A rich, narrative explanation of the mathematics that has brought us machine learning and the ongoing explosion of artificial intelligence Machine learning systems are making life-altering decisions for us: approving mortgage loans, determining whether a tumor is cancerous, or deciding if someone gets bail. They now influence developments and discoveries in chemistry, biology, and physics—the study of genomes, extrasolar planets, even the intricacies of quantum systems. And all this before large language models such as ChatGPT came on the scene. We are living through a revolution in machine learning-powered AI that shows no signs of slowing down. This technology is based on relatively simple mathematical ideas, some of which go back centuries, including linear algebra and calculus, the stuff of seventeenth- and eighteenth-century mathematics. It took the birth and advancement of computer science and the kindling of 1990s computer chips designed for video games to ignite the explosion of AI that we see today. In this enlightening book, Anil Ananthaswamy explains the fundamental math behind machine learning, while suggesting intriguing links between artificial and natural intelligence. Might the same math underpin them both? As Ananthaswamy resonantly concludes, to make safe and effective use of artificial intelligence, we need to understand its profound capabilities and limitations, the clues to which lie in the math that makes machine learning possible. Read more

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 Read more

The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this comprehensive workbook (with full solutions to every problem) to share his strategies for mastering calculus. This workbook covers a variety of essential calculus skills, including:derivatives of polynomials, trig functions, exponentials, and logarithmsthe chain rule, product rule, and quotient rulesecond derivativeshow to find the extreme values of a functionlimits, including l’Hopital’s ruleantiderivatives of polynomials, trig functions, exponentials, and logarithmsdefinite and indefinite integralstechniques of integration, including substitution, trig sub, and integration by partsmultiple integralsThe goal of this workbook isn’t to cover every possible topic from calculus, but to focus on the most essential skills needed to apply calculus to other subjects, such as physics or engineering. Read more

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INSTANT NEW YORK TIMES BESTSELLER“A new masterpiece from one of my favorite authors… [How The World Really Works] is a compelling and highly readable book that leaves readers with the fundamental grounding needed to help solve the world’s toughest challenges.”—Bill Gates “Provocative but perceptive . . . You can agree or disagree with Smil—accept or doubt his ‘just the facts’ posture—but you probably shouldn’t ignore him.”—The Washington PostAn essential analysis of the modern science and technology that makes our twenty-first century lives possible—a scientist's investigation into what science really does, and does not, accomplish.We have never had so much information at our fingertips and yet most of us don’t know how the world really works. This book explains seven of the most fundamental realities governing our survival and prosperity. From energy and food production, through our material world and its globalization, to risks, our environment and its future, How the World Really Works offers a much-needed reality check—because before we can tackle problems effectively, we must understand the facts. In this ambitious and thought-provoking book we see, for example, that globalization isn’t inevitable—the foolishness of allowing 70 per cent of the world’s rubber gloves to be made in just one factory became glaringly obvious in 2020—and that our societies have been steadily increasing their dependence on fossil fuels, such that any promises of decarbonization by 2050 are a fairy tale. For example, each greenhouse-grown supermarket-bought tomato has the equivalent of five tablespoons of diesel embedded in its production, and we have no way of producing steel, cement or plastics at required scales without huge carbon emissions. Ultimately, Smil answers the most profound question of our age: are we irrevocably doomed or is a brighter utopia ahead? Compelling, data-rich and revisionist, this wonderfully broad, interdisciplinary guide finds faults with both extremes. Looking at the world through this quantitative lens reveals hidden truths that change the way we see our past, present and uncertain future. Read more

