork for the modern world. A Brief History of Mathematical Thought situates mathematics as part of, and essential to, lived experience. Understanding it requires not abstract thought or numbing memorization but an historical imagination and a view to its origins. --
Download and read online To Be a Machine in PDF and EPUB An eye-opening journey into a world of visionaries, billionaires, and eccentrics harnessing technology for nothing less than the salvation of mankind Transhumanism is a movement pushing the limits of our bodies—our capabilities, intelligence, and lifespans—in the hopes that, through technology, we can become something better than ourselves. It has found support among Silicon Valley billionaires and some of the world’s biggest businesses. In To Be a Machine, journalist Mark O'Connell explores the staggering possibilities and moral quandaries that present themselves when you of think of your body as a device. He visits the world's foremost cryonics facility to witness how some have chosen to forestall death. He discovers an underground collective of biohackers, implanting electronics under their skin to enhance their senses. He meets a team of scientists urgently investigating how to protect mankind from artificial superintelligence. Where is our obsession with technology leading us? What does the rise of AI mean not just for our offices and homes, but for our humanity? Could the technologies we create to help us eventually bring us to harm? Addressing these questions, O'Connell presents a profound, provocative, often laugh-out-loud-funny look at an influential movement. In investigating what it means to be a machine, he offers a surprising meditation on what it means to be human.
Download and read online Finding Fibonacci in PDF and EPUB A compelling firsthand account of Keith Devlin's ten-year quest to tell Fibonacci's story In 2000, Keith Devlin set out to research the life and legacy of the medieval mathematician Leonardo of Pisa, popularly known as Fibonacci, whose book Liber abbaci has quite literally affected the lives of everyone alive today. Although he is most famous for the Fibonacci numbers—which, it so happens, he didn't invent—Fibonacci's greatest contribution was as an expositor of mathematical ideas at a level ordinary people could understand. In 1202, Liber abbaci—the "Book of Calculation"—introduced modern arithmetic to the Western world. Yet Fibonacci was long forgotten after his death, and it was not until the 1960s that his true achievements were finally recognized. Finding Fibonacci is Devlin's compelling firsthand account of his ten-year quest to tell Fibonacci's story. Devlin, a math expositor himself, kept a diary of the undertaking, which he draws on here to describe the project's highs and lows, its false starts and disappointments, the tragedies and unexpected turns, some hilarious episodes, and the occasional lucky breaks. You will also meet the unique individuals Devlin encountered along the way, people who, each for their own reasons, became fascinated by Fibonacci, from the Yale professor who traced modern finance back to Fibonacci to the Italian historian who made the crucial archival discovery that brought together all the threads of Fibonacci's astonishing story. Fibonacci helped to revive the West as the cradle of science, technology, and commerce, yet he vanished from the pages of history. This is Devlin's search to find him.
Download and read online The Mathematics of Secrets in PDF and EPUB The Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptography—the science of sending secret messages. Most books about cryptography are organized historically, or around how codes and ciphers have been used, such as in government and military intelligence or bank transactions. Joshua Holden instead shows how mathematical principles underpin the ways that different codes and ciphers operate. Holden focuses on both code making and code breaking and he discusses the majority of ancient and modern ciphers currently known. Holden begins by looking at substitution ciphers, built by substituting one letter or block of letters for another. Explaining one of the simplest and historically well-known ciphers, the Caesar cipher, Holden establishes the key mathematical idea behind the cipher and discusses how to introduce flexibility and additional notation. Holden goes on to explore polyalphabetic substitution ciphers, transposition ciphers, including one developed by the Spartans, connections between ciphers and computer encryption, stream ciphers, and ciphers involving exponentiation. He also examines public-key ciphers, where the methods used to encrypt messages are public knowledge, and yet, intended recipients are still the only ones who are able to read the message. He concludes with a look at the future of ciphers and where cryptography might be headed. Only basic mathematics up to high school algebra is needed to understand and enjoy the book. With a plethora of historical anecdotes and real-world examples, The Mathematics of Secrets reveals the mathematics working stealthily in the science of coded messages.
Download and read online The Mathematics Bible in PDF and EPUB Mathematics has a history filled with brilliant minds and world-changing discoveries. It just needs to be made accessible. And that's exactly what "The Mathematics Bible" does. It describes the history and development of mathematics in easily understood language. It introduces the most important players, societies and cultures, like the Ancient Egyptians and Pythagoreans, and key figures such as Galileo, Dodgson, Babbage and Lovelace. It brings the ancient science and art of mathematics into the contemporary world of the 21st century. Accessible, well-informed and fully illustrated, this is a book that shows perfectly just how varied and fascinating mathematics can be. These definitive guides to their subjects together have sold over three million copies worldwide. Their success is undoubtedly owed to the comprehensiveness and quality of content, for an excellent price, and the smaller size is nonetheless filled with 400 illustrations.