How to Solve It

A New Aspect of Mathematical Method

Author: G. Polya,John H. Conway

Publisher: Princeton University Press

ISBN: 069111966X

Category: Mathematics

Page: 253

View: 599

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Outlines a method of solving mathematical problems for teachers and students based upon the four steps of understanding the problem, devising a plan, carrying out the plan, and checking the results.

The Stanford Mathematics Problem Book

With Hints and Solutions

Author: George Polya,Jeremy Kilpatrick

Publisher: Courier Corporation

ISBN: 048631832X

Category: Mathematics

Page: 80

View: 8113

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Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.

Proofs from THE BOOK

Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer

ISBN: 3662442051

Category: Mathematics

Page: 308

View: 4641

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This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questio ns so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011.

Proofs and Refutations

The Logic of Mathematical Discovery

Author: Imre Lakatos

Publisher: Cambridge University Press

ISBN: 1316425339

Category: Science

Page: N.A

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Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.

Problem-Solving Strategies

Author: Arthur Engel

Publisher: Springer Science & Business Media

ISBN: 0387226419

Category: Mathematics

Page: 403

View: 1014

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A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.

Problem Solving Through Recreational Mathematics

Author: Bonnie Averbach,Orin Chein

Publisher: Courier Corporation

ISBN: 0486131742

Category: Mathematics

Page: 480

View: 9097

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Fascinating approach to mathematical teaching stresses use of recreational problems, puzzles, and games to teach critical thinking. Logic, number and graph theory, games of strategy, much more. Includes answers to selected problems. Free solutions manual available for download at the Dover website.

Journey into Mathematics

An Introduction to Proofs

Author: Joseph J. Rotman

Publisher: Courier Corporation

ISBN: 0486151689

Category: Mathematics

Page: 256

View: 9651

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This treatment covers the mechanics of writing proofs, the area and circumference of circles, and complex numbers and their application to real numbers. 1998 edition.

Makers of Mathematics

Author: Stuart Hollingdale

Publisher: Courier Corporation

ISBN: 0486174506

Category: Mathematics

Page: 464

View: 6126

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Each chapter of this accessible portrait of the evolution of mathematics examines the work of an individual — Archimedes, Descartes, Newton, Einstein, others — to explore the mathematics of his era. 1989 edition.

Sync

How Order Emerges from Chaos In the Universe, Nature, and Daily Life

Author: Steven H. Strogatz

Publisher: Hachette Books

ISBN: 140130446X

Category: Science

Page: 352

View: 2382

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At the heart of the universe is a steady, insistent beat, the sound of cycles in sync. Along the tidal rivers of Malaysia, thousands of fireflies congregate and flash in unison; the moon spins in perfect resonance with its orbit around the earth; our hearts depend on the synchronous firing of ten thousand pacemaker cells. While the forces that synchronize the flashing of fireflies may seem to have nothing to do with our heart cells, there is in fact a deep connection. Synchrony is a science in its infancy, and Strogatz is a pioneer in this new frontier in which mathematicians and physicists attempt to pinpoint just how spontaneous order emerges from chaos. From underground caves in Texas where a French scientist spent six months alone tracking his sleep-wake cycle, to the home of a Dutch physicist who in 1665 discovered two of his pendulum clocks swinging in perfect time, this fascinating book spans disciplines, continents, and centuries. Engagingly written for readers of books such as Chaos and The Elegant Universe, Sync is a tour-de-force of nonfiction writing.

Recreations in the Theory of Numbers

The Queen of Mathematics Entertains

Author: Albert H. Beiler

Publisher: Courier Corporation

ISBN: 0486210960

Category: Games

Page: 349

View: 8788

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Number theory proves to be a virtually inexhaustible source of intriguing puzzle problems. Includes divisors, perfect numbers, the congruences of Gauss, scales of notation, the Pell equation, more. Solutions to all problems.

