It is highly recommended for anyone planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.

    From manhole covers to bubbles to subway maps, each page gives you a glimpse of the world through renowned mathematicians' eyes and reveals how their theorems and equations can be applied to nearly everything you encounter. Covering dozens of your favorite math topics, you'll find fascinating answers to questions like:How are the waiting times for buses determined?Why is Romanesco Broccoli so mesmerizing?How do you divide a cake evenly?Should you run or walk to avoid rain showers?Filled with compelling mathematical explanations, Math Geek sheds light on the incredible world of numbers hidden deep within your day-to-day life.

    It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.

    In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, challenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory. Throughout the text, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.

    It draws on extensive interviews with Kissinger, as well as 150 other sources, including Richard Nixon and Gerald Ford. In addition, it makes use of many of Kissinger's private papers. The result is an intimate narrative, filled with surprising revelations, that takes this century's most colorful statesman from his childhood as a persecuted Jew in Nazi Germany, through his tortured relationship with Richard Nixon, to his twilight years as a globe-trotting business consultant.

    Meridian exercise is a technique developed and perfected over the course of thousands of years in the Asian healing arts traditions.

    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.

    Ranging from the poignant to the comical via the simply surreal, these selections include writing by Aldous Huxley, Martin Gardner, H.G. Wells, George Gamow, G.H. Hardy, Robert Heinlein, Arthur C. Clarke, and many others. Humorous, mysterious, and always entertaining, this collection is sure to bring a smile to the faces of mathematicians and non-mathematicians alike.

    It resurrects from the vaults of neglect the polymath Jerome Cardano, a Milanese of the sixteenth century. Who is he? A gambler and blasphemer, inventor and chancer, plagued by demons and anxieties, astrologer to kings, emperors and popes. This stubborn and unworldly man was the son of a lawyer and a brothel keeper, but also a gifted physician and the unacknowledged discoverer of the mathematical foundations of quantum physics. That is the argument of this charming and intoxicatingly clever book, which is truly original in its style, and in the manner of the modernists embodies in its very form its theories about the world.'The Quantum Astrologer’s Handbook' is a science book with the panache of a novel, for readers of Carlo Rovelli or Umberto Eco. It is a work of and about genius.

    Short-Cut Math is a concise, remarkably clear compendium of about 150 math short-cuts — timesaving tricks that provide faster, easier ways to add, subtract, multiply, and divide.By using the simple foolproof methods in this volume, you can double or triple your calculation speed — even if you always hated math in school. Here's a sampling of the amazingly effective techniques you will learn in minutes: Adding by 10 Groups; No-Carry Addition; Subtraction Without Borrowing; Multiplying by Aliquot Parts; Test for Divisibility by Odd and Even Numbers; Simplifying Dividends and Divisors; Fastest Way to Add or Subtract Any Pair of Fractions; Multiplying and Dividing with Mixed Numbers, and more.The short-cuts in this book require no special math ability. If you can do ordinary arithmetic, you will have no trouble with these methods. There are no complicated formulas or unfamiliar jargon — no long drills or exercises. For each problem, the author provides an explanation of the method and a step-by-step solution. Then the short-cut is applied, with a proof and an explanation of why it works.Students, teachers, businesspeople, accountants, bank tellers, check-out clerks — anyone who uses numbers and wishes to increase his or her speed and arithmetical agility, can benefit from the clear, easy-to-follow techniques given here.

    AI is all the rage, and the buzziest AI buzz surrounds adaptive machine learning computer systems that learn intelligent behavior from massive amounts of data. This is what powers a driverless car, for example. In this book, Hector Levesque shifts the conversation to -good old fashioned artificial intelligence, - which is based not on heaps of data but on understanding commonsense intelligence. This kind of artificial intelligence is equipped to handle situations that depart from previous patterns -- as we do in real life, when, for example, we encounter a washed-out bridge or when the barista informs us there's no more soy milk.Levesque considers the role of language in learning. He argues that a computer program that passes the famous Turing Test could be a mindless zombie, and he proposes another way to test for intelligence -- the Winograd Schema Test, developed by Levesque and his colleagues. -If our goal is to understand intelligent behavior, we had better understand the difference between making it and faking it, - he observes. He identifies a possible mechanism behind common sense and the capacity to call on background knowledge: the ability to represent objects of thought symbolically. As AI migrates more and more into everyday life, we should worry if systems without common sense are making decisions where common sense is needed.

    This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.

