The Real Analysis Lifesaver
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The Real Analysis Lifesaver
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Author : Raffi Grinberg
language : en
Publisher: Princeton University Press
Release Date : 2017-01-03
The Real Analysis Lifesaver written by Raffi Grinberg and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-03 with Mathematics categories.
The essential "lifesaver" that every student of real analysis needs Real analysis is difficult. For most students, in addition to learning new material about real numbers, topology, and sequences, they are also learning to read and write rigorous proofs for the first time. The Real Analysis Lifesaver is an innovative guide that helps students through their first real analysis course while giving them the solid foundation they need for further study in proof-based math. Rather than presenting polished proofs with no explanation of how they were devised, The Real Analysis Lifesaver takes a two-step approach, first showing students how to work backwards to solve the crux of the problem, then showing them how to write it up formally. It takes the time to provide plenty of examples as well as guided "fill in the blanks" exercises to solidify understanding. Newcomers to real analysis can feel like they are drowning in new symbols, concepts, and an entirely new way of thinking about math. Inspired by the popular Calculus Lifesaver, this book is refreshingly straightforward and full of clear explanations, pictures, and humor. It is the lifesaver that every drowning student needs. The essential “lifesaver” companion for any course in real analysis Clear, humorous, and easy-to-read style Teaches students not just what the proofs are, but how to do them—in more than 40 worked-out examples Every new definition is accompanied by examples and important clarifications Features more than 20 “fill in the blanks” exercises to help internalize proof techniques Tried and tested in the classroom
The Calculus Lifesaver
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Author : Adrian Banner
language : en
Publisher: Princeton University Press
Release Date : 2009-11-28
The Calculus Lifesaver written by Adrian Banner and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-28 with Mathematics categories.
For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it. All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory. The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus. Serves as a companion to any single-variable calculus textbook Informal, entertaining, and not intimidating Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures More than 475 examples (ranging from easy to hard) provide step-by-step reasoning Theorems and methods justified and connections made to actual practice Difficult topics such as improper integrals and infinite series covered in detail Tried and tested by students taking freshman calculus
Real Mathematical Analysis
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Author : Charles Chapman Pugh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19
Real Mathematical Analysis written by Charles Chapman Pugh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-19 with Mathematics categories.
Was plane geometry your favorite math course in high school? Did you like proving theorems? Are you sick of memorizing integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is pure mathematics, and I hope it appeals to you, the budding pure mathematician. Berkeley, California, USA CHARLES CHAPMAN PUGH Contents 1 Real Numbers 1 1 Preliminaries 1 2 Cuts . . . . . 10 3 Euclidean Space . 21 4 Cardinality . . . 28 5* Comparing Cardinalities 34 6* The Skeleton of Calculus 36 Exercises . . . . . . . . 40 2 A Taste of Topology 51 1 Metric Space Concepts 51 2 Compactness 76 3 Connectedness 82 4 Coverings . . . 88 5 Cantor Sets . . 95 6* Cantor Set Lore 99 7* Completion 108 Exercises . . . 115 x Contents 3 Functions of a Real Variable 139 1 Differentiation. . . . 139 2 Riemann Integration 154 Series . . 179 3 Exercises 186 4 Function Spaces 201 1 Uniform Convergence and CO[a, b] 201 2 Power Series . . . . . . . . . . . . 211 3 Compactness and Equicontinuity in CO . 213 4 Uniform Approximation in CO 217 Contractions and ODE's . . . . . . . . 228 5 6* Analytic Functions . . . . . . . . . . . 235 7* Nowhere Differentiable Continuous Functions . 240 8* Spaces of Unbounded Functions 248 Exercises . . . . . 251 267 5 Multivariable Calculus 1 Linear Algebra . . 267 2 Derivatives. . . . 271 3 Higher derivatives . 279 4 Smoothness Classes . 284 5 Implicit and Inverse Functions 286 290 6* The Rank Theorem 296 7* Lagrange Multipliers 8 Multiple Integrals . .
Understanding Real Analysis
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Author : Paul Zorn
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Understanding Real Analysis written by Paul Zorn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
Understanding Real Analysis, Second Edition offers substantial coverage of foundational material and expands on the ideas of elementary calculus to develop a better understanding of crucial mathematical ideas. The text meets students at their current level and helps them develop a foundation in real analysis. The author brings definitions, proofs, examples and other mathematical tools together to show how they work to create unified theory. These helps students grasp the linguistic conventions of mathematics early in the text. The text allows the instructor to pace the course for students of different mathematical backgrounds. Key Features: Meets and aligns with various student backgrounds Pays explicit attention to basic formalities and technical language Contains varied problems and exercises Drives the narrative through questions
Naked Statistics Stripping The Dread From The Data
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Author : Charles Wheelan
language : en
Publisher: W. W. Norton & Company
Release Date : 2013-01-07
Naked Statistics Stripping The Dread From The Data written by Charles Wheelan and has been published by W. W. Norton & Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-07 with Mathematics categories.
