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Author: Brian W. Kernighan
Publisher: Princeton University Press
ISBN: 069120909X
Category : Mathematics
Languages : en
Pages : 176
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Book Description
"Numbers are often intimidating, confusing, and even deliberately deceptive--especially when they are really big. The media loves to report on millions, billions, and trillions, but frequently makes basic mistakes or presents such numbers in misleading ways. And misunderstanding numbers can have serious consequences, since they can deceive us in many of our most important decisions, including how to vote, what to buy, and whether to make a financial investment. In this short, accessible, enlightening, and entertaining book, leading computer scientist Brian Kernighan teaches anyone--even diehard math-phobes--how to demystify the numbers that assault us every day. With examples drawn from a rich variety of sources, including journalism, advertising, and politics, Kernighan demonstrates how numbers can mislead and misrepresent. In chapters covering big numbers, units, dimensions, and more, he lays bare everything from deceptive graphs to speciously precise numbers. And he shows how anyone--using a few basic ideas and lots of shortcuts--can easily learn to recognize common mistakes, determine whether numbers are credible, and make their own sensible estimates when needed. Giving you the simple tools you need to avoid being fooled by dubious numbers, Millions, Billions, Zillions is an essential survival guide for a world drowning in big--and often bad--data"--Jacket
Author: Brian W. Kernighan
Publisher: Princeton University Press
ISBN: 069120909X
Category : Mathematics
Languages : en
Pages : 176
Get Book Here
Book Description
"Numbers are often intimidating, confusing, and even deliberately deceptive--especially when they are really big. The media loves to report on millions, billions, and trillions, but frequently makes basic mistakes or presents such numbers in misleading ways. And misunderstanding numbers can have serious consequences, since they can deceive us in many of our most important decisions, including how to vote, what to buy, and whether to make a financial investment. In this short, accessible, enlightening, and entertaining book, leading computer scientist Brian Kernighan teaches anyone--even diehard math-phobes--how to demystify the numbers that assault us every day. With examples drawn from a rich variety of sources, including journalism, advertising, and politics, Kernighan demonstrates how numbers can mislead and misrepresent. In chapters covering big numbers, units, dimensions, and more, he lays bare everything from deceptive graphs to speciously precise numbers. And he shows how anyone--using a few basic ideas and lots of shortcuts--can easily learn to recognize common mistakes, determine whether numbers are credible, and make their own sensible estimates when needed. Giving you the simple tools you need to avoid being fooled by dubious numbers, Millions, Billions, Zillions is an essential survival guide for a world drowning in big--and often bad--data"--Jacket
Author: Daniel Kriz
Publisher: Princeton University Press
ISBN: 0691225737
Category : Mathematics
Languages : en
Pages : 277
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Book Description
A groundbreaking contribution to number theory that unifies classical and modern results This book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to period sheaves coming from relative p-adic Hodge theory. This makes it possible to trivialize the Hodge bundle on the infinite-level modular curve by a "canonical differential" that restricts to the Katz canonical differential on the ordinary Igusa tower. Daniel Kriz defines generalized p-adic modular forms as sections of relative period sheaves transforming under the Galois group of the modular curve by weight characters. He introduces the fundamental de Rham period, measuring the position of the Hodge filtration in relative de Rham cohomology. This period can be viewed as a counterpart to Scholze's Hodge-Tate period, and the two periods satisfy a Legendre-type relation. Using these periods, Kriz constructs splittings of the Hodge filtration on the infinite-level modular curve, defining p-adic Maass-Shimura operators that act on generalized p-adic modular forms as weight-raising operators. Through analysis of the p-adic properties of these Maass-Shimura operators, he constructs new p-adic L-functions interpolating central critical Rankin-Selberg L-values, giving analogues of the p-adic L-functions of Katz, Bertolini-Darmon-Prasanna, and Liu-Zhang-Zhang for imaginary quadratic fields in which p is inert or ramified. These p-adic L-functions yield new p-adic Waldspurger formulas at special values.
Author: Andrea Menotti
Publisher: Chronicle Books
ISBN: 1452113076
Category : Juvenile Fiction
Languages : en
Pages : 27
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Book Description
How many jelly beans are enough? How many are too many? Aiden and Emma can't decide. Is 10 enough? How about 1,000? That's a lot of jelly beans. But eaten over a whole year, it's only two or three a day. This giant picture book offers kids a fun and easy way to understand large numbers. Starting with 10, each page shows more and more colorful candies, leading up to a big surprise—ONE MILLION JELLY BEANS! With bright illustrations, How Many Jelly Beans? makes learning about big numbers absolutely scrumptious!
