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When Least Is Best

by Paul J. Nahin

What is the best way to photograph a speeding bullet? Why does light move through glass in the least amount of time possible? How can lost hikers find their way out of a forest? What will rainbows look like in the future? Why do soap bubbles have a shape that gives them the least area? By combining the mathematical history of extrema with contemporary examples, Paul J. Nahin answers these intriguing questions and more in this engaging and witty volume. He shows how life often works at the extremes--with values becoming as small (or as large) as possible--and how mathematicians over the centuries have struggled to calculate these problems of minima and maxima. From medieval writings to the development of modern calculus to the current field of optimization, Nahin tells the story of Dido's problem, Fermat and Descartes, Torricelli, Bishop Berkeley, Goldschmidt, and more. Along the way, he explores how to build the shortest bridge possible between two towns, how to shop for garbage bags, how to vary speed during a race, and how to make the perfect basketball shot. Written in a conversational tone and requiring only an early undergraduate level of mathematical knowledge, When Least Is Best is full of fascinating examples and ready-to-try-at-home experiments. This is the first book on optimization written for a wide audience, and math enthusiasts of all backgrounds will delight in its lively topics.

When Shea Was Home: The Story of the 1975 Mets, Yankees, Giants, and Jets

by Brett Topel

Four teams, 175 games, 3,738,546 fans--one stadium. If 1975 wasn’t the most successful year in New York sports--and it wasn’t--then it was certainly one of the oddest. For that one crazy season, all four New York teams--the Mets, Jets, Yankees, and Giants--called Shea Stadium home. When Shea was Home includes interviews with the stadium’s former head groundskeeper, the legendary Pete Flynn, as well as Jerry Koosman, Bud Harrelson and Ed Kranepool of the Mets, Giants owner John Mara, Rich Caster of the Jets, former Super Bowl MVP quarterback Doug Williams, who played that year at Shea for Grambling, and many more! This well-written narrative includes information about the stadium, the teams, the players, how the teams coexisted, and how they didn't. When Shea was Home takes New York sports fans on a unique trip down memory lane, offering context on the national and local history and culture of the time. It is perfect for the avid New York sports aficionado--regardless of team allegiance!

When the Braves Ruled the Diamond: Fourteen Flags over Atlanta

by Dan Schlossberg

From 1991 through 2005, the Atlanta Braves did something no pro sports team can match, finishing in first place for fourteen consecutive seasons. <P><P>During that stretch, the Braves paired powerful pitching with potent hitting that produced under pressure. Hall of Fame manager Bobby Cox won with veteran teams, young teams, slugging teams, and several times with teams that emphasized speed and defense. His teams captured on hundred wins in six different seasons. <P><P>In When the Braves Ruled the Diamond, now newly updated to include a discussion of the team's latest Hall of Fame inductees, former AP sportswriter Dan Schlossberg covers the record-breaking era that transformed Atlanta from the Bad-News Braves to America's Team. <P><P>With separate chapters on Cox, fabled pitching coach Leo Mazzone, and Hall of Fame pitchers Greg Maddux, Tom Glavine, and John Smoltz, this book also highlights the contributions of Andres Galarraga, Andruw Jones, Chipper Jones, Brian Jordan, Javy Lopez, Terry Pendleton, and many more Braves stars. <P><P>It features year-by-year summaries, Opening Day lineups, and even oddball anecdotes that explain why the fourteen-year streak may never be duplicated. It is the perfect gift for fans of baseball history as well as fans of the Atlanta Braves!