The classic book on systems thinking—with more than half a million copies sold worldwide!"This is a fabulous book… This book opened my mind and reshaped the way I think about investing."—Forbes "Thinking in Systems is required reading for anyone hoping to run a successful company, community, or country. Learning how to think in systems is now part of change-agent literacy. And this is the best book of its kind."—Hunter Lovins In the years following her role as the lead author of the international bestseller, Limits to Growth—the first book to show the consequences of unchecked growth on a finite planet—Donella Meadows remained a pioneer of environmental and social analysis until her untimely death in 2001.Thinking in Systems is a concise and crucial book offering insight for problem solving on scales ranging from the personal to the global. Edited by the Sustainability Institute’s Diana Wright, this essential primer brings systems thinking out of the realm of computers and equations and into the tangible world, showing readers how to develop the systems-thinking skills that thought leaders across the globe consider critical for 21st-century life.Some of the biggest problems facing the world—war, hunger, poverty, and environmental degradation—are essentially system failures. They cannot be solved by fixing one piece in isolation from the others, because even seemingly minor details have enormous power to undermine the best efforts of too-narrow thinking.While readers will learn the conceptual tools and methods of systems thinking, the heart of the book is grander than methodology. Donella Meadows was known as much for nurturing positive outcomes as she was for delving into the science behind global dilemmas. She reminds readers to pay attention to what is important, not just what is quantifiable, to stay humble, and to stay a learner.In a world growing ever more complicated, crowded, and interdependent, Thinking in Systems helps readers avoid confusion and helplessness, the first step toward finding proactive and effective solutions. Read more

A groundbreaking treatise by one of the great mathematicians of our age, who outlines a style of thinking by which great ideas are conceived.What inspires and spurs on a great idea? Can we train ourselves to think in a way that will enable world-changing understandings and insights to emerge?Richard Hamming said we can. He first inspired a generation of engineers, scientists, and researchers in 1986 with “You and Your Research,” an electrifying sermon on why some scientists do great work, why most don’t, why he did, and why you can—and should—too. The Art of Doing Science and Engineering is the full expression of what “You and Your Research” outlined. It's a book about thinking; more specifically, a style of thinking by which great ideas are conceived.The book is filled with stories of great people performing mighty deeds—but they are not meant simply to be admired. Instead, they are to be aspired to, learned from, and surpassed. Hamming consistently returns to Shannon’s information theory, Einstein’s theory of relativity, Grace Hopper’s work on high-level programming, Kaiser’s work on digital filters, and his own work on error-correcting codes. He also recounts a number of his spectacular failures as clear examples of what to avoid.Originally published in 1996 and adapted from a course that Hamming taught at the US Naval Postgraduate School, this edition includes an all-new foreword by designer, engineer, and founder of Dynamicland Bret Victor, plus more than 70 redrawn graphs and charts.The Art of Doing Science and Engineering is a reminder that a capacity for learning and creativity are accessible to everyone. Hamming was as much a teacher as a scientist, and having spent a lifetime forming and confirming a theory of great people and great ideas, he prepares the next generation for even greater distinction. Read more

Named a Best Book of the Year by Forbes and The EconomistFrom our "greatest living statistical communicator" (Tim Harford) comes an invaluable, data-driven guide for understanding—and learning to embrace—risk and uncertainty in our daily lives.How dangerous is our diet? How much of sports falls into the realm of luck? When authorities categorize a given event as “highly likely”—how likely is that, really? Whether we’re trying to decide if the benefits of a new medication are worth the chance of side effects or if artificial intelligence truly threatens humanity, our lives are riddled with uncertainties both everyday and existential—yet it can be difficult to know how to properly weigh all those unknowns. Luckily for us, renowned statistician David Spiegelhalter has spent his career dissecting data to resolve the apparently random and decode the many decisions we face with imperfect information. In The Art of Uncertainty, he shows how we can become better at dealing with what we don’t know to make smarter choices in a world so full of puzzling variablesIn lucid, lively prose, Spiegelhalter guides us through the principles of probability, illustrating how they can help us think more analytically about everything from medical advice to sports to climate change forecasts. He demonstrates how taking a mathematical approach to phenomena we might otherwise attribute to fate or luck can help us sort hidden patterns from mere coincidences, better evaluate cause and effect, and predict what’s likely to happen in the future. Along the way, we learn how a misinterpretation of a probability contributed to the infamous Bay of Pigs fiasco, why a ship twice the size of the Titanic sank without a trace, and why we can be so confident that no two properly shuffled decks of cards have ever been in the same orderSparkling with wit and fascinating real-world examples, this is an essential guide to navigating uncertainty while also retaining the humility to admit what we don’t, or simply cannot, know. Read more

