The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    Twelve Step Sponsorship delivers both the theory and practice--how to do it and why--in a clear, step-by-step presentation. Written by the author of Getting Started in AA, a widely acclaimed guide for the newcomer to the program of AA, Twelve Step Sponsorship is the first truly comprehensive look at sponsorship, a role recovering people benefit from both as sponsees and ultimately as sponsors. Twelve Step Sponsorship includes informative sections that deal with: finding a sponsor and being a sponsor. Twelve Step Sponsorship offers a welcome reinforcement to the tradition of "passing it on" from one generation of sponsors to the next.

    His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Equally legendary were Gö's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first popular biography of this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life. After describing his childhood in the Moravian capital of Brno, the authors trace the arc of Gö's remarkable career, from the famed Vienna Circle, where philosophers and scientists debated notions of truth, to the Institute for Advanced Study in Princeton, New Jersey, where he lived and worked until his death in 1978. In the process, they shed light on Gö's contributions to mathematics, philosophy, computer science, artificial intelligence -- even cosmology -- in an entertaining and accessible way.

    There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study.Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.)Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc. The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references.

    Purchasers are entitled to a free trial membership in the General Books Club where they can select from more than a million books without charge. Subjects: Astronomy; History / General; Juvenile Nonfiction / Science

    On a crisp winter morning, Richard, a successful, self-made CEO runs into Zoya, a quirky, free-spirited artist. The meeting leaves them struggling to find a balance between what they believe about life, and what is actually out there.What You Seek is Seeking You is a heart-warming tale about what happens when you are forced to question everything you ever knew to be true. Refreshingly honest, it helps you rethink some of your most fundamental beliefs – the ones that hold the very canvas of your life in place, but which in fact may be limiting you.Setting the scene with a lively fable, Azim & Brian share insightful and tangible ways to:• Invite Positive Coincidences and Attract What You Seek• Set Goals, Remain Focused and yet Stay Detached from the Outcome• Enhance Your Business AcumenBrian Tracy is one of the finest self-help speakers of all times, a bestselling author of 70 books and a human potential expert. He has consulted for more than 1,000 companies and has spoken to 5,000,000 people in 65 countries. Brian is the Chairman and CEO of Brian Tracy International and his goal is to help you achieve your personal and business goals faster and easier than you ever imagined.Azim Jamal is one of the finest inspirational life altering speakers who has spoken to more than 1,000,000 people worldwide in 26 countries and his various media messages have been heard by more than 5,000,000 people. He is the CEO and founder of Corporate Sufi Worldwide whose mission is to inspire individuals and corporations to unleash their power within and find harmony between Business, Balance and Beyond.

    It's extremely selfish to think we are the only existing intelligent life. Science and religion are on the verge of discovering the truth. Super ancient societies and their archaeological evidence uncovered to this day is a vault of stored information waiting to be unlocked. All we need to do is find the key. Help us uncover the truth by learning about Ancient Earth Mysteries.

    Beat him to death with a tree branch after he threatened to rape her. But what started as self-defense became problematic for two reasons. First, she killed Robert Sims after he’d been rendered completely defenseless. And second, she inadvertently left her fingerprints at the scene. Allie is young, beautiful, the smartest person in any room. But she’s also been diagnosed as clinically insane. As her past catches up with her and her marriage starts to crumble, Allie is determined to survive at all costs. Size Matters is a taut, compelling novel that teaches us never to underestimate a woman with nothing to lose. PRELIMINARY REVIEWS: “Size Matters is so full of twists and turns and surprises I couldn’t have flipped the pages faster if you paid me! This novel surprised and delighted and kept me shaking my head time and again. Fans of Donovan Creed should be aware that he and Callie make a brief appearance that furthers their saga.” “‘I’ve done bad things,’ says Allie McPherson, ‘but that doesn’t make me a bad person.’ Well, that’s one opinion!” “This book is crazy! There are twists and turns on virtually every page! While I consider myself an expert on Locke novels, I have to admit he took me on a wild ride that made me guess wrong every single time.” “Size Matters is a cross between Alfred Hitchcock and Quentin Tarantino. From start to finish I was shocked, surprised, and hopelessly entertained.”

