Over 100 problems at ends of chapters. Answers in back of book. 1962 edition.

    The stories show that, as James Gleick puts it in the foreword, "inspiration strikes willy-nilly." One researcher thinks of quantum chaotic systems at a bus stop; another suddenly realizes a path to proving a theorem of number theory while in a friend's backyard; a statistician has a "bathroom sink epiphany" and discovers the key to solving the Gaussian correlation inequality. Readers of The Prime Number Conspiracy, says Quanta editor-in-chief Thomas Lin, are headed on "breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge."Quanta is the only popular publication that offers in-depth coverage of the latest breakthroughs in understanding our mathematical universe. It communicates mathematics by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves. Readers of this volume will learn that prime numbers have decided preferences about the final digits of the primes that immediately follow them (the "conspiracy" of the title); consider whether math is the universal language of nature (allowing for "a unified theory of randomness"); discover surprising solutions (including a pentagon tiling proof that solves a century-old math problem); ponder the limits of computation; measure infinity; and explore the eternal question "Is mathematics good for you?"ContributorsAriel Bleicher, Robbert Dijkgraaf, Kevin Hartnett, Erica Klarreich, Thomas Lin, John Pavlus, Siobhan Roberts, Natalie WolchoverCopublished with Quanta Magazine

     Learn the essential concepts using concrete analogies and vivid diagrams, not mechanical definitions. Calculus isn't a set of rules, it's a specific, practical viewpoint we can apply to everyday thinking. Frustrated With Abstract, Mechanical Lessons? I was too. Despite years of classes, I didn't have a strong understanding of calculus concepts. Sure, I could follow mechanical steps, but I had no lasting intuition. The classes I've seen are too long, taught in the wrong order, and without solid visualizations. Here's how this course is different: 1) It gets to the point. A typical class plods along, saving concepts like Integrals until Week 8. I want to see what calculus can offer by Minute 8. Each compact, tightly-written lesson can be read in 15 minutes. 2) Concepts are taught in their natural order. Most classes begin with the theory of limits, a technical concept discovered 150 years after calculus was invented. That's like putting a new driver into a Formula-1 racecar on day 1. We can begin with the easy-to-grasp concepts discovered 2000 years ago. 3) It has vivid analogies and visualizations. Calculus is usually defined as the "study of change"... which sounds like history or geology. Instead of an abstract definition, we'll see calculus a step-by-step viewpoint to explore patterns. 4) It's written by a human, for humans. I'm not a haughty professor or strict schoolmarm. I'm a friend who saw a fun way to internalize some difficult ideas. This course is a chat over coffee, not a keep-your-butt-in-your-seat lecture. The goal is to help you grasp the Aha! moments behind calculus in hours, not a painful semester (or a decade, in my case). Join Thousands Of Happy Readers Here's a few samples of anonymous feedback as people went through the course. The material covers a variety of levels, whether you're looking for intuitive appreciation or the specifics of the rules. "I've done all of this stuff before, and I do understand calculus intuitively, but this was the most fun I've had going through this kind of thing. The informal writing and multitude of great analogies really helps this become an enjoyable read and the rest is simple after that - you make this seem easy, but at the same time, you aren't doing it for us…This is what math education is supposed to be like :)" "I have psychology and medicine background so I relate your ideas to my world. To me the most useful idea was what each circle production feels like. Rings are natural growth…Slices are automatable chunks and automation cheapens production… Boards in the shape on an Arch are psychologically most palatable for work (wind up, hard part, home stretch). Brilliant and kudos, from one INTP to another." "I like how you're introducing both derivatives and integrals at the same time - it's really helps with understanding the relationship between them. Also, I appreciate how you're coming from such a different angle than is traditionally taken - it's always interesting to see where you decide to go next." "That was breathtaking. Seriously, mail my air back please, I've grown used to it. Beautiful work, thank you. Lesson 15 was masterful. I am starting to feel calculus. "d/dx is good" (sorry, couldn't resist!)."

    The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it.All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an inner monologue--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.Serves as a companion to any single-variable calculus textbookInformal, entertaining, and not intimidatingInformative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lecturesMore than 475 examples (ranging from easy to hard) provide step-by-step reasoningTheorems and methods justified and connections made to actual practiceDifficult topics such as improper integrals and infinite series covered in detailTried and tested by students taking freshman calculus

      Statistics are everywhere, as integral to science as they are to business, and in the popular media hundreds of times a day. In this age of big data, a basic grasp of statistical literacy is more important than ever if we want to separate the fact from the fiction, the ostentatious embellishments from the raw evidence -- and even more so if we hope to participate in the future, rather than being simple bystanders. In The Art of Statistics, world-renowned statistician David Spiegelhalter shows readers how to derive knowledge from raw data by focusing on the concepts and connections behind the math. Drawing on real world examples to introduce complex issues, he shows us how statistics can help us determine the luckiest passenger on the Titanic, whether a notorious serial killer could have been caught earlier, and if screening for ovarian cancer is beneficial. The Art of Statistics not only shows us how mathematicians have used statistical science to solve these problems -- it teaches us how we too can think like statisticians. We learn how to clarify our questions, assumptions, and expectations when approaching a problem, and -- perhaps even more importantly -- we learn how to responsibly interpret the answers we receive. Combining the incomparable insight of an expert with the playful enthusiasm of an aficionado, The Art of Statistics is the definitive guide to stats that every modern person needs.