A New York Times bestseller "Brilliant, funny…the best math teacher you never had." —San Francisco Chronicle Once considered tedious, the field of statistics is rapidly evolving into a discipline Hal Varian, chief economist at Google, has actually called "sexy." From batting averages and political polls to game shows and medical research, the real-world application of statistics continues to grow by leaps and bounds. How can we catch schools that cheat on standardized tests? How does Netflix know which movies you’ll like? What is causing the rising incidence of autism? As best-selling author Charles Wheelan shows us in Naked Statistics, the right data and a few well-chosen statistical tools can help us answer these questions and more. For those who slept through Stats 101, this book is a lifesaver. Wheelan strips away the arcane and technical details and focuses on the underlying intuition that drives statistical analysis. He clarifies key concepts such as inference, correlation, and regression analysis, reveals how biased or careless parties can manipulate or misrepresent data, and shows us how brilliant and creative researchers are exploiting the valuable data from natural experiments to tackle thorny questions. And in Wheelan’s trademark style, there’s not a dull page in sight. You’ll encounter clever Schlitz Beer marketers leveraging basic probability, an International Sausage Festival illuminating the tenets of the central limit theorem, and a head-scratching choice from the famous game show Let’s Make a Deal—and you’ll come away with insights each time. With the wit, accessibility, and sheer fun that turned Naked Economics into a bestseller, Wheelan defies the odds yet again by bringing another essential, formerly unglamorous discipline to life.
Real Analysis
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Author : Elias M. Stein
language : en
Publisher: Princeton University Press
Release Date : 2009-11-28
Real Analysis written by Elias M. Stein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-28 with Mathematics categories.
Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. Also available, the first two volumes in the Princeton Lectures in Analysis:
Vaccine
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Author : Arthur Allen
language : en
Publisher: W. W. Norton
Release Date : 2008
Vaccine written by Arthur Allen and has been published by W. W. Norton this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Communicable diseases categories.
"A timely, fair-minded and crisply written account."--New York Times Book Review Vaccine juxtaposes the stories of brilliant scientists with the industry's struggle to produce safe, effective, and profitable vaccines. It focuses on the role of military and medical authority in the introduction of vaccines and looks at why some parents have resisted this authority. Political and social intrigue have often accompanied vaccination--from the divisive introduction of smallpox inoculation in colonial Boston to the 9,000 lawsuits recently filed by parents convinced that vaccines caused their children's autism. With narrative grace and investigative journalism, Arthur Allen reveals a history illuminated by hope and shrouded by controversy, and he sheds new light on changing notions of health, risk, and the common good. "Arthur Allen adroitly chronicles the development of the polio vaccine and many others, describing the science and serendipity behind each breakthrough and breathing life into the researchers who achieved them."--Henry I. Miller, Wall Street Journal "Allen's comprehensive, often unexpected and intelligently told history illuminates the complexity of ... public health policy."--Publishers Weekly
Quantitative Data Analysis In Education
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Author : Paul Connolly
language : en
Publisher: Routledge
Release Date : 2007-08-07
Quantitative Data Analysis In Education written by Paul Connolly and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-07 with Education categories.
An accessible and user-friendly guide to quantitative data analysis in educational research, aimed at those with little or no prior knowledge of statistical methods.
99 Variations On A Proof
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Author : Philip Ording
language : en
Publisher: Princeton University Press
Release Date : 2019-02-05
99 Variations On A Proof written by Philip Ording and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-05 with Mathematics categories.
An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.
Russia S Life Saver
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Author : Albert Loren Weeks
language : en
Publisher: Lexington Books
Release Date : 2004-01-01
Russia S Life Saver written by Albert Loren Weeks and has been published by Lexington Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with History categories.
Russia's Life-Saver brilliantly examines the diplomatic rationale for and results of the U.S. decision to grant over $12 billion in Lend-Lease aid to Soviet Russia during World War II. Author Albert L. Weeks wields many facts and statistics never before published in the U.S. Of particular interest is the statement by Soviet Army Marshal Georgy K. Zhukov that U.S. Lend-Lease aid was indispensable, despite Soviet propaganda that sought to minimize its importance.