This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could ...

Understanding Analysis outlines an elementary, one-semester course designed to expose students to the rich rewards inherent in taking a mathematically rigorous approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on the questions that give analysis its inherent fascination. Does the Cantor set contain any irrat...

Even before the hit TV show whose name she inspired ever aired, Ms. Abbott was a larger-than-life figure. The teacher who put the “Abbott” in TV’s hit Abbott Elementary is just as serious about education—and caring—as the show is funny. In her classroom, in the hallways, and in her Philadelphia neighborhood, she could do what other teachers couldn’t. But even the legendary Ms. Abbott wasn’t always prepared for the situations she faced, though she was always up to the challenge. Now, Teachi...

How playwrights from Alfred Jarry and Samuel Beckett to Tom Stoppard and Simon McBurney brought the power of mathematics to life on the stageThe discovery of alternate geometries, paradoxes of the infinite, incompleteness, and chaos theory revealed that, despite its reputation for certainty, mathematical truth is not immutable, perfect, or even perfectible. Beginning in the last century, a handful of adventurous playwrights took inspiration from the fractures of mo...

Getting certified to teach high school mathematics typically requires completing a course in real analysis. Yet most teachers point out real analysis content bears little resemblance to secondary mathematics and report it does not influence their teaching in any significant way. This textbook is our attempt to change the narrative. It is our belief that analysis can be a meaningful part of a teacher's mathematical education and preparation for teaching. This book is a companion text. It is...

Wall Street Journal BestsellerMuch of the advice we’ve been told about achievement and personal development is logical, earnest…and downright wrong. In Barking Up the Wrong Tree, Eric Barker reveals the extraordinary behavioral science behind what actually determines success and most importantly, how anyone can achieve it. You’ll learn:• Why valedictorians rarely become millionaires, and how your biggest weakness might actually be your gre...

From the bestselling author of the acclaimed Chaos and Genius comes a thoughtful and provocative exploration of the big ideas of the modern era: Information, communication, and information theory.Acclaimed science writer James Gleick presents an eye-opening vision of how our relationship to information has transformed the very nature of human consciousness. A fascinating intellectual journey through the history of communication and information, from the language o...

This QuickStudy guide includes everything the first year calculus student needs to gain a strong understanding of the basic calculus concepts. It includes: functions, limits, continuity, derivatives & analysis, integration, and much more!

“I can imagine few more enjoyable ways of thinking than to read this book.”—Sarah Bakewell, New York Times Book Review, front-page reviewTackling the “darkest question in all of philosophy” with “raffish erudition” (Dwight Garner, New York Times), author Jim Holt explores the greatest metaphysical mystery of all: why is there something rather than nothing? This runaway bestseller, which has captured the imagination of critics and the public alike, traces ...

Only one thing stands between you and success.It isn't experience.It isn't talent.World-renowned leadership expert John C. Maxwell says if you want to succeed, you must learn how to connect with people. And while it may seem like some folks are just born with it, the fact is anyone can learn how to make every communication an opportunity for a powerful connection. In Everyone Communicates, Few Connect, Maxwell shares the Five Principles and Five Pr...

‘I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.’It was with these words, written in the 1630s, that Pierre de Fermat intrigued and infuriated the mathematics community. For over 350 years, proving Fermat’s Last Theorem was the most notorious unsolved mathematical problem, a puzzle whose basics most children could grasp but whose solution eluded the greatest minds in the world. In 1993, after years of secret toil, Englishman A...

The world's greatest mental mathematical magician takes us on a spellbinding journey through the wonders of numbers (and more)"Arthur Benjamin . . . joyfully shows you how to make nature's numbers dance." -- Bill Nye (the science guy)The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples-from ice-cream scoops and poker hands to measuring mountains and making magic squares-this book revels in key mat...