Where Did You Get This Number?: A Pollster's Guide to Making Sense of the World

by Anthony Salvanto

CBS News’ Elections and Surveys Director Anthony Salvanto takes you behind the scenes of polling to show you how to think about who we are and where we’re headed as a nation.As Elections and Surveys Director for CBS News, it’s Anthony Salvanto’s job to understand you—what you think and how you vote. He’s the person behind so many of the poll numbers you see today, making the winner calls on election nights and surveying thousands of Americans. In Where Did You Get This Number? A Pollster’s Guide to Making Sense of the World, Salvanto takes readers on a fast-paced, eye-opening tour through the world of polling and elections and what they really show about America today, beyond the who's-up-who’s-down headlines and horse races. Salvanto is just the person to bring much-needed clarity in a time when divisions seem to run so deep. The language of polling may be numbers, but the stories it tells are about people. In this engaging insider’s account, Salvanto demystifies jargon with plain language and answers readers’ biggest questions about polling and pollsters. How can they talk to 1,000 people and know the country? How do they know the winner so fast? How do they decide what questions to ask? Why didn't they call you? Salvanto offers data-driven perspective on how Americans see the biggest issues of our time, from the surprising 2016 election, to the shocks of the financial crisis, the response to terrorism and the backlash against big money. He doesn’t shy away from pointing out what’s worked and what hasn’t. Salvanto takes readers inside the CBS newsroom on Election Night 2016 and makes readers rethink conventional wisdom and punditry just in time for the 2018 midterms. He shows who really decides elections and why you should think about a poll differently from the forecasts popularized by Nate Silver and others. Where Did You Get This Number? is an essential resource for anyone interested in politics—and how to better measure and understand patterns of human behavior. For any American who wants to get a better read on what America is thinking, this book shows you how to make sense of it all.

Where Do Numbers Come From?

by T. W. Körner

Why do we need the real numbers? How should we construct them? These questions arose in the nineteenth century, along with the ideas and techniques needed to address them. Nowadays it is commonplace for apprentice mathematicians to hear 'we shall assume the standard properties of the real numbers' as part of their training. But exactly what are those properties? And why can we assume them? This book is clearly and entertainingly written for those students, with historical asides and exercises to foster understanding. Starting with the natural (counting) numbers and then looking at the rational numbers (fractions) and negative numbers, the author builds to a careful construction of the real numbers followed by the complex numbers, leaving the reader fully equipped with all the number systems required by modern mathematical analysis. Additional chapters on polynomials and quarternions provide further context for any reader wanting to delve deeper.

Where is the Gödel-point hiding: Gentzen's Consistency Proof of 1936 and His Representation of Constructive Ordinals

by Anna Horská

This book explains the first published consistency proof of PA. It contains the original Gentzen's proof, but it uses modern terminology and examples to illustrate the essential notions. The author comments on Gentzen's steps which are supplemented with exact calculations and parts of formal derivations. A notable aspect of the proof is the representation of ordinal numbers that was developed by Gentzen. This representation is analysed and connection to set-theoretical representation is found, namely an algorithm for translating Gentzen's notation into Cantor normal form. The topic should interest researchers and students who work on proof theory, history of proof theory or Hilbert's program and who do not mind reading mathematical texts. ​

Where's the Wonder in Elementary Math?: Encouraging Mathematical Reasoning in the Classroom

by Judith McVarish

This book argues that even in today's high-stakes testing environment, 'teaching to the test' need not be teachers’ only focus as they introduce young children to mathematics. Judith McVarish demonstrates how building a community of learners and using problem solving to engage students can help teachers encourage students’ disposition to creative thinking and reasoning—skills that can otherwise become lost due to the pressure of the many other expectations placed upon both teachers and students. This book offers strategies for infusing mathematics learning and reasoning into elementary school classrooms while meeting curriculum and testing mandates. The teacher researcher component of each chapter provides a vehicle for teachers to bring their own expertise and questions back into the teaching and learning equation.

Who Gets What — and Why

by Alvin E. Roth

A Nobel laureate reveals the often surprising rules that govern a vast array of activities -- both mundane and life-changing -- in which money may play little or no role. If you've ever sought a job or hired someone, applied to college or guided your child into a good kindergarten, asked someone out on a date or been asked out, you've participated in a kind of market. Most of the study of economics deals with commodity markets, where the price of a good connects sellers and buyers. But what about other kinds of "goods," like a spot in the Yale freshman class or a position at Google? This is the territory of matching markets, where "sellers" and "buyers" must choose each other, and price isn't the only factor determining who gets what. Alvin E. Roth is one of the world's leading experts on matching markets. He has even designed several of them, including the exchange that places medical students in residencies and the system that increases the number of kidney transplants by better matching donors to patients. In Who Gets What -- And Why, Roth reveals the matching markets hidden around us and shows how to recognize a good match and make smarter, more confident decisions.

