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With the same style and insight he brought to his previous studies of American cinema, acclaimed critic David Thomson masterfully evokes the history of America’s love affair with the movies and the tangled history of Hollywood in The Whole Equation. Thomson takes us from D.W. Griffith, Charlie Chaplin, and the first movies of mass appeal to Louis B. Mayer, who understood what movies meant to America–and reaped the profits. From Capra to Kidman and Hitchcock to Nicholson, Thomson examines the passion, vanity, calculation and gossip of Hollywood and the films it has given us. This one-volume history is a brilliant and illuminating overview of “the wonder in the dark”–and the staggering impact Hollywood and its films has had on American culture.
In 1951, Carl Jung published what he considered the highest synthesis and exposition of the transformation of Self and the discovery of the divine in one of his latest and most difficult works, Aion. The equation’s complexity and uncharacteristic elements of mysticism have caused it to fall by the wayside in traditional Jungian and psychological analysis. No major work has tackled this fascinating concept until now. Leslie Stein, a disciple of noted Jungian analyst Rix Weaver, here explores this groundbreaking equation to its fullest capacity. Tracing the roots of Jung’s research back to his influences in the world of the Kabbalah and Sufi mysticism, and grounding the more esoteric philosophy toward the modern sense of identity, Stein has produced both a rigorous work of scholarship on a major figure and a guide that challenges readers to reflect on our own truths.
Pell’s Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related to this equation over the past decade. However, very few modern books have been published on Pell’s Equation, and this will be the first to give a historical development of the equation, as well as to develop the necessary tools for solving the equation. The authors provide a friendly introduction for advanced undergraduates to the delights of algebraic number theory via Pell’s Equation. The only prerequisites are a basic knowledge of elementary number theory and abstract algebra. There are also numerous references and notes for those who wish to follow up on various topics.
A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.
The objective of this book is to present for the first time the complete algorithm for roots of the general quintic equation with enough background information to make the key ideas accessible to non-specialists and even to mathematically oriented readers who are not professional mathematicians. The book includes an initial introductory chapter on group theory and symmetry, Galois theory and Tschirnhausen transformations, and some elementary properties of elliptic function in order to make some of the key ideas more accessible to less sophisticated readers. The book also includes a discussion of the much simpler algorithms for roots of the general quadratic, cubic, and quartic equations before discussing the algorithm for the roots of the general quintic equation. A brief discussion of algorithms for roots of general equations of degrees higher than five is also included. "If you want something truly unusual, try [this book] by R. Bruce King, which revives some fascinating, long-lost ideas relating elliptic functions to polynomial equations." --New Scientist
Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems associated with the covered material. These vary in difficulty, with the easiest being accessible to any high school student who has read the chapter carefully. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition. An appendix provides a springboard for further investigation of the concepts of limits, infinite series and continuity.
#1 NEW YORK TIMES BESTSELLER • The epic story of the greatest quest in all of science—the holy grail of physics that would explain the creation of the universe—from renowned theoretical physicist and author of The Future of the Mind and The Future of Humanity. When Newton discovered the law of gravity, he unified the rules governing the heavens and the Earth. Since then, physicists have been placing new forces into ever-grander theories. But perhaps the ultimate challenge is achieving a monumental synthesis of the two remaining theories—relativity and the quantum theory. This would be the crowning achievement of science, a profound merging of all the forces of nature into one beautiful, magnificent equation to unlock the deepest mysteries in science: What happened before the Big Bang? What lies on the other side of a black hole? Are there other universes and dimensions? Is time travel possible? Why are we here? Kaku also explains the intense controversy swirling around this theory, with Nobel laureates taking opposite sides on this vital question. It is a captivating, gripping story; what’s at stake is nothing less than our conception of the universe. Written with Kaku’s trademark enthusiasm and clarity, this epic and engaging journey is the story of The God Equation.
This two-part treatment explains basic theory and details, including oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention to stability problems and coexistence of periodic solutions. 1966 edition.
Why is marriage worth £200,000 a year? Why will having children make you unhappy? Why does happiness from winning the lottery take two years to arrive? Why does time heal the pain of divorce or the death of a loved one – but not unemployment? Everybody wants to be happy. But how much happiness – precisely – will each life choice bring? Should I get married? Am I really going to feel happy about the career that I picked? How can we decide not only which choice is better for us, but how much it's better for us? The result of new, unique research, The Happiness Equation brings to a general readership for the first time the new science of happiness economics. It describes how we can measure emotional reactions to different life experiences and present them in ways we can relate to. How, for instance, monetary values can be put on things that can't be bought or sold in the market – such as marriage, friendship, even death – so that we can objectively rank them in order of preference. It also explains why some things matter more to our happiness than others (like why seeing friends is worth more than a Ferrari) while others are worth almost nothing (like sunny weather). Nick Powdthavee – whose work on happiness has been discussed on both the Undercover Economist and Freakanomics blogs – brings cutting-edge research on how we value our happiness to a general audience, with a style that wears its learning lightly and is a joy to read.
"A mathematician pulls back the curtain and reveals the hidden patterns--from dating sites to divorce, sex to marriage--behind the rituals of love ... applying mathematical formulas to the most common yet complex questions pertaining to love: What's the chance of finding love? What's the probability that it will last? How do online dating algorithms work, exactly? Can game theory help us decide who to approach in a bar? At what point in your dating life should you settle down?"--Amazon.com.