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Author: Avner Ash
Publisher: Princeton University Press
ISBN: 0691178518
Category : Mathematics
Languages : en
Pages : 248
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Book Description
The power and properties of numbers, from basic addition and sums of squares to cutting-edge theory We use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series—long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms—the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem. Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers.
Author: Avner Ash
Publisher: Princeton University Press
ISBN: 0691178518
Category : Mathematics
Languages : en
Pages : 248
Get Book Here
Book Description
The power and properties of numbers, from basic addition and sums of squares to cutting-edge theory We use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series—long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms—the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem. Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers.
Author: Robert Eaker
Publisher: Solution Tree
ISBN: 9781949539738
Category : Education
Languages : en
Pages : 256
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Book Description
"In A Summing Up: Teaching and Learning in Effective Schools and PLCs at Work author Robert Eaker tells the story of his career in education and, through this story, provides a contextual guide to the PLC at Work framework that is both insightful and full of real-world advice. After a career that has spanned almost half a century, Dr. Eaker has gathered all of his insights and knowledge regarding the improvement of schools, teaching, and student learning into this autobiographical work. Readers will learn about the lives of those who developed the PLC at Work framework, the events that led to its development, and the founders' experiences creating and implementing the system. Consequently, readers will gain in-depth, contextual knowledge of the theories and concepts of the PLC at Work system, as well as advice and strategies on how the framework should be implemented. Through this book, readers will learn directly from the masters as they develop their knowledge and skills within the PLC at Work system"--
Author: Richard J. LIGHT
Publisher: Harvard University Press
ISBN: 0674040244
Category : Education
Languages : en
Pages : 208
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Book Description
How can a scientist or policy analyst summarize and evaluate what is already known about a particular topic? This book offers practical guidance. The amount and diversity of information generated by academic and policy researchers in the contemporary world is staggering. How is an investigator to cope with the tens or even hundreds of studies on a particular problem? How can conflicting findings be reconciled? Richard Light and David Pillemer have developed both general guidelines and step-by-step procedures that can be used to synthesize existing data. They show how to apply quantitative methods, including the newest statistical procedures and simple graphical displays, to evaluate a mass of studies and combine separate data sets. At the same time, they insist on the value of qualitative information, of asking the right questions, and of considering the context in which research is conducted. The authors use exemplary reviews in education, psychology, health, and the policy sciences to illustrate their suggestions. Written in nontechnical language and addressed to the beginning researcher as well as to the practicing professional, Summing Up will set a new standard for valid research reviews and is likely to become a methodological classic.
Author: W. Somerset Maugham
Publisher: DigiCat
ISBN:
Category : Fiction
Languages : en
Pages : 210
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Book Description
DigiCat Publishing presents to you this special edition of "The Summing Up" by W. Somerset Maugham. DigiCat Publishing considers every written word to be a legacy of humankind. Every DigiCat book has been carefully reproduced for republishing in a new modern format. The books are available in print, as well as ebooks. DigiCat hopes you will treat this work with the acknowledgment and passion it deserves as a classic of world literature.
Author: Irving Singer
Publisher: MIT Press
ISBN: 0262261162
Category : Philosophy
Languages : en
Pages : 145
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Book Description
The author of the classic philosophical treatment of love reflects on the trajectory, over decades, of his thoughts on love and other topics. In 1984, Irving Singer published the first volume of what would become a classic and much acclaimed trilogy on love. Trained as an analytical philosopher, Singer first approached his subject with the tools of current philosophical methodology. Dissatisfied by the initial results (finding the chapters he had written “just dreary and unproductive of anything”), he turned to the history of ideas in philosophy and the arts for inspiration. He discovered an immensity of speculation and artistic practice that reached wholly beyond the parameters he had been trained to consider truly philosophical. In his three-volume work The Nature of Love, Singer tried to make sense of this historical progression within a framework that reflected his precise distinction-making and analytical background. In this new book, he maps the trajectory of his thinking on love. It is a “partial” summing-up of a lifework: partial because it expresses the author's still unfolding views, because it is a recapitulation of many published pages, because love—like any subject of that magnitude—resists a neatly comprehensive, all-inclusive formulation. Adopting an informal, even conversational, tone, Singer discusses, among other topics, the history of romantic love, the Platonic ideal, courtly and nineteenth-century Romantic love; the nature of passion; the concept of merging (and his critique of it); ideas about love in Freud, Schopenhauer, Nietzsche, Dewey, Santayana, Sartre, and other writers; and love in relation to democracy, existentialism, creativity, and the possible future of scientific investigation. Singer's writing on love embodies what he has learned as a contemporary philosopher, studying other authors in the field and “trying to get a little further.” This book continues his trailblazing explorations.
