Millions Billions Zillions

"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

How can an old man and his wife select one cat from a choice of millions and trillions?

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.

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.

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!

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.

"The quality of the deep-sky images is outstanding--a tribute to the various photographers as well as the book's printer. But it's the written word that will make or break a book like this, and Sue's writing is superb... [For] an occasional stargazer, a serious observer, or anyone in between, you won't go wrong with Deep-Sky Wonders. This is a great introduction to deep-sky stargazing for novice and experienced amateur astronomers alike." --Mercury, publication of the Astronomical Society of the Pacific Sue French writes the popular column "Deep-Sky Wonders" for Sky and Telescope magazine and also teaches deep sky observation. She has earned a loyal following among enthusiasts and is welcomed by beginners for her skill at presenting astronomy in an understandable way. After selling 10,000 copies of Deep-Sky Wonders in hardcover, we expect a good response for this paperback edition at an accessible price. Deep-Sky Wonders is a collection of 100 of French's best "Deep-Sky Wonders" columns originally published in Sky and Telescope, which has a monthly readership exceeding 100,000. The book is organized by season and subdivided into months for a total of 100 in-depth tours of the deep sky. Each deep sky tour illuminates little-known seasonal wonders that lie off the beaten path. Features include: Full-color photographs and detailed sketches of each deep sky tour Descriptions of double and variable stars, star clusters, nebulae, galaxies and exotics Historical and scientific background of particular interest A tabular listing of the deep-sky sites Color charts showing the position of each target in the night sky An index to all of the deep-sky objects covered. Deep-Sky Wonders also features a variety of challenging objects that encourage observers to test the limits of their equipment and skills. Suitable for beginner and intermediate small-scope astronomers as well as large-scope viewers and astrophotographers, this book will be greeted enthusiastically by all Sky and Telescope readers. It is also an outstanding introduction to deep-sky viewing for novice observers.

Written in a friendly style for a general mathematically literate audience, 'Fearless Symmetry', starts with the basic properties of integers and permutations and reaches current research in number theory.