How Numbers Work

Author: New Scientist
Publisher: John Murray
ISBN: 1473629756
Category : Mathematics
Languages : en
Pages : 224

Book Description
Think of a number between one and ten. No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like pi which never end. It literally never ends. The world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - pi, e, the "imaginary" number i and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed: is it a number, or isn't it? How Numbers Work takes a tour of this mind-blowing but beautiful realm of numbers and the mathematical rules that connect them. Not only that, but take a crash course on the biggest unsolved problems that keep mathematicians up at night, find out about the strange and unexpected ways mathematics influences our everyday lives, and discover the incredible connection between numbers and reality itself. ABOUT THE SERIES New Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.

Really Big Numbers

Author: Richard Evan Schwartz
Publisher: American Mathematical Soc.
ISBN: 1470414252
Category : Juvenile Nonfiction
Languages : en
Pages : 194

Book Description
In the American Mathematical Society's first-ever book for kids (and kids at heart), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names! Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual interested in exploring the vast universe of numbers.

Where Do Numbers Come From?

Author: T. W. Körner
Publisher: Cambridge University Press
ISBN: 1108488064
Category : Mathematics
Languages : en
Pages : 273

Book Description
A clear, entertaining development of the number systems required in any course of modern mathematics.

Making Numbers Count

Author: Chip Heath
Publisher: Simon and Schuster
ISBN: 1982165456
Category : Business & Economics
Languages : en
Pages : 208

Book Description
A clear, practical, first-of-its-kind guide to communicating and understanding numbers and data—from bestselling business author Chip Heath. How much bigger is a billion than a million? Well, a million seconds is twelve days. A billion seconds is…thirty-two years. Understanding numbers is essential—but humans aren’t built to understand them. Until very recently, most languages had no words for numbers greater than five—anything from six to infinity was known as “lots.” While the numbers in our world have gotten increasingly complex, our brains are stuck in the past. How can we translate millions and billions and milliseconds and nanometers into things we can comprehend and use? Author Chip Heath has excelled at teaching others about making ideas stick and here, in Making Numbers Count, he outlines specific principles that reveal how to translate a number into our brain’s language. This book is filled with examples of extreme number makeovers, vivid before-and-after examples that take a dry number and present it in a way that people click in and say “Wow, now I get it!” You will learn principles such as: -SIMPLE PERSPECTIVE CUES: researchers at Microsoft found that adding one simple comparison sentence doubled how accurately users estimated statistics like population and area of countries. -VIVIDNESS: get perspective on the size of a nucleus by imagining a bee in a cathedral, or a pea in a racetrack, which are easier to envision than “1/100,000th of the size of an atom.” -CONVERT TO A PROCESS: capitalize on our intuitive sense of time (5 gigabytes of music storage turns into “2 months of commutes, without repeating a song”). -EMOTIONAL MEASURING STICKS: frame the number in a way that people already care about (“that medical protocol would save twice as many women as curing breast cancer”). Whether you’re interested in global problems like climate change, running a tech firm or a farm, or just explaining how many Cokes you’d have to drink if you burned calories like a hummingbird, this book will help math-lovers and math-haters alike translate the numbers that animate our world—allowing us to bring more data, more naturally, into decisions in our schools, our workplaces, and our society.

Numbers

Author: Graham Flegg
Publisher: Courier Corporation
ISBN: 0486166511
Category : Mathematics
Languages : en
Pages : 307

Book Description
Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." — Choice.

A Mind for Numbers

Author: Barbara A. Oakley
Publisher: TarcherPerigee
ISBN: 039916524X
Category : Mathematics
Languages : en
Pages : 338

Book Description
Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. In her book, she offers you the tools needed to get a better grasp of that intimidating but inescapable field.

Are Numbers Real?

Author: Brian Clegg
Publisher: Macmillan
ISBN: 1250081041
Category : Mathematics
Languages : en
Pages : 303

Book Description
Presents an accessible, in-depth look at the history of numbers and their applications in life and science, from math's surreal presence in the virtual world to the debates about the role of math in science.

Which Numbers Are Real?

Author: Michael Henle
Publisher: American Mathematical Soc.
ISBN: 1614441073
Category : Mathematics
Languages : en
Pages : 219

Book Description
Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics. Alternative real numbers include many different kinds of numbers, for example multidimensional numbers (the complex numbers, the quaternions and others), infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). Each system has a well-developed theory, including applications to other areas of mathematics and science, such as physics, the theory of games, multi-dimensional geometry, and formal logic. They are all active areas of current mathematical research and each has unique features, in particular, characteristic methods of proof and implications for the philosophy of mathematics, both highlighted in this book. Alternative real number systems illuminate the central, unifying role of the real numbers and include some exciting and eccentric parts of mathematics. Which Numbers Are Real? Will be of interest to anyone with an interest in numbers, but specifically to upper-level undergraduates, graduate students, and professional mathematicians, particularly college mathematics teachers.

Strength in Numbers: How Polls Work and Why We Need Them

Author: G. Elliott Morris
Publisher: W. W. Norton & Company
ISBN: 039386698X
Category : Political Science
Languages : en
Pages : 178

Book Description
An insightful exploration of political polling and a bold defense of its crucial role in a modern democracy. Public opinion polling is the ultimate democratic process; it gives every person an equal voice in letting elected leaders know what they need and want. But in the eyes of the public, polls today are tarnished. Recent election forecasts have routinely missed the mark and media coverage of polls has focused solely on their ability to predict winners and losers. Polls deserve better. In Strength in Numbers, data journalist G. Elliott Morris argues that the larger purpose of political polls is to improve democracy, not just predict elections. Whether used by interest groups, the press, or politicians, polling serves as a pipeline from the governed to the government, giving citizens influence they would otherwise lack. No one who believes in democracy can afford to give up on polls; they should commit, instead, to understanding them better. In a vibrant history of polling, Morris takes readers from the first semblance of data-gathering in the ancient world through to the development of modern-day scientific polling. He explains how the internet and “big data” have solved many challenges in polling—and created others. He covers the rise of polling aggregation and methods of election forecasting, reveals how data can be distorted and misrepresented, and demystifies the real uncertainty of polling. Candidly acknowledging where polls have gone wrong in the past, Morris charts a path for the industry’s future where it can truly work for the people. Persuasively argued and deeply researched, Strength in Numbers is an essential guide to understanding and embracing one of the most important and overlooked democratic institutions in the United States.

An Illustrated Theory of Numbers

Author: Martin H. Weissman
Publisher: American Mathematical Soc.
ISBN: 1470463717
Category : Education
Languages : en
Pages : 341

Book Description
News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.