    She wants to cover the hard-hitting issues, like world affairs and politics, but does she have the smarts for it? Thankfully, her overbearing and math-minded boss, Mr. Seki, is here to teach her how to analyze her stories with a mathematical eye.In The Manga Guide to Calculus, you'll follow along with Noriko as she learns that calculus is more than just a class designed to weed out would-be science majors. You'll see that calculus is a useful way to understand the patterns in physics, economics, and the world around us, with help from real-world examples like probability, supply and demand curves, the economics of pollution, and the density of Shochu (a Japanese liquor).Mr. Seki teaches Noriko how to:Use differentiation to understand a function's rate of change Apply the fundamental theorem of calculus, and grasp the relationship between a function's derivative and its integral Integrate and differentiate trigonometric and other complicated functions Use multivariate calculus and partial differentiation to deal with tricky functions Use Taylor Expansions to accurately imitate difficult functions with polynomials Whether you're struggling through a calculus course for the first time or you just need a painless refresher, you'll find what you're looking for in The Manga Guide to Calculus.This EduManga book is a translation from a bestselling series in Japan, co-published with Ohmsha, Ltd. of Tokyo, Japan.

    As they see matters, wealth in the form of means of production and wealth in the form of consumers’ goods are essentially indistinguishable. For all practical purposes, they have no awareness of the existence of capital and of its importance. Thus, capitalists are generally depicted as fat men, whose girth allegedly signifies an excessive consumption of food and of wealth in general, while their alleged victims, the wage earners, are typically depicted as substantially underweight, allegedly signifying their inability to consume, thanks to the allegedly starvation wages paid by the capitalists.The truth is that in a capitalist economic system, the wealth of the capitalists is not only overwhelmingly in the form of means of production, such as factory buildings, machinery, farms, mines, stores, warehouses, and means of transportation and communication, but all of this wealth is employed in producing for the market, where its benefit is made available to everyone in the economic system who is able to afford to buy its products.Consider. Whoever can afford to buy an automobile benefits from the existence of the automobile factory and its equipment where that car was made. He also benefits from the existence of all the other automobile factories, whose existence and competition served to reduce the price he had to pay for his automobile. He benefits from the existence of the steel mill that provided the steel for his car, and from the iron mine that provided the iron ore needed for the production of that steel, and, of course, from the existence of all the other steel mills and iron mines whose existence and competition served to hold down the prices of the steel and iron ore that contributed to the production of his car.And, thanks to the great magnitude of wealth employed as capital, the demand for labor, of which capital is the foundation, is great enough and thus wages are high enough that virtually everyone is able to afford to a substantial degree most of the products of the economic system. For the capital of the capitalists is the foundation both of the supply of products that everyone buys and of the demand for the labor that all wage earners sell. More capital—a greater amount of wealth in the possession of the capitalists—means a both a larger and better supply of products for wage earners to buy and a greater demand for the labor that wage earners sell. Everyone, wage earners and capitalists alike, benefits from the wealth of the capitalists, because, as I say, that wealth is the foundation of the supply of the products that everyone buys and of the demand for the labor that all wage earners sell. More capital in the hands of the capitalists always means a more abundant, better quality of goods and services offered for sale and a larger demand for labor. The further effect is lower prices and higher wages, and thus a higher standard of living for wage earners.Furthermore, the combination of the profit motive and competition operates continually to improve the products offered in the market and the efficiency with which they are produced, thus steadily further improving the standard of living of everyone.In the alleged conflict between the so-called 99 percent and the so-called 1 percent, the program of the 99 percent is to seize as far as possible the wealth of the 1 percent and consume it. To the extent that it is enacted, the effect of this program can only be to impoverish everyone, and the 99 percent to a far greater extent than the 1 percent. To the extent that the 1 percent loses its mansions, luxury cars, and champagne and caviar, 99 times as many people lose their houses, run-of-the mill cars, and steak and hamburger.

    This network has been called a greater invention than the steam engine, comparable only to the development of the printing press.Robert P. Crease traces the evolution of this international system from the use of flutes to measure distance in the dynasties of ancient China and figurines to weigh gold in West Africa to the creation of the French metric and British imperial systems. The former prevailed, with the United States one of three holdout nations. Into this captivating history Crease weaves stories of colorful individuals, including Thomas Jefferson, an advocate of the metric system, and American philosopher Charles S. Peirce, the first to tie the meter to the wavelength of light. Tracing the dynamic struggle for ultimate precision, World in the Balance demonstrates that measurement is both stranger and more integral to our lives than we ever suspected.