It Didn't Start with You

How Inherited Family Trauma Shapes Who We Are and How to End the Cycle

Author: Mark Wolynn

Publisher: Penguin

ISBN: 1101980370

Category: Psychology

Page: 256

View: 5366

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A groundbreaking approach to transforming traumatic legacies passed down in families over generations, by an acclaimed expert in the field Depression. Anxiety. Chronic Pain. Phobias. Obsessive thoughts. The evidence is compelling: the roots of these difficulties may not reside in our immediate life experience or in chemical imbalances in our brains—but in the lives of our parents, grandparents, and even great-grandparents. The latest scientific research, now making headlines, supports what many have long intuited—that traumatic experience can be passed down through generations. It Didn’t Start with You builds on the work of leading experts in post-traumatic stress, including Mount Sinai School of Medicine neuroscientist Rachel Yehuda and psychiatrist Bessel van der Kolk, author of The Body Keeps the Score. Even if the person who suffered the original trauma has died, or the story has been forgotten or silenced, memory and feelings can live on. These emotional legacies are often hidden, encoded in everything from gene expression to everyday language, and they play a far greater role in our emotional and physical health than has ever before been understood. As a pioneer in the field of inherited family trauma, Mark Wolynn has worked with individuals and groups on a therapeutic level for over twenty years. It Didn’t Start with You offers a pragmatic and prescriptive guide to his method, the Core Language Approach. Diagnostic self-inventories provide a way to uncover the fears and anxieties conveyed through everyday words, behaviors, and physical symptoms. Techniques for developing a genogram or extended family tree create a map of experiences going back through the generations. And visualization, active imagination, and direct dialogue create pathways to reconnection, integration, and reclaiming life and health. It Didn’t Start With You is a transformative approach to resolving longstanding difficulties that in many cases, traditional therapy, drugs, or other interventions have not had the capacity to touch. From the Hardcover edition.

Randomness

Author: Deborah J. Bennett

Publisher: Harvard University Press

ISBN: 9780674020771

Category: Mathematics

Page: 256

View: 7367

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From the ancients' first readings of the innards of birds to your neighbor's last bout with the state lottery, humankind has put itself into the hands of chance. Today life itself may be at stake when probability comes into play--in the chance of a false negative in a medical test, in the reliability of DNA findings as legal evidence, or in the likelihood of passing on a deadly congenital disease--yet as few people as ever understand the odds. This book is aimed at the trouble with trying to learn about probability. A story of the misconceptions and difficulties civilization overcame in progressing toward probabilistic thinking, "Randomness" is also a skillful account of what makes the science of probability so daunting in our own day. To acquire a (correct) intuition of chance is not easy to begin with, and moving from an intuitive sense to a formal notion of probability presents further problems. Author Deborah Bennett traces the path this process takes in an individual trying to come to grips with concepts of uncertainty and fairness, and also charts the parallel path by which societies have developed ideas about chance. Why, from ancient to modern times, have people resorted to chance in making decisions? Is a decision made by random choice "fair"? What role has gambling played in our understanding of chance? Why do some individuals and societies refuse to accept randomness at all? If understanding randomness is so important to probabilistic thinking, why do the experts disagree about what it really is? And why are our intuitions about chance almost always dead wrong? Anyone who has puzzled over a probability conundrum is struck by the paradoxes and counterintuitive results that occur at a relatively simple level. Why this should be, and how it has been the case through the ages, for bumblers and brilliant mathematicians alike, is the entertaining and enlightening lesson of "Randomness."

Weapons of Math Destruction

How Big Data Increases Inequality and Threatens Democracy

Author: Cathy O'Neil

Publisher: Crown Books

ISBN: 0553418815

Category: Big data

Page: 259

View: 6398

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"A former Wall Street quantitative analyst sounds an alarm on mathematical modeling, a pervasive new force in society that threatens to undermine democracy and widen inequality, "--NoveList.

