How Not To Be Wrong The Power Of Mathematical Thinking

How Not to Be Wrong

Publisher : National Geographic Books
Release Date : 2015-05-26
ISBN : 0143127535
Pages : 0 pages
Rating Book: 4.4/5 (143 users)

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Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by National Geographic Books. This book was released on 2015-05-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

How Not to Be Wrong

by Jordan Ellenberg

Publisher : Penguin UK
Release Date : 2014-06-03
ISBN : 0718196058
Pages : 480 pages
Rating Book: 4.1/5 (718 users)

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Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by Penguin UK. This book was released on 2014-06-03 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

How Not to be Wrong by Jordan Ellenberg

Publisher :
Release Date : 2015
ISBN : 9781785671876
Pages : pages
Rating Book: 4.7/5 (671 users)

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Download or read book How Not to be Wrong by Jordan Ellenberg written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

How Not to Be Wrong

by Jordan Ellenberg

Publisher : Penguin
Release Date : 2014-05-29
ISBN : 0698163842
Pages : 480 pages
Rating Book: 4.9/5 (698 users)

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Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by Penguin. This book was released on 2014-05-29 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

Summary of How Not to Be Wrong

by Better Business Summaries

Publisher : Createspace Independent Publishing Platform
Release Date : 2016-08-31
ISBN : 9781537303789
Pages : 44 pages
Rating Book: 4.0/5 (33 users)

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Download or read book Summary of How Not to Be Wrong written by Better Business Summaries and published by Createspace Independent Publishing Platform. This book was released on 2016-08-31 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg - Summary

Shape

by Jordan Ellenberg

Publisher : Penguin
Release Date : 2021-05-25
ISBN : 1984879065
Pages : 480 pages
Rating Book: 4.8/5 (984 users)

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Download or read book Shape written by Jordan Ellenberg and published by Penguin. This book was released on 2021-05-25 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.

Twenty-one Mental Models That Can Change Policing

by Renée J. Mitchell

Publisher : Routledge
Release Date : 2021-09-15
ISBN : 100040272X
Pages : 228 pages
Rating Book: 4.0/5 ( users)

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Download or read book Twenty-one Mental Models That Can Change Policing written by Renée J. Mitchell and published by Routledge. This book was released on 2021-09-15 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book goes beyond other police leadership books to teach practitioners how to think about policing in a structured way that synthesizes criminological theory, statistics, research design, applied research, and what works and what doesn’t in policing into Mental Models. A Mental Model is a representation of how something works. Using a Mental Model framework to simplify complex concepts, readers will take away an in-depth understanding of how cognitive biases affect our ability to understand and interpret data, what empirical research says about effective police interventions, how statistical data should be structured for management meetings, and how to evaluate interventions for efficiency and effectiveness. While evidence-based practice is critical to advancing the police profession, it is limited in scope, and is only part of what is necessary to support sustainable change in policing. Policing requires a scientifically based framework to understand and interpret data in a way that minimizes cognitive bias to allow for better responses to complex problems. Data and research have advanced so rapidly in the last several decades that it is difficult for even the most ambitious of police leaders to keep pace. The Twenty-one Mental Models were synthesized to create a framework for any police, public, or community leader to better understand how cognitive bias contributes to misunderstanding data and gives the reader the tools to overcome those biases to better serve their communities. The book is intended for a wide range of audiences, including law enforcement and community leaders; scholars and policy experts who specialize in policing; students of criminal justice, organizations, and management; reporters and journalists; individuals who aspire to police careers; and citizen consumers of information about policing. Anyone who is going to make decisions about their communities based on data has a responsibility to be numerate and this book Twenty-one Mental Models That Can Change Policing: A Framework For Using Data and Research For Overcoming Cognitive Bias, will help you become just that.

Political Tribalism in America

by Timothy J. Redmond

Publisher : McFarland
Release Date : 2022-10-18
ISBN : 1476646961
Pages : 244 pages
Rating Book: 4.7/5 (476 users)

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Download or read book Political Tribalism in America written by Timothy J. Redmond and published by McFarland. This book was released on 2022-10-18 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The democratic ideal demands that the citizenry think critically about matters of public import. Yet many Democrats and Republicans in the United States have fallen short of that standard because political tribalism motivates them to acquire, perceive and evaluate political information in a biased manner. The result is an electorate that is more extreme, hostile and willing to reject unfavorable democratic outcomes. In this work, the author provides a host of actionable strategies that are designed to reduce the influence of political tribalism in our lives. The text includes instructions for plumbing the depths of political views; evaluating sources of political information; engaging in difficult political conversations; appraising political data; and assessing political arguments. The first of its kind, this how-to guide is a must-read for partisans who want to become more critical political thinkers.