Who Gets What — and Why: The New Economics of Matchmaking and Market Design

by Alvin E. Roth

"In his fluent and accessible book, Mr. Roth vividly describes the successes of market design." -- "In this fascinating, often surprising book, Alvin Roth guides us through the jungles of modern life, pointing to the many markets that are hidden in plain view all around us." -- Dan Ariely, author of Predictably Irrational and The (Honest) Truth About Dishonesty Most of the study of economics deals with commodity markets, where the price of a good connects sellers and buyers. But what about other kinds of "goods," like a spot in the Yale freshman class or a position at Google? If you've ever sought a job or hired someone, applied to college or guided your child into a good kindergarten, asked someone out on a date or been asked out, you've participated in a kind of market. This is the territory of matching markets, where "sellers" and "buyers" must choose each other, and price isn't the only factor determining who gets what. In Who Gets What--and Why, Nobel laureate Alvin E. Roth reveals the matching markets hidden around us and shows us how to recognize a good match and make smarter, more confident decisions. "Mr. Roth's work has been to discover the most efficient and equitable methods of matching, and implement them in the world. He writes with verve and style . . . Who Gets What--and Why is a pleasure to read." -- Wall Street Journal "A book filled with wit, charm, common sense, and uncommon wisdom." -- Paul Milgrom, professor of economics, Stanford University and Stanford Business School

The Whole Truth About Whole Numbers

by Sylvia Forman Agnes M. Rash

The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather than giving brief introductions to a wide variety of topics, this book provides an in-depth introduction to the field of Number Theory. The topics covered are many of those included in an introductory Number Theory course for mathematics majors, but the presentation is carefully tailored to meet the needs of elementary education, liberal arts, and other non-mathematical majors. The text covers logic and proofs, as well as major concepts in Number Theory, and contains an abundance of worked examples and exercises to both clearly illustrate concepts and evaluate the students' mastery of the material.

Who's #1?

by Amy N. Langville Carl D. Meyer

A website's ranking on Google can spell the difference between success and failure for a new business. NCAA football ratings determine which schools get to play for the big money in postseason bowl games. Product ratings influence everything from the clothes we wear to the movies we select on Netflix. Ratings and rankings are everywhere, but how exactly do they work? Who's #1? offers an engaging and accessible account of how scientific rating and ranking methods are created and applied to a variety of uses.Amy Langville and Carl Meyer provide the first comprehensive overview of the mathematical algorithms and methods used to rate and rank sports teams, political candidates, products, Web pages, and more. In a series of interesting asides, Langville and Meyer provide fascinating insights into the ingenious contributions of many of the field's pioneers. They survey and compare the different methods employed today, showing why their strengths and weaknesses depend on the underlying goal, and explaining why and when a given method should be considered. Langville and Meyer also describe what can and can't be expected from the most widely used systems.The science of rating and ranking touches virtually every facet of our lives, and now you don't need to be an expert to understand how it really works. Who's #1? is the definitive introduction to the subject. It features easy-to-understand examples and interesting trivia and historical facts, and much of the required mathematics is included.


by Samantha Kleinberg

Can drinking coffee help people live longer? What makes a stock's price go up? Why did you get the flu? Causal questions like these arise on a regular basis, but most people likely have not thought deeply about how to answer them.This book helps you think about causality in a structured way: What is a cause, what are causes good for, and what is compelling evidence of causality? Author Samantha Kleinberg shows you how to develop a set of tools for thinking more critically about causes. You'll learn how to question claims, identify causes, make decisions based on causal information, and verify causes through further tests.Whether it's figuring out what data you need, or understanding that the way you collect and prepare data affects the conclusions you can draw from it, Why will help you sharpen your causal inference skills.

Why Cats Land on Their Feet

by Mark Levi

Ever wonder why cats land on their feet? Or what holds a spinning top upright? Or whether it is possible to feel the Earth's rotation in an airplane? Why Cats Land on Their Feet is a compendium of paradoxes and puzzles that readers can solve using their own physical intuition. And the surprising answers to virtually all of these astonishing paradoxes can be arrived at with no formal knowledge of physics.Mark Levi introduces each physical problem, sometimes gives a hint or two, and then fully explains the solution. Here readers can test their critical-thinking skills against a whole assortment of puzzles and paradoxes involving floating and diving, sailing and gliding, gymnastics, bike riding, outer space, throwing a ball from a moving car, centrifugal force, gyroscopic motion, and, of course, falling cats.Want to figure out how to open a wine bottle with a book? Or how to compute the square root of a number using a tennis shoe and a watch? Why Cats Land on Their Feet shows you how, and all that's required is a familiarity with basic high-school mathematics. This lively collection also features an appendix that explains all physical concepts used in the book, from Newton's laws to the fundamental theorem of calculus.