Author: Heather McGhee
Publisher: One World
ISBN: 0525509585
Category : Social Science
Languages : en
Pages : 465
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Book Description
NEW YORK TIMES BESTSELLER • LONGLISTED FOR THE NATIONAL BOOK AWARD • One of today’s most insightful and influential thinkers offers a powerful exploration of inequality and the lesson that generations of Americans have failed to learn: Racism has a cost for everyone—not just for people of color. WINNER OF THE PORCHLIGHT BUSINESS BOOK AWARD • ONE OF THE BEST BOOKS OF THE YEAR: Time, The Washington Post, St. Louis Post-Dispatch, Ms. magazine, BookRiot, Library Journal “This is the book I’ve been waiting for.”—Ibram X. Kendi, #1 New York Times bestselling author of How to Be an Antiracist Look for the author’s podcast, The Sum of Us, based on this book! Heather McGhee’s specialty is the American economy—and the mystery of why it so often fails the American public. From the financial crisis of 2008 to rising student debt to collapsing public infrastructure, she found a root problem: racism in our politics and policymaking. But not just in the most obvious indignities for people of color. Racism has costs for white people, too. It is the common denominator of our most vexing public problems, the core dysfunction of our democracy and constitutive of the spiritual and moral crises that grip us all. But how did this happen? And is there a way out? McGhee embarks on a deeply personal journey across the country from Maine to Mississippi to California, tallying what we lose when we buy into the zero-sum paradigm—the idea that progress for some of us must come at the expense of others. Along the way, she meets white people who confide in her about losing their homes, their dreams, and their shot at better jobs to the toxic mix of American racism and greed. This is the story of how public goods in this country—from parks and pools to functioning schools—have become private luxuries; of how unions collapsed, wages stagnated, and inequality increased; and of how this country, unique among the world’s advanced economies, has thwarted universal healthcare. But in unlikely places of worship and work, McGhee finds proof of what she calls the Solidarity Dividend: the benefits we gain when people come together across race to accomplish what we simply can’t do on our own. The Sum of Us is not only a brilliant analysis of how we arrived here but also a heartfelt message, delivered with startling empathy, from a black woman to a multiracial America. It leaves us with a new vision for a future in which we finally realize that life can be more than a zero-sum game. LONGLISTED FOR THE ANDREW CARNEGIE MEDAL
Author: Pat Head Summitt
Publisher: Crown
ISBN: 0385347057
Category : Biography & Autobiography
Languages : en
Pages : 434
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Book Description
Pat Summitt, the all-time winningest coach in NCAA basketball history and bestselling author of Reach for the Summitt and Raise The Roof, tells for the first time her remarkable story of victory and resilience as well as facing down her greatest challenge: early-onset Alzheimer's disease. Pat Summitt was only 21 when she became head coach of the Tennessee Vols women's basketball team. For 38 years, she broke records, winning more games than any NCAA team in basketball history. She coached an undefeated season, co-captained the first women's Olympic team, was inducted into the Basketball Hall of Fame, and was named Sports Illustrated 'Sportswoman of the Year'. She owed her coaching success to her personal struggles and triumphs. She learned to be tough from her strict, demanding father. Motherhood taught her to balance that rigidity with communication and kindness. She was a role model for the many women she coached; 74 of her players have become coaches. Pat's life took a shocking turn in 2011, when she was diagnosed with early-onset Alzheimer's disease, an irreversible brain condition that affects 5 million Americans. Despite her devastating diagnosis, she led the Vols to win their sixteenth SEC championship in March 2012. Pat continued to be a fighter, facing this new challenge the way she's faced every other--with hard work, perseverance, and a sense of humor.
Author: Yitzhak Shamir
Publisher:
ISBN: 9780788157363
Category :
Languages : en
Pages : 276
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Book Description
0-7881-5736-1 Yitzhak Shamir, former Prime Minister of Israel, tells the story of his life, from the years of deep cover in the underground that fought for Jewish independence in the Palestine of the 1940s to the decade he spent in the shadows of the Mossad, Israel1s intelligence service, and to his emergence as the leader of Israel1s complex and precarious foreign and domestic involvements. Discloses his own view of the peace process and U.S.-Israeli relations. Also provides insights into such personalities as Menachem Begin, Anwar Sadat, Reagan, Bush and John Major and into Israel1s right wing, its origins, its philosophies and its political heroes. Photos.
Author: Avner Ash
Publisher: Princeton University Press
ISBN: 0691138710
Category : Mathematics
Languages : en
Pages : 308
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Book Description
Written in a friendly style for a general mathematically literate audience, 'Fearless Symmetry', starts with the basic properties of integers and permutations and reaches current research in number theory.
Author: Arthur Koestler
Publisher: Last Century Media
ISBN: 9781939438959
Category :
Languages : en
Pages : 368
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Book Description
The most adventourous, polymathic - and readable - scientific populariser of the age offers in Janus a summing up of a quarter of a century's study and speculations on the life sciences and their philosophic implications. Koestler has an interesting theme to propose. It is this; the human brain has developed a terrible biological flaw, such that it is working now against the survival of the race. Something has "snapped" inside the brain. It is no longer necessarily a function which will lead us to a better world, but something demonic, possessed, perhaps even evil. The anguished humanity of Koestler's concepts and the lucid energy of his style comman respect. Here is one of the major political "experiencers" an dmost widely informed spirits of the age turning to the crux of human survival on a ravaged planet. The title of the book tells not only of a central allegory of division in the human species. It stands for the rare tension on Koestler's discourses: between desolation and zest, between darkness and noon.
