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Author: Martin Aigner
Publisher: Springer Science & Business Media
ISBN: 3662223430
Category : Mathematics
Languages : en
Pages : 194
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Book Description
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author: Martin Aigner
Publisher: Springer Science & Business Media
ISBN: 3662223430
Category : Mathematics
Languages : en
Pages : 194
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Book Description
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author: Joseph E. Aoun
Publisher: MIT Press
ISBN: 0262344327
Category : Education
Languages : en
Pages : 211
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Book Description
How to educate the next generation of college students to invent, to create, and to discover—filling needs that even the most sophisticated robot cannot. Driverless cars are hitting the road, powered by artificial intelligence. Robots can climb stairs, open doors, win Jeopardy, analyze stocks, work in factories, find parking spaces, advise oncologists. In the past, automation was considered a threat to low-skilled labor. Now, many high-skilled functions, including interpreting medical images, doing legal research, and analyzing data, are within the skill sets of machines. How can higher education prepare students for their professional lives when professions themselves are disappearing? In Robot-Proof, Northeastern University president Joseph Aoun proposes a way to educate the next generation of college students to invent, to create, and to discover—to fill needs in society that even the most sophisticated artificial intelligence agent cannot. A “robot-proof” education, Aoun argues, is not concerned solely with topping up students' minds with high-octane facts. Rather, it calibrates them with a creative mindset and the mental elasticity to invent, discover, or create something valuable to society—a scientific proof, a hip-hop recording, a web comic, a cure for cancer. Aoun lays out the framework for a new discipline, humanics, which builds on our innate strengths and prepares students to compete in a labor market in which smart machines work alongside human professionals. The new literacies of Aoun's humanics are data literacy, technological literacy, and human literacy. Students will need data literacy to manage the flow of big data, and technological literacy to know how their machines work, but human literacy—the humanities, communication, and design—to function as a human being. Life-long learning opportunities will support their ability to adapt to change. The only certainty about the future is change. Higher education based on the new literacies of humanics can equip students for living and working through change.
Author: Richard H. Hammack
Publisher:
ISBN: 9780989472111
Category : Mathematics
Languages : en
Pages : 314
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Book Description
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Author: Jia Jiang
Publisher: Harmony
ISBN: 0804141398
Category : Business & Economics
Languages : en
Pages : 242
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Book Description
The inspiring, relatable, and sometimes outrageous true story of how one man used 100 days of rejection therapy to overcome fear and dare to live more boldly “Rejection Proof smashes fear in the face with a one-two punch. You’ll laugh out loud at Jia’s crazy social experiments, but you’ll also go away thinking differently about what you can accomplish.”—Chris Guillebeau, New York Times bestselling author of The Happiness Pursuit Jia Jiang’s TEDx Talk, “What I learned from 100 days of rejection,” has amassed over ten million views! Jia Jiang came to the United States with the dream of being the next Bill Gates. But despite early success in the corporate world, his first attempt to pursue his entrepreneurial dream ended in rejection. Jia was crushed and spiraled into a period of deep self-doubt. Jia realized that his fear of rejection was a bigger obstacle than any single rejection would ever be; he needed to find a way to cope with being told “no” that wouldn’t destroy him. Inspired by rejection therapy, which uses similar modalities as exposure therapy to desensitize you to the effects of being rejected, he undertook the “100 days of rejection” experiment, during which he willfully sought out rejection on a daily basis—from requesting a lesson in sales from a car salesman (no) to asking a flight attendant if he could make an announcement on the loud speaker (yes) to his famous request to get Krispy Kreme donuts in the shape of Olympic rings (yes, with a viral video to prove it). Over the course of one hundred rejection attempts, Jia realized that even the most preposterous wish might be granted if you ask the right way. He learned the secrets to making successful requests, tactics for picking the right people to approach at the right time, and strategies for converting an initial no into something positive. More important, Jia discovered ways to steel himself against rejection and live more fearlessly—skills that can’t be derailed by a single setback. The changes Jia experienced from his rejection therapy experiment went far beyond becoming more successful in business; he realized that he could apply these techniques to get more out of his relationships with friends, family, and even casual encounters with strangers. Filled with great stories and valuable insight, Rejection Proof shares the secrets of Jia’s rejection journey, distilling each lesson into a strategy that can be used in any negotiation or pitch.
