This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician's treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements, Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.

    An extremely clever account.--The New Yorker.

    With fresh insight, Martie Haselton explains how the fertility cycle has evolved over millions of years into a fine-tuned signaling system. Among the fascinating findings: During ovulation, women's attractiveness peaks because their "mate search effort" is turned on. Their walking gait, voice, skin condition, and dance moves are more alluring, and they wear more revealing clothes. They also tend to shop more. Being on the Pill affects women's preferences in men, and PMS may have evolved to get rid of boyfriends with unfit sperm. The research is provocative, but Haselton also presents practical advice for women to use their hormonal cycles to their advantage, helping them achieve success in their relationships, careers, and lives. Groundbreaking and counter-intuitive, HORMONAL will empower women everywhere to embrace their biology.

    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.

    

     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!)."

    Here Lawrence M. Krauss, himself a theoretical physicist and best-selling author, offers a unique scientific biography: a rollicking narrative coupled with clear and novel expositions of science at the limits. An immensely colorful persona in and out of the office, Feynman revolutionized our understanding of nature amid a turbulent life. Krauss presents that life—from the death of Feynman’s childhood sweetheart during the Manhattan Project to his reluctant rise as a scientific icon—as seen through the science, providing a new understanding of the legacy of a man who has fascinated millions. An accessible reflection on the issues that drive physics today, Quantum Man captures the story of a man who was willing to break all the rules to tame a theory that broke all the rules.

    Collected here to keep your wits sharp, The Best Brain Teasers of All Time features the cleverest brain teasers from around the world and throughout history.The Best Brain Teasers of All Time gives you hours of fun-filled entertainment with brain teasers that develop your problem-solving skills in math, logic, and wordplay. Organized as an integrated challenge, these brain teasers build in momentum as they increase in difficulty from classic nursery rhymes to the riddle of the sphinx.The Best Brain Teasers of All Time puts your mind to the test with: 125 Brain Teasers that require no special skills to solve. Plus, each question comes with an optional clue in case you get stumped and a handy answer key in the back to test yourself or play with friends Brain Teasers for Every Level that cater to beginners and advanced masterminds alike, with brain teasers organized by level of difficulty to improve your skills as you move forward Hints of History that provide fun facts and background information for every brain teaser Get ready to sharpen your wit with every “aha” moment. The Best Brain Teasers of All Time is a go-to source for timeless fun and mind-blowing challenges.

    The Golden Section—otherwise known as phi, the golden mean, or the golden ratio—is one of the most elegant and beautiful rations in the universe.Defined as a line segment divided into two unequal parts, such that the ratio of the shorter portion to the longer portion is the same as the ratio of the longer portion to the whole, it pops up throughout nature—in water, DNA, the proportions of fish and butterflies, and the number of teeth we possess—as well as in art and architecture, music, philosophy, science, and mathematics.Beautifully illustrated, The Golden Section tells the story of this remarkable construct and its wide-ranging impact on civilization and the natural world.

    But a dispute over its discovery sowed the seeds of discontent between two of the greatest scientific giants of all time - Sir Isaac Newton and Gottfried Wilhelm Leibniz." "Today Newton and Leibniz are generally considered the twin independent inventors of calculus. They are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret." This long and bitter dispute has been swept under the carpet by historians - perhaps because it reveals Newton and Leibniz in their worst light - but The Calculus Wars tells the full story in narrative form for the first time. This history ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad, and in the end completely human.

    It will make you angry. It will amaze you with the courage of some of the people described in the book...The Autoimmune Epidemic is every bit as compelling as Upton Sinclair's The Jungle...It is also every bit as necessary as An Inconvenient Truth.... You will leave this book with no reservations about the veracity of the conclusions: put simply, there is no doubt that autoimmune diseases are on the rise and increasing environmental exposures of toxins and chemicals is fueling this rise. The research is sound. The conclusions unassailable.... Reading The Autoimmune Epidemic is a necessary first step. Reading The Autoimmune Epidemic is a life-altering event. It needs to be."

    This well-established two-book course is designed for class teaching and private study leading to GCSE examinations in mathematics and further Mathematics at A Level.

    QED--the edited version of four lectures on quantum electrodynamics that Feynman gave to the general public at UCLA as part of the Alix G. Mautner Memorial Lecture series--is perhaps the best example of his ability to communicate both the substance and the spirit of science to the layperson.The focus, as the title suggests, is quantum electrodynamics (QED), the part of the quantum theory of fields that describes the interactions of the quanta of the electromagnetic field-light, X rays, gamma rays--with matter and those of charged particles with one another. By extending the formalism developed by Dirac in 1933, which related quantum and classical descriptions of the motion of particles, Feynman revolutionized the quantum mechanical understanding of the nature of particles and waves. And, by incorporating his own readily visualizable formulation of quantum mechanics, Feynman created a diagrammatic version of QED that made calculations much simpler and also provided visual insights into the mechanisms of quantum electrodynamic processes.In this book, using everyday language, spatial concepts, visualizations, and his renowned "Feynman diagrams" instead of advanced mathematics, Feynman successfully provides a definitive introduction to QED for a lay readership without any distortion of the basic science. Characterized by Feynman's famously original clarity and humor, this popular book on QED has not been equaled since its publication.

    It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.

    Laughlin transports us two centuries into the future, when we've ceased to use carbon from the ground--either because humans have banned carbon burning or because fuel has simply run out. Boldly, Laughlin predicts no earth-shattering transformations will have taken place. Six generations from now, there will still be soccer moms, shopping malls, and business trips. Firesides will still be snug and warm.How will we do it? Not by discovering a magic bullet to slay our energy problems, but through a slew of fascinating technologies, drawing on wind, water, and fire. Powering the Future is an objective yet optimistic tour through alternative fuel sources, set in a world where we've burned every last drop of petroleum and every last shovelful of coal.The Predictable: Fossil fuels will run out. The present flow of crude oil out of the ground equals in one day the average flow of the Mississippi River past New Orleans in thirteen minutes. If you add the energy equivalents of gas and coal, it's thirty-six minutes. At the present rate of consumption, we'll be out of fossil fuels in two centuries' time. We always choose the cheapest gas. From the nineteenth-century consolidation of the oil business to the California energy crisis of 2000-2001, the energy business has shown, time and again, how low prices dominate market share. Market forces--not green technology--will be the driver of energy innovation in the next 200 years. The laws of physics remain fixed. Energy will still be conserved, degrade entropically with use, and have to be disposed of as waste heat into outer space. How much energy a fuel can pack away in a given space is fixed by quantum mechanics--and if we want to keep flying jet planes, we will need carbon-based fuels. The Potential: Animal waste. If dried and burned, the world's agricultural manure would supply about one-third as much energy as all the coal we presently consume. Trash. The United States disposes of 88 million tons of carbon in its trash per year. While the incineration of waste trash is not enough to contribute meaningfully to the global demand for energy, it will constrain fuel prices by providing a cheap supply of carbon. Solar energy. The power used to light all the cities around the world is only one-millionth of the total power of sunlight pouring down on earth's daytime side. And the amount of hydropump storage required to store the world's daily electrical surge is equal to only eight times the volume of Lake Mead. PRAISE FOR ROBERT B. LAUGHLIN -Perhaps the most brilliant theoretical physicist since Richard Feynman---George Chapline, Lawrence Livermore National Laboratory -Powerful but controversial.--- Financial Times -[Laughlin's] company ... is inspirational.- --New Scientist