    Actions include his words too. And life is all about these three facets of hands, heart and head. But there is also a fourth facet that of consciousness on the background of which actions, feelings and thoughts emanate from. There is a lot said and written about these three facets. There is a lot of training given to these three areas. But what about the fourth? In engineering everybody understands the three facets of input, process and output. People understand that improving the output is not possible until process and specially input is changed. But is there a fourth aspect besides input, process and output. And the fourth aspect is the context in which workers are creating the output by changing the output through a process. Visionary thinkers have now begun thinking and impacting the fourth aspect too. They are understanding that the context or the culture in which workers operate are more important.In human engineering, actions are equivalent to output, feelings are equivalent to the process and thoughts are the input. Behaviour and actions are brought forth because of the input of thought and the further power that feelings process. That is why to change behaviour, it is important to change your feelings (process) and more importantly your thoughts (input). Yes, thoughts are very important. Change in thoughts through positive thinking is essential. But the fourth dimension is even more important. Yes, the context in which actions, feelings and thoughts arise is that of consciousness silence experience of being alive. Very little has been understood about this fourth dimension. Some call it The Self. When that is accessed, then harnessing thoughts, feelings and actions is very simple and easy. When the context in an organization is changed, then inputs, processes and outputs can all take a quantum jump. What a leader in an organization has to do is to precisely do that ??? change the context. The three facets are all lying on the foundation of the fourth. As a leader leading your life, it is similarly important to understand and access the consciousness from where actions, feelings and thoughts arise from. That is why it is called the source. Imagine, not being clear about your own source. But that is what is happening most people don't know their own source. The secret of the third aspect of thoughts is not just enough. The source of the thoughts is what matters. Even in the name of spirituality, which is actually the study of the source, everything other than the fourth dimension is being focused on. The three dimensions spirituality focuses on are exercising, breathing and thinking: Yoga, Pranayama and Gyan. But the fourth dimension of silence, that of Moun is the missing link. In the name of spirituality yogic asanas or breathing exercises or concentration exercises in the name of meditation are given importance to. But until, the source is accessed, until consciousness is manifested, it is not complete. Man is always comfortable with the three dimensions of length, breath and depth. But the fourth dimension is what gives colour to his life. Spirituality talks about the three states of sleeping, awakening and dream states. But discovering the fourth state (turiya) is the missing link. Discovering this fourth state should be the highest priority in life.

    With his messages going beyond the centuries, Mawlana is a guide and a leader who, ages ago, told the unchanging rules of all times. Rumi is primarily an intellectual, scientist and lawyer speaking Persian, Turkish, Arabic, Greek and Hebrew languages, secondly the greatest poet of all times with his poems on love, justice and freedom accompanied by mystical passion and pain, and above all a universal wise man and a philosopher. He interprets people, humanity, life and permanent values in a holistic approach and brings forward recipes for the problems and dilemmas of all people.In this book, readers will find a pearl of inspiration from the source of eternal wisdom for each day of year.

    According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

    At the time we were hoping that our approach of writing a book which would be both accessible without mathematical sophistication and portray these exiting new fields in an authentic manner would find an audience. Now we know it did. We know from many reviews and personal letters that the book is used in a wide range of ways: researchers use it to acquaint themselves, teachers use it in college and university courses, students use it for background reading, and there is also a substantial audience of lay people who just want to know what chaos and fractals are about. Every book that is somewhat technical in nature is likely to have a number of misprints and errors in its first edition. Some of these were caught and brought to our attention by our readers. One of them, Hermann Flaschka, deserves to be thanked in particular for his suggestions and improvements. This second edition has several changes. We have taken out the two appendices from the firstedition. At the time of the first edition Yuval Fishers contribution, which we published as an appendix was probably the first complete expository account on fractal image compression. Meanwhile, Yuvals book Fractal Image Compression: Theory and Application appeared and is now the publication to refer to.

    Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems.

    I referred them to Doctor Who's Tardis.'Frank Skinner wants you to read more poetry. Wait, wait - don't stop reading. Whether you're a frequent poetry reader or haven't read any since sixth form, Frank's infectious passion for language, rhythm and metre will win you over and provide you with the basic tools you need to tackle any poem.In this short, easy-to-digest and delightful book, Frank guides us through the twists and turns of 'Pad, pad' by Stevie Smith, a short, seemingly simple poem that contains multitudes of meaning and a deceptive depth of emotion. Revel in the mastery of Stevie Smith's choice of words, consider the eternal mystery of the speaker of the poem and be moved by rhyming couplets like you never have before.Give it a go. You never know, you might even enjoy it.

    Describing experiments that show that human infants have a rudimentary number sense, Stanislas Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how our mathematics opens up a window on the human mind.