Author: Adam Rogers
Publisher: Houghton Mifflin Harcourt
ISBN: 0547897960
Category : Cooking
Languages : en
Pages : 277
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Book Description
Presents a look at the science of alcohol production and consumption, from the principles behind the fermentation, distillation, and aging of alcoholic beverages, to the psychology and neurobiology of what happens after it is consumed.
Author: Douglas Kruger
Publisher: Penguin Random House South Africa
ISBN: 1776094522
Category : Business & Economics
Languages : en
Pages : 96
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Book Description
Why is it that some people work hard, yet remain poor? How is it that others seem to rise out of poverty and become affluent in a short span of time? If you want to know how to become rich relatively quickly, and avoid spending years working back-breakingly hard without ever breaking even, then read on. The answers to escaping poverty and becoming wealthy are actually well known and based on a number of powerful principles that have been tested by time and replicated in different countries, by families and individuals who have become astonishingly rich. So, what are these ideas that genuinely lift people out of poverty and ensure their personal wealth? Here are 50. They all work. They will make you richer. They remove the emotion, the politics and the clutter from our thoughts about wealth, and they go straight to the heart of one simple issue: what it genuinely takes to become rich. Prepare to train your brain for wealth. Prepare to become ‘poverty proof’ for life,
Author: Daniel Montgomery
Publisher: Zondervan
ISBN: 0310513901
Category : Religion
Languages : en
Pages : 239
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Book Description
It’s time to open your eyes to the freeing power of authentic grace—grace that releases us from trying to earn God's favor, grace that enables us to rest in the finished work of Christ, grace that liberates from the tyranny of trying to please others. That's what the theology of Martin Luther and John Calvin did in their own day for the people around them. Time magazine recently dubbed Calvinism as one of the top ten ideas changing the world right now. And yet most of these discussions center on the issue of predestination or on whether particular people agree with the five points of Calvinism. Daniel Montgomery and Timothy Paul Jones think it's time to rescue the theology of the Reformers from such stale scholasticizing and to declare anew the dangerous and intoxicating joy of the gospel that theyproclaimed. PROOF stands for planned grace, resurrecting grace, outrageous grace, overcoming grace, and forever grace. The authors offer proof of God’s grace upon which people can stand against the attacks of legalism that have led many of God's people to lose sight of the freedom and joy of the gospel. And this proof is intoxicating—it’s like a 200-proof drink that will leave you spiritually staggering at its effect on your life. God’s grace not only declares us “not guilty!” in his presence, it changes our relationship with God—forever.?
Author: Frederick Schauer
Publisher: Harvard University Press
ISBN: 0674276256
Category : Law
Languages : en
Pages : 321
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Book Description
Winner of the Scribes Book Award “Displays a level of intellectual honesty one rarely encounters these days...This is delightful stuff.” —Barton Swaim, Wall Street Journal “At a time when the concept of truth itself is in trouble, this lively and accessible account provides vivid and deep analysis of the practices addressing what is reliably true in law, science, history, and ordinary life. The Proof offers both timely and enduring insights.” —Martha Minow, former Dean of Harvard Law School “His essential argument is that in assessing evidence, we need, first of all, to recognize that evidence comes in degrees...and that probability, the likelihood that the evidence or testimony is accurate, matters.” —Steven Mintz, Inside Higher Education “I would make Proof one of a handful of books that all incoming law students should read...Essential and timely.” —Emily R. D. Murphy, Law and Society Review In the age of fake news, trust and truth are hard to come by. Blatantly and shamelessly, public figures deceive us by abusing what sounds like evidence. To help us navigate this polarized world awash in misinformation, preeminent legal theorist Frederick Schauer proposes a much-needed corrective. How we know what we think we know is largely a matter of how we weigh the evidence. But evidence is no simple thing. Law, science, public and private decision making—all rely on different standards of evidence. From vaccine and food safety to claims of election fraud, the reliability of experts and eyewitnesses to climate science, The Proof develops fresh insights into the challenge of reaching the truth. Schauer reveals how to reason more effectively in everyday life, shows why people often reason poorly, and makes the case that evidence is not just a matter of legal rules, it is the cornerstone of judgment.
Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 0521861241
Category : Mathematics
Languages : en
Pages : 401
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Book Description
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Author: Andrew Wohlgemuth
Publisher: Courier Corporation
ISBN: 0486141683
Category : Mathematics
Languages : en
Pages : 385
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Book Description
The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.