Why Is There Philosophy of Mathematics At All?

by Ian Hacking

This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.

Why Life Matters

by Michael Charles Tobias Jane Gray Morrison

Dr. Michael Charles Tobias and Jane Gray Morrison are world-renowned ecological philosophers and activists, interdisciplinary social and environmental scientists and broad-ranging, deeply committed humanists. This collection of fifty essays and interviews comprises an invigorating, outspoken, provocative and eloquent overview of the ecological humanities in one highly accessible volume. The components of this collection were published in the authors' "Green Conversations" blog series, and pieces in the Eco News Network from 2011 to 2013 and feature luminaries from Jane Goodall to Ted Turner to the Secretary of the Smithsonian Institution to the former head of the UN Convention on Biological Diversity. Stunning color photographs captured by the authors and contributors make Why Life Matters: Fifty Ecosystems of the Heart and Mind a feast for the eyes as well as the mind and soul. Ethics, science, technology, ecological literacy, grass-roots renaissance thinkers, conservation innovation from the U. S. to the U. K. ; from India to Ecuador; from Bhutan to Haiti; from across Africa, the Neo-Tropics, Central Asia and Japan, to Rio, Shanghai and Manhattan - this humanistic ode to the future of life on earth is a relevant and resonating read. Michael Tobias and Jane Gray Morrison, partners who between them have authored some 50 books and written, directed and produced some 170 films, a prolific body of work that has been read, translated and/or broadcast around the world, have been married for more than a quarter-of-a-century. Their field research across the disciplines of comparative literature, anthropology, the history of science and philosophy, ecology and ethics, in over 80 countries, has served as a telling example of what two people - deeply in love with one another - can accomplish in spreading that same unconditional love to others - of all species.

Why Prove it Again?

by John W. Dawson

This monograph considers several well-known mathematical theorems and asks the question, "Why prove it again?" while examining alternative proofs. It explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how they judge whether two proofs of a given result are different. While a number of books have examined alternative proofs of individual theorems, this is the first that presents comparative case studies of other methods for a variety of different theorems. The author begins by laying out the criteria for distinguishing among proofs and enumerates reasons why new proofs have, for so long, played a prominent role in mathematical practice. He then outlines various purposes that alternative proofs may serve. Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues' Theorem, the Prime Number Theorem, and the proof of the irreducibility of cyclotomic polynomials. Why Prove It Again? will appeal to a broad range of readers, including historians and philosophers of mathematics, students, and practicing mathematicians. Additionally, teachers will find it to be a useful source of alternative methods of presenting material to their students.

Why Stock Markets Crash: Critical Events in Complex Financial Systems

by Didier Sornette

The scientific study of complex systems has transformed a wide range of disciplines in recent years, enabling researchers in both the natural and social sciences to model and predict phenomena as diverse as earthquakes, global warming, demographic patterns, financial crises, and the failure of materials. In this book, Didier Sornette boldly applies his varied experience in these areas to propose a simple, powerful, and general theory of how, why, and when stock markets crash. Most attempts to explain market failures seek to pinpoint triggering mechanisms that occur hours, days, or weeks before the collapse. Sornette proposes a radically different view: the underlying cause can be sought months and even years before the abrupt, catastrophic event in the build-up of cooperative speculation, which often translates into an accelerating rise of the market price, otherwise known as a "bubble." Anchoring his sophisticated, step-by-step analysis in leading-edge physical and statistical modeling techniques, he unearths remarkable insights and some predictions--among them, that the "end of the growth era" will occur around 2050. Sornette probes major historical precedents, from the decades-long "tulip mania" in the Netherlands that wilted suddenly in 1637 to the South Sea Bubble that ended with the first huge market crash in England in 1720, to the Great Crash of October 1929 and Black Monday in 1987, to cite just a few. He concludes that most explanations other than cooperative self-organization fail to account for the subtle bubbles by which the markets lay the groundwork for catastrophe. Any investor or investment professional who seeks a genuine understanding of looming financial disasters should read this book. Physicists, geologists, biologists, economists, and others will welcome Why Stock Markets Crash as a highly original "scientific tale," as Sornette aptly puts it, of the exciting and sometimes fearsome--but no longer quite so unfathomable--world of stock markets.