The Unimaginable Mathematics of Borges' Library of Babel

Author: William Goldbloom Bloch

Publisher: Oxford University Press

ISBN: 9780199715169

Category: Mathematics

Page: 224

View: 5944

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"The Library of Babel" is arguably Jorge Luis Borges' best known story--memorialized along with Borges on an Argentine postage stamp. Now, in The Unimaginable Mathematics of Borges' Library of Babel, William Goldbloom Bloch takes readers on a fascinating tour of the mathematical ideas hidden within one of the classic works of modern literature. Written in the vein of Douglas R. Hofstadter's Pulitzer Prize-winning G?del, Escher, Bach, this original and imaginative book sheds light on one of Borges' most complex, richly layered works. Bloch begins each chapter with a mathematical idea--combinatorics, topology, geometry, information theory--followed by examples and illustrations that put flesh on the theoretical bones. In this way, he provides many fascinating insights into Borges' Library. He explains, for instance, a straightforward way to calculate how many books are in the Library--an easily notated but literally unimaginable number--and also shows that, if each book were the size of a grain of sand, the entire universe could only hold a fraction of the books in the Library. Indeed, if each book were the size of a proton, our universe would still not be big enough to hold anywhere near all the books. Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature but also exposes the reader--including those more inclined to the literary world--to many intriguing and entrancing mathematical ideas.

Algorithmic Graph Theory

Author: Alan Gibbons

Publisher: Cambridge University Press

ISBN: 9780521288811

Category: Computers

Page: 259

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An introduction to pure and applied graph theory with an emphasis on algorithms and their complexity.

On Being

A scientist's exploration of the great questions of existence

Author: Peter Atkins

Publisher: OUP Oxford

ISBN: 0191615870

Category: Science

Page: 128

View: 4000

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In this scientific 'Credo', Peter Atkins considers the universal questions of origins, endings, birth, and death to which religions have claimed answers. With his usual economy, wit, and elegance, unswerving before awkward realities, Atkins presents what science has to say. While acknowledging the comfort some find in belief, he declares his own faith in science's capacity to reveal the deepest truths.

Keys to Good Cooking

A Guide to Making the Best of Foods and Recipes

Author: Harold McGee

Publisher: Appetite by Random House

ISBN: 0449015998

Category: Cooking

Page: 576

View: 3028

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A requisite countertop companion for all home chefs, Keys to Good Cooking distils the modern scientific understanding of cooking and translates it into immediately useful information. The book provides simple statements of fact and advice, along with brief explanations that help cooks understand why, and apply that understanding to other situations. Not a cookbook, Keys to Good Cooking is, simply put, a book about how to cook well. A work of astounding scholarship and originality, this is a concise and authoritative guide designed to help home cooks navigate the ever-expanding universe of recipes and ingredients and appliances, and arrive at the promised land of a satisfying dish.

The Great Unknown

Seven Journeys to the Frontiers of Science

Author: Marcus du Sautoy

Publisher: Penguin

ISBN: 0735221812

Category: Science

Page: 464

View: 5128

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“An engaging voyage into some of the great mysteries and wonders of our world." --Alan Lightman, author of Einstein’s Dream and The Accidental Universe “No one is better at making the recondite accessible and exciting.” —Bill Bryson Brain Pickings and Kirkus Best Science Book of the Year Every week seems to throw up a new discovery, shaking the foundations of what we know. But are there questions we will never be able to answer—mysteries that lie beyond the predictive powers of science? In this captivating exploration of our most tantalizing unknowns, Marcus du Sautoy invites us to consider the problems in cosmology, quantum physics, mathematics, and neuroscience that continue to bedevil scientists and creative thinkers who are at the forefront of their fields. At once exhilarating, mind-bending, and compulsively readable, The Great Unknown challenges us to consider big questions—about the nature of consciousness, what came before the big bang, and what lies beyond our horizons—while taking us on a virtuoso tour of the great breakthroughs of the past and celebrating the men and women who dared to tackle the seemingly impossible and had the imagination to come up with new ways of seeing the world.