#1 INTERNATIONAL BESTSELLER AN ADAM SAVAGE BOOK CLUB PICKThe book-length answer to anyone who ever put their hand up in math class and asked, “When am I ever going to use this in the real world?” “Fun, informative, and relentlessly entertaining, Humble Pi is a charming and very readable guide to some of humanity's all-time greatest miscalculations—that also gives you permission to feel a little better about some of your own mistakes.” —Ryan North, author of How to Invent Everything Our whole world is built on math, from the code running a website to the equations enabling the design of skyscrapers and bridges. Most of the time this math works quietly behind the scenes . . . until it doesn’t. All sorts of seemingly innocuous mathematical mistakes can have significant consequences. Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean. Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun. Read more

INSTANT NEW YORK TIMES BESTSELLER“One of the most important books I’ve ever read—an indispensable guide to thinking clearly about the world.” – Bill Gates“Hans Rosling tells the story of ‘the secret silent miracle of human progress’ as only he can. But Factfulness does much more than that. It also explains why progress is so often secret and silent and teaches readers how to see it clearly.” —Melinda Gates"Factfulness by Hans Rosling, an outstanding international public health expert, is a hopeful book about the potential for human progress when we work off facts rather than our inherent biases." - Former U.S. President Barack ObamaFactfulness: The stress-reducing habit of only carrying opinions for which you have strong supporting facts. When asked simple questions about global trends—what percentage of the world’s population live in poverty; why the world’s population is increasing; how many girls finish school—we systematically get the answers wrong. So wrong that a chimpanzee choosing answers at random will consistently outguess teachers, journalists, Nobel laureates, and investment bankers.In Factfulness, Professor of International Health and global TED phenomenon Hans Rosling, together with his two long-time collaborators, Anna and Ola, offers a radical new explanation of why this happens. They reveal the ten instincts that distort our perspective—from our tendency to divide the world into two camps (usually some version of us and them) to the way we consume media (where fear rules) to how we perceive progress (believing that most things are getting worse). Our problem is that we don’t know what we don’t know, and even our guesses are informed by unconscious and predictable biases.It turns out that the world, for all its imperfections, is in a much better state than we might think. That doesn’t mean there aren’t real concerns. But when we worry about everything all the time instead of embracing a worldview based on facts, we can lose our ability to focus on the things that threaten us most. Inspiring and revelatory, filled with lively anecdotes and moving stories, Factfulness is an urgent and essential book that will change the way you see the world and empower you to respond to the crises and opportunities of the future. ---“This book is my last battle in my life-long mission to fight devastating ignorance…Previously I armed myself with huge data sets, eye-opening software, an energetic learning style and a Swedish bayonet for sword-swallowing. It wasn’t enough. But I hope this book will be.” Hans Rosling, February 2017. Read more

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Dive into the realm of mathematical mastery with Silvanus P. Thompson's timeless guide, "Calculus Made Easy: Your Guide to Mastering Mathematical Concepts." Thompson's approachable style and clear explanations make calculus not just understandable but enjoyable.As Thompson demystifies complex mathematical concepts, you'll find yourself empowered with a newfound understanding of calculus. Gone are the days of confusion and frustration; welcome to a world where calculus becomes second nature.But here's the intriguing question that arises: What if mastering calculus isn't just about solving equations, but unlocking the secrets of the universe itself? Could calculus be the key to understanding the very fabric of reality?Unravel the intricacies of calculus through Thompson's expert guidance, where each concept builds upon the last, leading you on a journey of intellectual discovery. Embrace the challenge and uncover the beauty hidden within mathematical equations.Are you ready to embark on a journey that will forever change the way you see the world around you?Engage with bite-sized explanations that make even the most daunting calculus problems seem manageable. Thompson's clarity of thought illuminates the path to mathematical enlightenment.Here's your opportunity to not just learn calculus, but to master it. This book is more than a guide; it's a roadmap to mathematical brilliance. Will you seize the chance to unlock the power of calculus?Take the first step towards mathematical proficiency. Acquire your copy of "Calculus Made Easy: Your Guide to Mastering Mathematical Concepts" now, and embark on a journey that will forever transform your understanding of the mathematical universe. Read more

