How does Jane Goodall’s relationship with her dog Rusty inform her thinking about our relationship to other species? Which time and place would Jared Diamond most prefer to live in, in light of his work on the role of chance in history? What does driving a sports car have to do with Steven Weinberg’s quest for the “theory of everything”? Physicist and journalist Stefan Klein’s intimate conversations with nineteen of the world’s best-known scientists (including three Nobel Laureates) let us listen in as they talk about their paradigm-changing work—and how it is deeply rooted in their daily lives. • Cosmologist Martin Rees on the beginning and end of the world • Evolutionary biologist Richard Dawkins on egoism and selflessness • Neuroscientist V. S. Ramachandran on consciousness • Molecular biologist Elizabeth Blackburn on aging • Philosopher Peter Singer on morality • Physician and social scientist Nicholas Christakis on human relationships • Biochemist Craig Venter on the human genome • Chemist and poet Roald Hoffmann on beauty

    This user-friendly self-study guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); simple black holes and relativistic cosmology. Following the historic 2015 LIGO (Laser Interferometer Gravitational-Wave Observatory) detection, there is now an additional chapter on gravitational waves, ripples in the fabric of spacetime that potentially provide a revolutionary new way to study the universe. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes.Understand even the basics of Einstein's amazing theory and the world will never seem the same again. ContentsPrefaceIntroduction1 Foundation mathematics2 Newtonian mechanics3 Special relativity4 Introducing the manifold5 Scalars, vectors, one-forms and tensors6 More on curvature7 General relativity8 The Newtonian limit9 The Schwarzschild metric10 Schwarzschild black holes11 Cosmology12 Gravitational wavesAppendix: The Riemann curvature tensorBibliographyAcknowledgementsJanuary 2019. This third edition has been revised to make the material even more accessible to the enthusiastic general reader who seeks to understand the mathematics of relativity.

    There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular “Good Math” blog, you’ll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird.Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing.If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark’s book will both entertain and enlighten you.

    

     They were preparing to compete in a poker tournament with million-dollar stakes, but those numbers meant nothing to them.  They were accustomed to risking billions.     At the card table that night was Peter Muller, an eccentric, whip-smart whiz kid who’d studied theoretical mathematics at Princeton and now managed a fabulously successful hedge fund called PDT…when he wasn’t playing his keyboard for morning commuters on the New York subway.  With him was Ken Griffin, who as an undergraduate trading convertible bonds out of his Harvard dorm room had outsmarted the Wall Street pros and made money in one of the worst bear markets of all time.  Now he was the tough-as-nails head of Citadel Investment Group, one of the most powerful money machines on earth. There too were Cliff Asness, the sharp-tongued, mercurial founder of the hedge fund AQR, a man as famous for his computer-smashing rages as for his brilliance, and Boaz Weinstein, chess life-master and king of the credit default swap, who while juggling $30 billion worth of positions for Deutsche Bank found time for frequent visits to Las Vegas with the famed MIT card-counting team.     On that night in 2006, these four men and their cohorts were the new kings of Wall Street.  Muller, Griffin, Asness, and Weinstein were among the best and brightest of a  new breed, the quants.  Over the prior twenty years, this species of math whiz --technocrats who make billions not with gut calls or fundamental analysis but with formulas and high-speed computers-- had usurped the testosterone-fueled, kill-or-be-killed risk-takers who’d long been the alpha males the world’s largest casino.  The quants believed that a dizzying, indecipherable-to-mere-mortals cocktail of differential calculus, quantum physics, and advanced geometry held the key to reaping riches from the financial markets.  And they helped create a digitized money-trading machine that could shift billions around the globe with the click of a mouse.     Few realized that night, though, that in creating this unprecedented machine, men like Muller, Griffin, Asness and Weinstein had sowed the seeds for history’s greatest financial disaster.     Drawing on unprecedented access to these four number-crunching titans, The Quants tells the inside story of what they thought and felt in the days and weeks when they helplessly watched much of their net worth vaporize – and wondered just how their mind-bending formulas and genius-level IQ’s had led them so wrong, so fast.  Had their years of success been dumb luck, fool’s gold, a good run that could come to an end on any given day?  What if The Truth they sought -- the secret of the markets -- wasn’t knowable? Worse, what if there wasn’t any Truth?   In The Quants, Scott Patterson tells the story not just of these men, but of Jim Simons, the reclusive founder of the most successful hedge fund in history; Aaron Brown, the quant who used his math skills to humiliate Wall Street’s old guard at their trademark game of Liar’s Poker, and years later found himself with a front-row seat to the rapid emergence of mortgage-backed securities; and gadflies and dissenters such as Paul Wilmott, Nassim Taleb, and Benoit Mandelbrot.     With the immediacy of today’s NASDAQ close and the timeless power of a Greek tragedy, The Quants is at once a masterpiece of explanatory journalism, a gripping tale of ambition and hubris…and an ominous warning about Wall Street’s future.