Imagine Math 7

by Michele Emmer

Publisher : Springer Nature
Release Date : 2020-10-07
ISBN : 303042653X
Pages : 471 pages
Rating Book: 4.3/5 (3 users)

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Download or read book Imagine Math 7 written by Michele Emmer and published by Springer Nature. This book was released on 2020-10-07 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. Imagine building mathematical models that make it possible to manage our world better, imagine solving great problems, imagine new problems never before thought of, imagine combining music, art, poetry, literature, architecture, theatre and cinema with mathematics. Imagine the unpredictable and sometimes counterintuitive applications of mathematics in all areas of human endeavour. This seventh volume starts with a homage to the Italian artist Mimmo Paladino who created exclusively for the Venice Conference 2019 ten original and unique works of art paper dedicated to the themes of the meeting. A large section is dedicated to the most recent Fields Medals including a Homage to Maryam Mirzakhani including a presentation of the exhibition on soap bubbles in art and science that took place in 2019. A section is dedicated to cinema and theatre including the performances by Claire Bardainne & Adrien Mondot. A part of the conference focused on the community of mathematicians, their role in literature and even in politics with the extraordinary example of Antanas Mockus Major of Bogotá. Mathematics in the constructions of bridges, in particular in Italy in the Sixties was presented by Tullia Iori. A very particular contribution on Origami by a mathematician, Marco Abate and an artist, Alessandro Beber. And many other topics. As usual the topics are treated in a way that is rigorous but captivating, detailed and full of evocations. This is an all-embracing look at the world of mathematics and culture. The world, life, culture, everything has changed in a few weeks with the Coronavirus. Culture, science are the main ways to safeguard people's physical and social life. Trust in humanity's creativity and ability. The motto today in Italy is Everything will be fine. This work is addressed to all those who have an interest in Mathematics.

Teaching Mathematics through Problem-Solving in K–12 Classrooms

by Matthew Oldridge

Publisher : Rowman & Littlefield
Release Date : 2018-10-31
ISBN : 1475843348
Pages : 134 pages
Rating Book: 4.7/5 (475 users)

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Download or read book Teaching Mathematics through Problem-Solving in K–12 Classrooms written by Matthew Oldridge and published by Rowman & Littlefield. This book was released on 2018-10-31 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how problems can be the vehicle for learning mathematics itself, and presents a comprehensive pedagogy based on classroom discourse, assessment, critical and creative thinking.

Bad at Math?

by Lidia Gonzalez

Publisher : Corwin Press
Release Date : 2023-02-21
ISBN : 1071907492
Pages : 173 pages
Rating Book: 4.7/5 (71 users)

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Download or read book Bad at Math? written by Lidia Gonzalez and published by Corwin Press. This book was released on 2023-02-21 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: Math really is for everyone—so let’s prove it. You’ve heard it from kids, from friends, and from celebrities: "I’m bad at math." It’s a line that society tends to accept without examination—after all, some people just aren’t "math people," right? Wrong. As we do with other essential skills, we need to expose the stereotypes, challenge the negative mindsets, and finally confront the systemic opportunity gaps in math education, and replace them with a new vision for what math is, who it’s for, and who can excel at it. In this book you’ll find Research on teacher and student mindsets and their effect on student achievement Audience-specific and differentiated tools, reflection questions, and suggested actions for educators at all levels of the system Examples from popular media, as well as personal stories and anecdotes Quotes, data-driven figures, and suggestions for deeper learning on all aspects of a positive and equitable vision of math education Both social commentary and a toolkit of solutions, this bold new book directly challenges the constructs that have historically dictated our perceptions of what makes someone a "math person". Only by dismantling those misplaced assumptions can we reform math education so it works for everyone. Because in truth, we are all math people.

The Grasshopper King

by Jordan Ellenberg

Publisher :
Release Date : 2003
ISBN :
Pages : 260 pages
Rating Book: 4.9/5 (39 users)

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Download or read book The Grasshopper King written by Jordan Ellenberg and published by . This book was released on 2003 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This debut novel is a profoundly absurd campus satire about immortality, obsession, obscurity, and true love.