An ode to triangles, the shape that makes our lives possible   Trigonometry is perhaps the most essential concept humans have ever devised. The simple yet versatile triangle allows us to record music, map the world, launch rockets into space, and be slightly less bad at pool. Triangles underpin our day-to-day lives and civilization as we know it.   In Love Triangle, Matt Parker argues we should all show a lot more love for triangles, along with all the useful trigonometry and geometry they enable. To prove his point, he uses triangles to create his own digital avatar, survive a harrowing motorcycle ride, cut a sandwich, fall in love, measure tall buildings in a few awkward bounds, and make some unusual art. Along the way, he tells extraordinary and entertaining stories of the mathematicians, engineers, and philosophers—starting with Pythagoras—who dared to take triangles seriously.   This is the guide you should have had in high school—a lively and definitive answer to “Why do I need to learn about trigonometry?” Parker reveals triangles as the hidden pattern beneath the surface of the contemporary world. Like love, triangles actually are all around. And in the air. And they’re all you need. Read more

An exquisite visual celebration of the 2,500-year history of geometryIf you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics. Read more

Game Theory 101: The Complete Textbook is a no-nonsense, games-centered introduction to strategic form (matrix) and extensive form (game tree) games. From the first lesson to the last, this textbook introduces games of increasing complexity and then teaches the game theoretical tools necessary to solve them. Inside, you will find: 1) All the basics fully explained, including pure strategy Nash equilibrium, mixed strategy Nash equilibrium, the mixed strategy algorithm, how to calculate payoffs, strict dominance, weak dominance, iterated elimination of strictly dominated strategies, iterated elimination of weakly dominated strategies, subgame perfect equilibrium, backward induction, forward induction, and more. 2) Dozens of games solved, including the prisoner’s dilemma, stag hunt, matching pennies, zero sum games, battle of the sexes/Bach or Stravinsky, chicken/snowdrift, pure coordination, deadlock, safety in numbers, Selten's game, the escalation game, the ultimatum game, the pirate game, nim, the centipede game, the hawk-dove game, the volunteer's dilemma, and rock-paper-scissors. 3) Rich descriptions of important economic concepts such as commitment problems, burning bridges, perverse incentives, and the chain store paradox. 4) Advanced topics such as generalized games, comparative statics, and knife-edge conditions. 5) Real world applications including wars, firm entry/exit, tournament strategy, arms races, advertising, game shows, soccer, baseball, video games, and more. 6) Crystal clear, line-by-line calculations of every step, with more than 400 images so you don’t miss a thing. Quick, efficient, and to the point, Game Theory 101: The Complete Textbook is perfect for introductory game theory, intermediate microeconomics, and political science. Read more

Has the abstract nature of linear algebra ever left you overwhelmed? Do you yearn to unlock the essence of machine learning but are bogged down by the intricacy of the mathematics? Dive into a realm where linear algebra unfolds not just as numerical operations, but as a powerful story. A story intertwined with the magic of machine learning, making sense of data, and unraveling algorithms that power tomorrow.I am Jorge, a mathematician with over a decade of hands-on experience in data science and machine learning. Having navigated the intricate pathways of mathematical computations and machine learning algorithms myself, I wrote this book that differs itself from a traditional text book. With a conversational style and humour, I will guide through what you've been seeking on your journey into the depths of linear algebra.This book isn’t just about understanding linear algebra—it’s about experiencing it. Dive into real-world applications, and grasp concepts that are foundational to machine learning:Intuitive Understanding: Approach linear algebra as a story, where vectors and matrices come alive, making complex ideas feel intuitive and relatable.Comprehensive Coverage: From the basics of vector addition and matrix multiplication to advanced topics like eigen decomposition and principal component analysis, get a 360-degree understanding.Practical Applications: Discover how linear algebra powers algorithms, aiding in data interpretation and model building.Key takeaways include:Mastering vectors and matrices in real-world scenarios.The magic behind eigenvectors, eigenvalues, and their applications.Gaining insights into advanced topics like the singular value decomposition.And this is just the tip of the iceberg. Dive in to uncover the essence of machine learning through the lens of linear algebra, and let mathematics weave its story.Ready to embark on this transformative journey? Don't miss out—let the power of linear algebra unveil the mysteries of machine learning.24/01/2024 - UPDATESRefined definition of vectors spaces.New example of the dot product.Notation fixes.Complementary exercises. Grab your copy now! Read more