     Learn the essential concepts using concrete analogies and vivid diagrams, not mechanical definitions. Calculus isn't a set of rules, it's a specific, practical viewpoint we can apply to everyday thinking. Frustrated With Abstract, Mechanical Lessons? I was too. Despite years of classes, I didn't have a strong understanding of calculus concepts. Sure, I could follow mechanical steps, but I had no lasting intuition. The classes I've seen are too long, taught in the wrong order, and without solid visualizations. Here's how this course is different: 1) It gets to the point. A typical class plods along, saving concepts like Integrals until Week 8. I want to see what calculus can offer by Minute 8. Each compact, tightly-written lesson can be read in 15 minutes. 2) Concepts are taught in their natural order. Most classes begin with the theory of limits, a technical concept discovered 150 years after calculus was invented. That's like putting a new driver into a Formula-1 racecar on day 1. We can begin with the easy-to-grasp concepts discovered 2000 years ago. 3) It has vivid analogies and visualizations. Calculus is usually defined as the "study of change"... which sounds like history or geology. Instead of an abstract definition, we'll see calculus a step-by-step viewpoint to explore patterns. 4) It's written by a human, for humans. I'm not a haughty professor or strict schoolmarm. I'm a friend who saw a fun way to internalize some difficult ideas. This course is a chat over coffee, not a keep-your-butt-in-your-seat lecture. The goal is to help you grasp the Aha! moments behind calculus in hours, not a painful semester (or a decade, in my case). Join Thousands Of Happy Readers Here's a few samples of anonymous feedback as people went through the course. The material covers a variety of levels, whether you're looking for intuitive appreciation or the specifics of the rules. "I've done all of this stuff before, and I do understand calculus intuitively, but this was the most fun I've had going through this kind of thing. The informal writing and multitude of great analogies really helps this become an enjoyable read and the rest is simple after that - you make this seem easy, but at the same time, you aren't doing it for us…This is what math education is supposed to be like :)" "I have psychology and medicine background so I relate your ideas to my world. To me the most useful idea was what each circle production feels like. Rings are natural growth…Slices are automatable chunks and automation cheapens production… Boards in the shape on an Arch are psychologically most palatable for work (wind up, hard part, home stretch). Brilliant and kudos, from one INTP to another." "I like how you're introducing both derivatives and integrals at the same time - it's really helps with understanding the relationship between them. Also, I appreciate how you're coming from such a different angle than is traditionally taken - it's always interesting to see where you decide to go next." "That was breathtaking. Seriously, mail my air back please, I've grown used to it. Beautiful work, thank you. Lesson 15 was masterful. I am starting to feel calculus. "d/dx is good" (sorry, couldn't resist!)."

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy.

    Now brought back into print in this revised and updated edition, the book is written within the great tradition of Abbott's Flatland, and Hinton's famous Sphereland. Accessible, imaginative, and clever, it will appeal to a wide array of readers, from serious mathematicians and computer scientists, to science fiction fans.

    Topics include: Trigonometric Identities & Equations, Circular Functions, and Polar Equations & Complex Numbers.

    More than 500 solved Examples to make concepter very clear. Exhautive Exercises for Each topic.

    H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

    Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics.In this follow-up to The Theoretical Minimum, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions. Unlike other popularizations that shy away from quantum mechanics’ weirdness, Quantum Mechanics embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area. Like The Theoretical Minimum, this volume runs parallel to Susskind’s eponymous Stanford University-hosted continuing education course.An approachable yet rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.

    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    Now that its basketball program has fallen apart, CSU’s only claim to fame is its Gravinics Department, dedicated to the study of an obscure European country—its mythology, its extraordinarily difficult language, and especially its bizarre star poet, Henderson.Having discovered Henderson’s poetry in a trash bin, Stanley Higgs becomes the foremost scholar of the poet’s work, accepts a position at Chandler State University, achieves international academic fame, marries the Dean’s daughter, and abruptly stops talking. With all of academia convinced that Higgs is formulating a great truth, the university employs Orwellian techniques to record Higgs’s every potential utterance and to save its reputation. A feckless Gravinics language student, Samuel Grapearbor, together with his long-suffering girlfriend Julia, is hired to monitor Higgs during the day. Over endless games of checkers and shared sandwiches, a uniquely silent friendship develops. As one man struggles to grow up and the other grows old, The Grasshopper King, in all of his glory, emerges.In this debut novel about treachery, death, academia, marriage, mythology, history, and truly horrible poetry, Jordan Ellenberg creates a world complete with its own geography, obscene folklore, and absurdly endearing -characters—a world where arcane subjects flourish and the smallest swerve from convention can result in -immortality.Jordan Ellenberg was born in Potomac, Maryland in 1971. His brilliance as a mathematical prodigy led to a feature in The National Enquirer, an interview with Charlie Rose on CBS’s Nightwatch, and gold medals at the Math Olympiad in Cuba and Germany. He is now an Assistant Professor of Math at Princeton University and his column, "Do the Math," appears regularly in the online journal Slate. This is his first novel.