Search results for: street-fighting-mathematics

Street Fighting Mathematics

Author : Sanjoy Mahajan
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An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Street Fighting Mathematics

Author : Sanjoy Mahajan
File Size : 64.52 MB
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An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Mathematics Matters in Education

Author : Yeping Li
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This book is inspired by Roger E. Howe's contributions to the international communities of mathematics and mathematics education. Renowned for his research contributions in the fields of representation theory, automorphic forms, harmonic analysis, and invariant theory, Dr. Howe has also fundamentally deepened our understanding of the mathematics taught in the early school grades and has challenged and stimulated mathematicians and mathematics educators to work together to examine this part of the mathematical universe more critically and in imaginative new ways. This volume will help summarize and highlight Howe's contributions to several topic areas in mathematics education, demonstrating the possibility and importance of engaging mathematicians in high-impact research in mathematics education, and showcasing the importance of cross-disciplinary collaboration and exchange.

The Best Writing on Mathematics 2021

Author : Mircea Pitici
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The year’s finest mathematical writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world—and you don’t need to be a mathematician to enjoy the pieces collected here. These essays—from leading names and fresh new voices—delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice, and taking readers behind the scenes of today’s hottest mathematical debates. Here, Viktor Blåsjö gives a brief history of “lockdown mathematics”; Yelda Nasifoglu decodes the politics of a seventeenth-century play in which the characters are geometric shapes; and Andrew Lewis-Pye explains the basic algorithmic rules and computational procedures behind cryptocurrencies. In other essays, Terence Tao candidly recalls the adventures and misadventures of growing up to become a leading mathematician; Natalie Wolchover shows how old math gives new clues about whether time really flows; and David Hand discusses the problem of “dark data”—information that is missing or ignored. And there is much, much more.

The Best Writing on Mathematics 2016

Author : Mircea Pitici
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The year's finest mathematics writing from around the world This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2016 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Burkard Polster shows how to invent your own variants of the Spot It! card game, Steven Strogatz presents young Albert Einstein's proof of the Pythagorean Theorem, Joseph Dauben and Marjorie Senechal find a treasure trove of math in New York's Metropolitan Museum of Art, and Andrew Gelman explains why much scientific research based on statistical testing is spurious. In other essays, Brian Greene discusses the evolving assumptions of the physicists who developed the mathematical underpinnings of string theory, Jorge Almeida examines the misperceptions of people who attempt to predict lottery results, and Ian Stewart offers advice to authors who aspire to write successful math books for general readers. And there's much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

Mathematics without Apologies

Author : Michael Harris
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What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.

Mengenlehre und ihre Logik

Author : Willard Van Orman Quine
File Size : 48.70 MB
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Physical Biology of the Cell

Author : Rob Phillips
File Size : 44.74 MB
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Physical Biology of the Cell is a textbook for a first course in physical biology or biophysics for undergraduate or graduate students. It maps the huge and complex landscape of cell and molecular biology from the distinct perspective of physical biology. As a key organizing principle, the proximity of topics is based on the physical concepts that