The Well-Trained Mind: A Guide to Classical Education at Home (Fourth Edition)

by Susan Wise Bauer

Publisher : W. W. Norton & Company
Release Date : 2016-08-09
ISBN : 0393253635
Pages : 880 pages
Rating Book: 4.9/5 (393 users)

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Download or read book The Well-Trained Mind: A Guide to Classical Education at Home (Fourth Edition) written by Susan Wise Bauer and published by W. W. Norton & Company. This book was released on 2016-08-09 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is your child getting lost in the system, becoming bored, losing his or her natural eagerness to learn? If so, it may be time to take charge of your child’s education—by doing it yourself. The Well-Trained Mind will instruct you, step by step, on how to give your child an academically rigorous, comprehensive education from preschool through high school—one that will train him or her to read, to think, to understand, to be well-rounded and curious about learning. Veteran home educators Susan Wise Bauer and Jessie Wise outline the classical pattern of education called the trivium, which organizes learning around the maturing capacity of the child’s mind and comprises three stages: the elementary school “grammar stage,” when the building blocks of information are absorbed through memorization and rules; the middle school “logic stage,” in which the student begins to think more analytically; and the high-school “rhetoric stage,” where the student learns to write and speak with force and originality. Using this theory as your model, you’ll be able to instruct your child—whether full-time or as a supplement to classroom education—in all levels of reading, writing, history, geography, mathematics, science, foreign languages, rhetoric, logic, art, and music, regardless of your own aptitude in those subjects. Thousands of parents and teachers have already used the detailed book lists and methods described in The Well-Trained Mind to create a truly superior education for the children in their care. This extensively revised fourth edition contains completely updated curricula and book lists, links to an entirely new set of online resources, new material on teaching children with learning challenges, cutting-edge math and sciences recommendations, answers to common questions about home education, and advice on practical matters such as standardized testing, working with your local school board, designing a high-school program, preparing transcripts, and applying to colleges. You do have control over what and how your child learns. The Well-Trained Mind will give you the tools you’ll need to teach your child with confidence and success.

Effective Mathematics Lessons through an Eclectic Singapore Approach

by Khoon Yoong Wong

Publisher : World Scientific
Release Date : 2015-05-21
ISBN : 9814696447
Pages : 324 pages
Rating Book: 4.1/5 (814 users)

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Download or read book Effective Mathematics Lessons through an Eclectic Singapore Approach written by Khoon Yoong Wong and published by World Scientific. This book was released on 2015-05-21 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this seventh volume, as part of the series of yearbooks by the Association of Mathematics Educators in Singapore, we aim to provide a range of learning experiences and teaching strategies that mathematics teachers can judiciously select and adapt in order to deliver effective lessons to their students at the primary to secondary level. Our ultimate goal is to develop successful problem solvers who are able to understand concepts, master fundamental skills, reason logically, apply mathematics, enjoy learning, and strategise their thinking. These qualities will prepare students for life-long learning and careers in the 21st century. The materials covered are derived from psychological theories, education praxis, research findings, and mathematics discourse, mediated by the author's professional experiences in mathematics education in four countries over the past four decades. They are organised into ten chapters aligned with the Singapore mathematics curriculum framework to help teachers and educators from Singapore and other countries deepen their understanding about the so-called "Singapore Maths". The book strikes a balance between mathematical rigour and pedagogical diversity, without rigid adherence to either. This is relevant to the current discussion about the relative roles of mathematics content knowledge and pedagogical content knowledge in effective teaching. It also encourages teachers to develop their own philosophy and teaching styles so that their lessons are effective, efficient, and enjoyable to teach. Contents:Curriculum: Map the Intended, Implemented, and Attained LandscapeConcepts: Build Meanings and ConnectionsSkills: Use Rules EfficientlyProcesses: Sharpen Mathematical Reasoning and Heuristic UseApplications: View the World Through Mathematical LensesICT: Be Its Prudent MasterAttitudes: Energise Learning with Emotional PowerMetacognition: Strategic Use of Cognitive ResourcesSchool Curriculum: Prepare Thoughtful PlansProfessional Development: Become Metacognitive Teachers Readership: Graduate students, researchers, practitioners and teachers in mathematics. Key Features:First, there is currently no mathematics methodology text that provides significant insights about learning and teaching based on the Singapore mathematics curriculum, yet supported by international perspectives and literatureThis fills a gap in the market about Singapore Maths, which has attracted much attention from overseas educatorsSecond, the teaching strategies discussed in the book are based on theories, research, and professional practices, and they satisfy the needs of both practitioners and researchers, hence widening the readership of the bookFinally, the author writes from the vintage point of having taught mathematics education and conducted research in Australia, Brunei Darussalam, Malaysia and Singapore and consulted with education institutes in Chile, Hong Kong, the Philippines and the US. This diverse experience allows the author to discuss mathematics education issues from an East-meets-West perspectiveKeywords:Mathematics;Pedagogy;Learning Experiences;Singapore;Teachers;Instruction;Curriculum