    First published in 1986, this mind-boggling and entertaining dictionary, arranged in order of magnitude, exposes the fascinating facts about certain numbers and number sequences - very large primes, amicable numbers and golden squares to give but a few examples.

    From Edward Lorenz’s discovery of the Butterfly Effect, to Mitchell Feigenbaum’s calculation of a universal constant, to Benoit Mandelbrot’s concept of fractals, which created a new geometry of nature, Gleick’s engaging narrative focuses on the key figures whose genius converged to chart an innovative direction for science. In Chaos, Gleick makes the story of chaos theory not only fascinating but also accessible to beginners, and opens our eyes to a surprising new view of the universe.

    Worked examples and exercises support the text. An ELBS/LPBB edition is available.

    This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round.Why one and two weren't considered numbers by the ancient Greeks.Why squares show up so often in goddess art and board games.What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster a cathedral, and much more.

    Distilled into 1001 mini-essays arranged thematically, this unique book moves steadily from the basics through to the most advanced areas of math, making it the ideal guide for both the beginner and the math wiz.The book covers all of the fundamental mathematical disciplines:Geometry Numbers Analysis Logic Algebra Probability and statistics Applied mathematics Discrete mathematics Games and recreational mathematics Philosophy and metamathematicsExpert mathematician Richard Elwes explains difficult concepts in the simplest language with a minimum of jargon. Along the way he reveals such mathematical magic as how to count to 1023 using just 10 fingers and how to make an unbreakable code.Enlightening and entertaining, Mathematics 1001 makes the language of math come alive.

    Take a journey through the fascinating story of fractions, numbers, patterns, and shapes in order to better understand the complex world we live in.Continuing the "Big Ideas" series' trademark combination of authoritative, clear text and bold graphics to chart the development of maths through history, the book explores and explains some of the most complex and fascinating mathematical subjects. Delve into everything from the mathematical ideas and inventions of the ancient world such as the first number systems, magic squares, and the Chinese abacus, through to the developments in mathematics during medieval and Renaissance Europe, to the rise of group theory and cryptography more recently.This diverse and inclusive account of mathematics will have something for everybody: for those interested in the maths behind world economies, secret spies, modern technology and plenty more, taking readers around the world from Babylon to Bletchley Park. Tracing maths through the Scientific Revolution to its 21st-century use in computers, the internet, and AI, The Maths Book uses an innovative visual approach to make the subject accessible to everyone, casual readers and students alike.

    In this lively and groundbreaking new book, economist Ian Ayres shows how today's best and brightest organizations are analyzing massive databases at lightening speed to provide greater insights into human behavior. They are the Super Crunchers. From internet sites like Google and Amazon that know your tastes better than you do, to a physician's diagnosis and your child's education, to boardrooms and government agencies, this new breed of decision makers are calling the shots. And they are delivering staggeringly accurate results. How can a football coach evaluate a player without ever seeing him play? Want to know whether the price of an airline ticket will go up or down before you buy? How can a formula outpredict wine experts in determining the best vintages? Super crunchers have the answers. In this brave new world of equation versus expertise, Ayres shows us the benefits and risks, who loses and who wins, and how super crunching can be used to help, not manipulate us.Gone are the days of solely relying on intuition to make decisions. No businessperson, consumer, or student who wants to stay ahead of the curve should make another keystroke without reading Super Crunchers.

    It givessyntax and output for accomplishing many analyses through the mostrecent releases of SAS, SPSS, and SYSTAT, some not available insoftware manuals. The book maintains its practical approach, stillfocusing on the benefits and limitations of applications of a techniqueto a data set -- when, why, and how to do it. Overall, it providesadvanced students with a timely and comprehensive introduction totoday's most commonly encountered statistical and multivariatetechniques, while assuming only a limited knowledge of higher-levelmathematics.

    It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the students existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research-based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.

    Len Fisher turns his attention to the science of cooperation in his lively and thought-provoking book. Fisher shows how the modern science of game theory has helped biologists to understand the evolution of cooperation in nature, and investigates how we might apply those lessons to our own society. In a series of experiments that take him from the polite confines of an English dinner party to crowded supermarkets, congested Indian roads, and the wilds of outback Australia, not to mention baseball strategies and the intricacies of quantum mechanics, Fisher sheds light on the problem of global cooperation. The outcomes are sometimes hilarious, sometimes alarming, but always revealing. A witty romp through a serious science, Rock, Paper, Scissors will both teach and delight anyone interested in what it what it takes to get people to work together.