Why We're Wrong About Nearly Everything: A Theory of Human Misunderstanding

by Bobby Duffy

A leading social researcher explains why humans so consistently misunderstand the outside world How often are women harassed? What percentage of the population are immigrants? How bad is unemployment? These questions are important, but most of us get the answers wrong. Research shows that people often wildly misunderstand the state of the world, regardless of age, sex, or education. And though the internet brings us unprecedented access to information, there's little evidence we're any better informed because of it. We may blame cognitive bias or fake news, but neither tells the complete story. In Why We're Wrong About Nearly Everything, Bobby Duffy draws on his research into public perception across more than forty countries, offering a sweeping account of the stubborn problem of human delusion: how society breeds it, why it will never go away, and what our misperceptions say about what we really believe. We won't always know the facts, but they still matter. Why We're Wrong About Nearly Everything is mandatory reading for anyone interested making humankind a little bit smarter.

Wie berechenbar ist unsere Welt: Herausforderungen Für Mathematik, Informatik Und Philosophie Im Zeitalter Der Digitalisierung (Essentials)

by Klaus Mainzer

Klaus Mainzer legt in diesem essential dar, dass die Zukunft von KI und Digitalisierung eine nüchterne Analyse erfordert, die Grundlagenforschung mit Anwendung verbindet. Berechenbarkeits- und Beweistheorie können dazu beitragen, Big Data und Machine Learning sicherer zu bewältigen. Dabei zeigt sich, dass die komplexen Herausforderungen der digitalen und analogen Welt in Grundlagenfragen der Mathematik, Informatik und Philosophie tief verwurzelt sind.

Wie kommt man darauf?: Einführung in das mathematische Aufgabenlösen

by Merlin Carl

Das Buch soll Studierende der Mathematik und verwandter Disziplinen in grundlegende Techniken und Prinzipien des selbstst#65533;ndigen mathematischen Aufgabenl#65533;sens einf#65533;hren. Dazu werden zun#65533;chst konkrete Beweisprinzipien wie das Schubfachprinzip, Invarianten, Induktion oder R#65533;ckw#65533;rtsarbeiten anhand von Beispielen und ausf#65533;hrlichen Erl#65533;uterungen eingef#65533;hrt, ehe zu allgemeineren Strategien wie Beobachtung und Mustererkennung, Verallgemeinerung, Spezialisierung und Analogie #65533;bergegangen wird. Bei den L#65533;sungen zu den zahlreichen Beispielaufgaben liegt der Schwerpunkt auf der Erkl#65533;rung, wie man auf die jeweiligen Beweisschritte selbst h#65533;tte kommen k#65533;nnen. Die so erlernten Strategien werden dann in verschiedenen mathematischen Gebieten erprobt, n#65533;mlich der elementaren Zahlentheorie, der Graphentheorie, der endlichen Kombinatorik, der linearen Algebra und der Analysis. Jedes Kapitel schlie#65533;t mit zahlreichen #65533;bungsaufgaben.

Wie macht man Karriere in der Wissenschaft

by Rainer Meckenstock Jan Frösler

Dieser Karriereratgeber liefert Transparenz im Dschungel des Wissenschaftssystems. Der erfahrene Wissenschaftler Rainer Meckenstock gibt konkrete Tipps für den eigenen Weg – vom Studium über die Doktoranden- und Postdoc-Zeit bis hin zur ersten Professur: Nach welchen Kriterien sollen sich angehende Forscher ihre Arbeitsgruppe aussuchen? Wie bauen sie ein Profil aus wissenschaftlicher und technischer Kompetenz auf? Welche Ziele sollten Jungforscher für die wissenschaftliche Arbeit im Auge behalten? Die Antworten werden mit Zeichnungen von Jan Frösler illustriert. Das Buch regt die Diskussion zwischen Nachwuchskräften und erfahrenen Wissenschaftlern oder Mentoren an und dient als Inspiration für ein Coaching. Es richtet sich an alle Wissenschaftler, um entweder die eigene Karriere oder die Ausbildung des Nachwuchses zu fördern. Ergänzend zeigen sieben Professorinnen und Professoren anhand ihrer Lebensläufe, wie vielfältig die Karrierewege in der Wissenschaft sein können, und geben ihre eigenen Erfolgsratschläge.