The Robot Factory

by Joseph Ganem

Publisher : Springer
Release Date : 2018-08-27
ISBN : 3319778609
Pages : 255 pages
Rating Book: 4.1/5 (319 users)

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Download or read book The Robot Factory written by Joseph Ganem and published by Springer. This book was released on 2018-08-27 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book exposes a disturbing misuse of the scientific method to advance policies and agendas that are in fact detrimental to both science and education. The author, a physics professor, examines two related trends in education – the practice of “data-driven” reform and the disparaging of the traditional liberal arts in favor of programs with a heavy emphasis on science and technology. Many of the reforms being foisted on educators have more in common with pseudo-science than real science. The reduction of education to a commodity, and the shilling of science as a means to enhance corporate profits, lead to an impoverished and stunted understanding of science in particular, and of education in general. How is it possible for: • schools with all students learning at grade-level to be rated as failing?• teachers to be rated as ineffective after all their students meet their learning outcomes?• rising grade-school math standards to result in more college students needing remedial math?• politicians to disparage scientists and their results but argue that more students should study science? These bizarre outcomes have happened and are the result of an education system that misuses and misrepresents math and science in the classroom and in crafting education policies. This book exposes the flawed and fallacious thinking that is damaging education at all levels throughout the United States, and makes a compelling case for rethinking the standardized, optimized, and quantified approaches in vogue in education today to accommodate the different needs of individual teachers and students.

Arguing with Numbers

by James Wynn

Publisher : Penn State Press
Release Date : 2021-03-18
ISBN : 0271089237
Pages : 302 pages
Rating Book: 4.7/5 (271 users)

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Download or read book Arguing with Numbers written by James Wynn and published by Penn State Press. This book was released on 2021-03-18 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: As discrete fields of inquiry, rhetoric and mathematics have long been considered antithetical to each other. That is, if mathematics explains or describes the phenomena it studies with certainty, persuasion is not needed. This volume calls into question the view that mathematics is free of rhetoric. Through nine studies of the intersections between these two disciplines, Arguing with Numbers shows that mathematics is in fact deeply rhetorical. Using rhetoric as a lens to analyze mathematically based arguments in public policy, political and economic theory, and even literature, the essays in this volume reveal how mathematics influences the values and beliefs with which we assess the world and make decisions and how our worldviews influence the kinds of mathematical instruments we construct and accept. In addition, contributors examine how concepts of rhetoric—such as analogy and visuality—have been employed in mathematical and scientific reasoning, including in the theorems of mathematical physicists and the geometrical diagramming of natural scientists. Challenging academic orthodoxy, these scholars reject a math-equals-truth reduction in favor of a more constructivist theory of mathematics as dynamic, evolving, and powerfully persuasive. By bringing these disparate lines of inquiry into conversation with one another, Arguing with Numbers provides inspiration to students, established scholars, and anyone inside or outside rhetorical studies who might be interested in exploring the intersections between the two disciplines. In addition to the editors, the contributors to this volume are Catherine Chaput, Crystal Broch Colombini, Nathan Crick, Michael Dreher, Jeanne Fahnestock, Andrew C. Jones, Joseph Little, and Edward Schiappa.

Mathematics (Education) in the Information Age

by Stacy A. Costa

Publisher : Springer Nature
Release Date : 2020-12-10
ISBN : 3030591778
Pages : 226 pages
Rating Book: 4.3/5 (3 users)

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Download or read book Mathematics (Education) in the Information Age written by Stacy A. Costa and published by Springer Nature. This book was released on 2020-12-10 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together ideas from experts in cognitive science, mathematics, and mathematics education to discuss these issues and to present research on how mathematics and its learning and teaching are evolving in the Information Age. Given the ever-broadening trends in Artificial Intelligence and the processing of information generally, the aim is to assess their implications for how math is evolving and how math should now be taught to a generation that has been reared in the Information Age. It will also look at the ever-spreading assumption that human intelligence may not be unique—an idea that dovetails with current philosophies of mind such as posthumanism and transhumanism. The role of technology in human evolution has become critical in the contemporary world. Therefore, a subgoal of this book is to illuminate how humans now use their sophisticated technologies to chart cognitive and social progress. Given the interdisciplinary nature of the chapters, this will be of interest to all kinds of readers, from mathematicians themselves working increasingly with computer scientists, to cognitive scientists who carry out research on mathematics cognition and teachers of mathematics in a classroom.