Author: Brian W. Kernighan
Publisher: Princeton University Press
ISBN: 069121896X
Category : Computers
Languages : en
Pages : 301
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Book Description
A brand-new edition of the popular introductory textbook that explores how computer hardware, software, and networks work Computers are everywhere. Some are highly visible, in laptops, tablets, cell phones, and smart watches. But most are invisible, like those in appliances, cars, medical equipment, transportation systems, power grids, and weapons. We never see the myriad computers that quietly collect, share, and sometimes leak personal data about us. Governments and companies increasingly use computers to monitor what we do. Social networks and advertisers know more about us than we should be comfortable with. Criminals have all-too-easy access to our data. Do we truly understand the power of computers in our world? In this updated edition of Understanding the Digital World, Brian Kernighan explains how computer hardware, software, and networks work. Topics include how computers are built and how they compute; what programming is; how the Internet and web operate; and how all of these affect security, privacy, property, and other important social, political, and economic issues. Kernighan touches on fundamental ideas from computer science and some of the inherent limitations of computers, and new sections in the book explore Python programming, big data, machine learning, and much more. Numerous color illustrations, notes on sources for further exploration, and a glossary explaining technical terms and buzzwords are included. Understanding the Digital World is a must-read for readers of all backgrounds who want to know more about computers and communications.
Author: Michael Harris
Publisher: Princeton University Press
ISBN: 0691090920
Category : Mathematics
Languages : en
Pages : 287
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Book Description
This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory. The local Langlands conjecture for GLn(K), where K is a p-adic field, asserts the existence of a correspondence, with certain formal properties, relating n-dimensional representations of the Galois group of K with the representation theory of the locally compact group GLn(K). This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties. And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties. The local Langlands conjecture is obtained as a corollary. Certain techniques developed in this book should extend to more general Shimura varieties, providing new instances of the local Langlands conjecture. Moreover, the geometry of the special fibers is strictly analogous to that of Shimura curves and can be expected to have applications to a variety of questions in number theory.
Author: John McPhee
Publisher: Farrar, Straus and Giroux
ISBN: 0374708460
Category : Science
Languages : en
Pages : 933
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Book Description
The Pulitzer Prize-winning view of the continent, across the fortieth parallel and down through 4.6 billion years Twenty years ago, when John McPhee began his journeys back and forth across the United States, he planned to describe a cross section of North America at about the fortieth parallel and, in the process, come to an understanding not only of the science but of the style of the geologists he traveled with. The structure of the book never changed, but its breadth caused him to complete it in stages, under the overall title Annals of the Former World. Like the terrain it covers, Annals of the Former World tells a multilayered tale, and the reader may choose one of many paths through it. As clearly and succinctly written as it is profoundly informed, this is our finest popular survey of geology and a masterpiece of modern nonfiction. Annals of the Former World is the winner of the 1999 Pulitzer Prize for Nonfiction.
Author: Kenkichi Iwasawa
Publisher: Princeton University Press
ISBN: 9780691081120
Category : Mathematics
Languages : en
Pages : 120
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Book Description
An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical L-functions of Dirichlet. Professor Iwasawa reviews the classical results on Dirichlet's L-functions and sketches a proof for some of them. Next he defines generalized Bernoulli numbers and discusses some of their fundamental properties. Continuing, he defines p-adic L-functions, proves their existence and uniqueness, and treats p-adic logarithms and p-adic regulators. He proves a formula of Leopoldt for the values of p-adic L-functions at s=1. The formula was announced in 1964, but a proof has never before been published. Finally, he discusses some applications, especially the strong relationship with cyclotomic fields.
Author: Umberto Zannier
Publisher: Princeton University Press
ISBN: 1400842719
Category : Mathematics
Languages : en
Pages : 175
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Book Description
This book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. More generally, the book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension. The book is an expansion of the Hermann Weyl Lectures delivered by Umberto Zannier at the Institute for Advanced Study in Princeton in May 2010. The book consists of four chapters and seven brief appendixes, the last six by David Masser. The first chapter considers multiplicative algebraic groups, presenting proofs of several developments, ranging from the origins to recent results, and discussing many applications and relations with other contexts. The second chapter considers an analogue in arithmetic and several applications of this. The third chapter introduces a new method for approaching some of these questions, and presents a detailed application of this (by Masser and the author) to a relative case of the Manin-Mumford issue. The fourth chapter focuses on the André-Oort conjecture (outlining work by Pila).
Author: Joshua Robinson
Publisher: Houghton Mifflin
ISBN: 1328506452
Category : Business & Economics
Languages : en
Pages : 381
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Book Description
Two veteran sports writers and editors take readers inside the history of the most-watched sports league on earth -- England's Premier League.
Author: Steven J. Miller
Publisher: Princeton University Press
ISBN: 0691215979
Category : Mathematics
Languages : en
Pages : 526
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Book Description
In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.