Are you looking for a clear, accessible guide to mathematics that can help you brush up your skills and rediscover the key concepts and techniques? Complete Mathematics provides an invaluable, step-by-step introduction to the subject. Packed full of worked examples and useful exercises, it will guide you through the essentials quickly and easily, giving you the knowledge you need to gain maths confidence.NOT GOT MUCH TIME?One, five and ten-minute introductions to key principles to get you started.AUTHOR INSIGHTSLots of instant help with common problems and quick tips for success, based on the author's many years of experience.TEST YOURSELFTests in the book and online to keep track of your progress.EXTEND YOUR KNOWLEDGEExtra online articles at www.teachyourself.com to give you a richer understanding of psychology.FIVE THINGS TO REMEMBERQuick refreshers to help you remember the key facts.TRY THISInnovative exercises illustrate what you've learnt and how to use it. Read more

Learn how to think like a physicist from a Nobel laureate and "one of the greatest minds of the twentieth century" (New York Review of Books) with these six classic and beloved lessons It was Richard Feynman's outrageous and scintillating method of teaching that earned him legendary status among students and professors of physics. From 1961 to 1963, Feynman delivered a series of lectures at the California Institute of Technology that revolutionized the teaching of physics around the world. Six Easy Pieces, taken from these famous Lectures on Physics, represent the most accessible material from the series. In these classic lessons, Feynman introduces the general reader to the following topics: atoms, basic physics, energy, gravitation, quantum mechanics, and the relationship of physics to other topics. With his dazzling and inimitable wit, Feynman presents each discussion with a minimum of jargon. Filled with wonderful examples and clever illustrations, Six Easy Pieces is the ideal introduction to the fundamentals of physics by one of the most admired and accessible physicists of modern times. "If one book was all that could be passed on to the next generation of scientists it would undoubtedly have to be Six Easy Pieces."- John Gribbin, New Scientist Read more

A look inside the world of “quants” and how science can (and can’t) predict financial markets: “Entertaining and enlightening” (The New York Times).   After the economic meltdown of 2008, Warren Buffett famously warned, “beware of geeks bearing formulas.” But while many of the mathematicians and software engineers on Wall Street failed when their abstractions turned ugly in practice, a special breed of physicists has a much deeper history of revolutionizing finance. Taking us from fin-de-siècle Paris to Rat Pack–era Las Vegas, from wartime government labs to Yippie communes on the Pacific coast, James Owen Weatherall shows how physicists successfully brought their science to bear on some of the thorniest problems in economics, from options pricing to bubbles.   The crisis was partly a failure of mathematical modeling. But even more, it was a failure of some very sophisticated financial institutions to think like physicists. Models—whether in science or finance—have limitations; they break down under certain conditions. And in 2008, sophisticated models fell into the hands of people who didn’t understand their purpose, and didn’t care. It was a catastrophic misuse of science. The solution, however, is not to give up on models; it’s to make them better.   This book reveals the people and ideas on the cusp of a new era in finance, from a geophysicist using a model designed for earthquakes to predict a massive stock market crash to a physicist-run hedge fund earning 2,478.6% over the course of the 1990s. Weatherall shows how an obscure idea from quantum theory might soon be used to create a far more accurate Consumer Price Index. The Physics of Wall Street will change how we think about our economic future.   “Fascinating history . . . Happily, the author has a gift for making complex concepts clear to lay readers.” —Booklist Read more

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