Wie Mathematiker ticken

by David Ruelle

Der renommierte mathematische Physiker David Ruelle schildert in dem Buch seine persönlichen Erfahrungen mit berühmten Mathematikern, deren Eigenarten und persönliche Tragödien - aber auch die erhabene Schönheit ihrer Entdeckungen. Jedes Kapitel stellt eine herausragende mathematische Idee und den visionären Verstand dahinter vor. Dabei gibt der Autor Einblick in die einzigartige Denkweise von Mathematikern und zeigt, weshalb er ihre Herangehensweise, um Fragen nach Sinn, Schönheit und Natur der Wirklichkeit zu diskutieren, für die beste hält.

Will You Be Alive 10 Years from Now?

by Paul J. Nahin

What are the chances of a game-show contestant finding a chicken in a box? Is the Hanukkah dreidel a fair game? Will you be alive ten years from now? These are just some of the one-of-a-kind probability puzzles that acclaimed popular math writer Paul Nahin offers in this lively and informative book. Nahin brings probability to life with colorful and amusing historical anecdotes as well as an electrifying approach to solving puzzles that illustrates many of the techniques that mathematicians and scientists use to grapple with probability. He looks at classic puzzles from the past--from Galileo's dice-tossing problem to a disarming dice puzzle that would have astonished even Newton--and also includes a dozen challenge problems for you to tackle yourself, with complete solutions provided in the back of the book. Nahin then presents twenty-five unusual probability puzzlers that you aren't likely to find anywhere else, and which range in difficulty from ones that are easy but clever to others that are technically intricate. Each problem is accompanied by an entertaining discussion of its background and solution, and is backed up by theory and computer simulations whenever possible in order to show how theory and computer experimentation can often work together on probability questions. All the MATLAB Monte Carlo simulation codes needed to solve the problems computationally are included in the book.With his characteristic wit, audacity, and insight, Nahin demonstrates why seemingly simple probability problems can stump even the experts.

Willful Ignorance

by Herbert I. Weisberg

An original account of willful ignorance and how this principle relates to modern probability and statistical methods Through a series of colorful stories about great thinkers and the problems they chose to solve, the author traces the historical evolution of probability and explains how statistical methods have helped to propel scientific research. However, the past success of statistics has depended on vast, deliberate simplifications amounting to willful ignorance, and this very success now threatens future advances in medicine, the social sciences, and other fields. Limitations of existing methods result in frequent reversals of scientific findings and recommendations, to the consternation of both scientists and the lay public.Willful Ignorance: The Mismeasure of Uncertainty exposes the fallacy of regarding probability as the full measure of our uncertainty. The book explains how statistical methodology, though enormously productive and influential over the past century, is approaching a crisis. The deep and troubling divide between qualitative and quantitative modes of research, and between research and practice, are reflections of this underlying problem. The author outlines a path toward the re-engineering of data analysis to help close these gaps and accelerate scientific discovery. Willful Ignorance: The Mismeasure of Uncertainty presents essential information and novel ideas that should be of interest to anyone concerned about the future of scientific research. The book is especially pertinent for professionals in statistics and related fields, including practicing and research clinicians, biomedical and social science researchers, business leaders, and policy-makers.

Willmore Energy and Willmore Conjecture (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

by Magdalena D. Toda

This book is the first monograph dedicated entirely to Willmore energy and Willmore surfaces as contemporary topics in differential geometry. While it focuses on Willmore energy and related conjectures, it also sits at the intersection between integrable systems, harmonic maps, Lie groups, calculus of variations, geometric analysis and applied differential geometry. Rather than reproducing published results, it presents new directions, developments and open problems. It addresses questions like: What is new in Willmore theory? Are there any new Willmore conjectures and open problems? What are the contemporary applications of Willmore surfaces? As well as mathematicians and physicists, this book is a useful tool for postdoctoral researchers and advanced graduate students working in this area.

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