Lean Math Figuring to Improve

Author : Mark R. Hamel
File Size : 46.69 MB
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Lean transformations are decidedly more challenging when the math is inconsistent with lean principles, misapplied, or just plain wrong. Math should never get in the way of a lean transformation, but instead should facilitate it. Lean Math is the indispensable reference for this very purpose. A single, comprehensive source, the book presents standard and specialized approaches to tackling the math required of lean and six sigma practitioners across all industries—seasoned and newly minted practitioners alike. Lean Math features more than 160 thoughtfully organized entries. Ten chapters cover system-oriented math, time, the “-ilities” (availability, repeatability, stability, etc.), work, inventory, performance metrics, basic math and hypothesis testing, measurement, experimentation, and more. Two appendices cover standard work for analyzing data and understanding and dealing with variation. Practitioners will quickly locate the precise entry(ies) that is relevant to the problem or continuous improvement opportunity at hand. Each entry not only provides background on the related lean principles, formulas, examples, figures, and tables, but also tips, cautions, cross-references to other associated entries, and the occasional “Gemba Tale” that shares real-world experiences. The book consistently encourages the practitioner to engage in math-assisted plan-do-check-act (PDCA) cycles, employing approaches that include simulation and “trystorming.” Lean Math truly transcends the “numbers” by reinforcing and refreshing lean thinking for the very purpose of Figuring to Improve. REVIEWER COMMENTS “Hamel and O’Connor provide both the novice and experienced lean practitioner a comprehensive, common-sense reference for lean math. For example, I know that our Lean Support Office team would have gladly used dozens of Lean Math entries during a recent lean management system pilot. The concepts, context, and examples would have certainly helped our execution and provided greater clarity during our training activities. Lean Math is a must have book for Lean Support Office people!” —Dave Pienta, Director, Lean Support Office, Moog, Inc. Aircraft Group “A practical math book may sound like an oxymoron, but Lean Math is both pragmatic and accessible. Hamel and O’Connor do an excellent job keeping the math as simple as possible, while bringing lean principles to the forefront of the discussion. The use of insurance and healthcare industry examples especially helps simplify the translation for lean practitioners in non-manufacturing industries. Readers will be able to use the numerous tables and figures to clearly illustrate and teach lean concepts to others. Lean Math is a reference book that every lean practitioner or Black Belt should have in their library!” —Peter Barnett, MBB, Liberty Management System Architect, Liberty Mutual Insurance “Lean Math is a comprehensive reference book within which the lean practitioner can quickly find straightforward examples illustrating how to perform almost any lean calculation. Equally useful, it imparts the importance of the relevant lean principal(s). While coaching some recent transformation efforts, I put Lean Math to the test by asking several novice practitioners to reference it during their work. They were promptly rewarded with deeper insight and effectiveness—a reflection of this book’s utility and value to the lean practitioner.” —Greg Lane, international lean transformation coach, speaker, and author of three books including, “Made-to-Order Lean: Excelling in a High-Mix, Low-Volume Environment” “While the technical, social, and management sciences behind lean must be learned by doing, their conceptual bases are absolutely validated by the math. This validation is particularly crucial to overcoming common blind spots ingrained by traditional practice. Hamel and O’Connor’s text is a comprehensive and readable resource for lean implementers at all levels who are seeking a deeper understanding of lean tools and systems. Clear diagrams and real-world examples create a bridge for readers between theory and practice—theory proven by practice. If math is the language of science, then Lean Math is indeed the language of lean science.” —Bruce Hamilton, President, Greater Boston Manufacturing Partnership, Director Emeritus for the Shingo Institute “Mark and Michael have done a tremendous service for the lean community by tackling this daunting subject. There are so many ways to quantify value, display improvement, and define complex problems that choosing the right methods and measures becomes an obstacle to progress. Lean Math helps remove that obstacle. Almost daily, operations leaders in every industry need the practical math and lean guidance in these pages. Now, finally, we have it in one place. Thank you.” —Zane Ferry, Executive Director, National Operations, QMS Continuous Improvement, Quest Diagnostics “Too many lean books dwell on principles, but offer little to address critical how-to questions, such as, ‘How do I use these concepts to solve my specific problem?’ With plain English explanations, simple illustrations, and examples across industries, Lean Math bridges a long-standing gap. Hamel and O’Connor’s Lean Math is sure to become a must-have reference for every lean practitioner working to improve performance in any modern workplace.” —Jeff Fuchs, Executive Director, Maryland World Class Consortia, Past Chairman, Lean Certification Oversight Committee “Lean Math fills a huge gap in the continuous improvement library, helping practitioners to translate data, activities, and ideas into meaningful information for effective experimentation and intelligent decisions. This reference comes at a critical time for the healthcare industry as we struggle to improve quality, while controlling costs. Though we don’t make widgets, our people, processes, and patients will benefit from the tools provided in this reference. The numerous examples, as well as the Gemba Tales scattered throughout the book, bring life to the principles and formulas. Lean Math is impressive in both scope and presentation of content.” —Tim Pettry, Senior Process Improvement Specialist, Cleveland Clinic “Lean Math is a great book for those times when only the correct answer will do. The math, along with the Gemba Tales, are helpful for those in the midst of the technical aspects of a transformation, as well as those of us who once knew much of this but haven’t used it in a while.” —Beau Keyte, organization transformation and performance improvement coach, author of two Shingo-Award winning books: “The Complete Lean Enterprise” and “Perfecting Patient Journeys” “Math and numbers aren’t exclusively the domain of six sigma! Toyota leaders describe lean as an organizational culture, a managerial approach, and a philosophy. They also maintain that the last piece of lean is technical methods, which includes the math we need for properly sizing inventory levels, validating hypotheses, gauging improvement, and more. Lean Math is a useful book that compiles important mathematical and quantitative methods that complement the people side of lean. Hamel and O’Connor are extremely qualified to deftly explain these methods. Lest you think it’s a dry math text, there are Gemba Tales and examples from multiple industries, including healthcare, which illustrate these approaches in very relatable ways.” —Mark Graban, Shingo-Award winning author, speaker, consultant, and blogger “When you begin a lean journey, it’s like starting an exercise regimen—the most important thing is to start. But as you mature, and as you achieve higher levels of excellence, rigor becomes increasingly important. Lean Math provides easy, elegant access to the necessary rigor required for effective measurement and analysis and does so in practical terms with excellent examples.” —Misael Cabrera, PE, Director, Arizona Department Environmental Quality

Art Centered Learning Across the Curriculum

Author : Julia Marshall
File Size : 47.1 MB
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This handbook provides teachers with a framework for implementing inquiry-based, substantive art integration across the curriculum, along with the background knowledge and models needed to do this. Drawing on ideas from Harvard Project Zero, the authors make a clear and compelling argument for how contemporary art supports student learning. The text features subject-specific chapters co-written by teaching scholars from that discipline. Each chapter includes examples of contemporary art with explanations of how these works explore the fundamental concepts of the academic discipline. The book concludes with a chapter on an integrated, inquiry-based curriculum inspired by contemporary art, including guidelines for developing art projects teachers can adapt to their students’ interests and needs. This resource is appropriate for art teachers, as well as subject-area teachers who are not familiar with using contemporary art in the classroom. “I am so excited about this book! The visuals alone are enough to clue teachers in on ways that Contemporary Art can blow their curriculums open to become engaging, relevant vehicles for their students to ride across the 21st century. From the first scan, readers cannot help but see the power of Contemporary Art in transforming classrooms and learning.” —From the Foreword by Lois Hetland, professor and chair of art education at Massachusetts College of Art and Design, and co-author of Studio Thinking 2 “Art-Centered Learning Across the Curriculum well surpasses its goal to demystify contemporary art for K–12 teachers. In this important text, the authors present a direct challenge to educators and public education reformers of all stripes to embrace the arts and design practices across disciplines as a potent means for building beautiful minds, not merely as a tool for beautifying dingy school corridors. This new book serves as a primer for fashioning the kinds of integrated curriculum frameworks required for success in today’s global knowledge economy.” —James Haywood Rolling Jr., chair of art education and a dual professor in art education and teaching and leadership, Syracuse University