But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    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.

    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.

    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.

    Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: ..". all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999..". the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals."

    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.

    This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

    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.

    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.

    Keeping an open mind, looking for unusual number combinations, using multiple skills (like subtracting to add) and looking for patterns will guarantee any child success in math. In MATH APPEAL, Tang continues to challenge kids with his innovative approach to math.

    Maisel, Monk) calmly tells the tale of how the ancient Greeks formalized the study of mathematics based on Phoenician teachings. Bedtime stories are narrated by the world’s most celebrated voices and written with no beginning, middle, or end so you don’t stay up to hear what happens next. They're interesting enough to give your mind something to focus on, but delivered in a way that encourages sleep. This title is part of the Audible Sleep Collection, exclusive audio experiences created to invite relaxation and sleep. New and free for members.Public Domain (P)2020 Audible

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

    First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as self-evident." --Arthur SchopenhauerThe Ponzi Factor is the most comprehensive research ever compiled on the negative-sum nature of capital gains (non-dividend stocks). The book shows why, as a whole, ALL investors will lose money from buying and selling stocks.Most people don’t realize that profits from buying and selling stocks come from other investors who are also buying and selling stocks. When one investor buys low and sells high, another investor is also buying high and needs to sell for even higher. Companies like Google, Telsa, Facebook never pay their investors. Their investors’ profits are dependent on the inflow of money from new investors, which by definition, is how a Ponzi scheme works.This book is not for everyone. If you are a finance junkie who wants to rationalize why companies don’t have to pay their investors and believe a system that shuffles money between investor can magically create more money than people contribute, then this book is not for you. On the other hand, if you understand why we can’t create money by shuffling it with imaginary paper, and that investors invest because they want money, not value, then you will learn something you will never forget: The mechanics of how the stock market works and what really makes a stock price move.A stock without dividends is a Ponzi asset. It’s not how equity instruments were designed to work historically and not how ownership instruments are supposed to work logically. The Ponzi Factor is not a perspective or an opinion. It is a proof that is based on definition, logic, and it is supported by observable facts and history. This is not a story that will disappear after another market crash. It is an idea that will remain relevant for as long as the stock market exists.Lastly, to critics, the naysayer, and the finance junkies who think the imaginary value = cash. The author will award $20,000 to anyone who can show why non-dividend stocks DO NOT meet the definition of a Ponzi scheme. That’s $20,000 in cash, not value. (Details on this book's website. The Ponzi Factor. Proof by Definition.)

    In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    Written by the well-known mathematics teacher consultant, this volume's collection of over 200 clearly illustrated mathematical ideas, concepts, puzzles, and games shows where they turn up in the real world. You'll find out what a googol is, visit hotel infinity, read a thorny logic problem that was stumping them back in the 8th century.THE JOY OF MATHEMATICS is designed to be opened at random...it's mini essays are self-contained providing the reader with an enjoyable way to explore and experience mathematics at its best.