The Mathematics Of Errors

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The Mathematics of Errors

Nicolas Bouleau
The Mathematics of Errors Book PDF

Author : Nicolas Bouleau
Publisher : Springer Nature
Page : 448 pages
File Size : 41,8 Mb
Release : 2022-03-27
Category : Mathematics
ISBN : 9783030885755

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The Mathematics of Errors by Nicolas Bouleau Pdf

The Mathematics of Errors presents an original, rigorous and systematic approach to the calculus of errors, targeted at both the engineer and the mathematician. Starting from Gauss's original point of view, the book begins as an introduction suitable for graduate students, leading to recent developments in stochastic analysis and Malliavin calculus, including contributions by the author. Later chapters, aimed at a more mature audience, require some familiarity with stochastic calculus and Dirichlet forms. Sensitivity analysis, in particular, plays an important role in the book. Detailed applications in a range of fields, such as engineering, robotics, statistics, financial mathematics, climate science, or quantum mechanics are discussed through concrete examples. Throughout the book, error analysis is presented in a progressive manner, motivated by examples and appealing to the reader’s intuition. By formalizing the intuitive concept of error and richly illustrating its scope for application, this book provides readers with a blueprint to apply advanced mathematics in practical settings. As such, it will be of immediate interest to engineers and scientists, whilst providing mathematicians with an original presentation. Nicolas Bouleau has directed the mathematics center of the Ecole des Ponts ParisTech for more than ten years. He is known for his theory of error propagation in complex models. After a degree in engineering and architecture, he decided to pursue a career in mathematics under the influence of Laurent Schwartz. He has also written on the production of knowledge, sustainable economics and mathematical models in finance. Nicolas Bouleau is a recipient of the Prix Montyon from the French Academy of Sciences.

Children's Errors in Mathematics

Alice Hansen,Doreen Drews,John Dudgeon,Fiona Lawton,Liz Surtees
Children s Errors in Mathematics Book PDF

Author : Alice Hansen,Doreen Drews,John Dudgeon,Fiona Lawton,Liz Surtees
Publisher : Learning Matters
Page : 321 pages
File Size : 40,9 Mb
Release : 2014-06-23
Category : Education
ISBN : 9781473905535

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Children's Errors in Mathematics by Alice Hansen,Doreen Drews,John Dudgeon,Fiona Lawton,Liz Surtees Pdf

This practical guide to children’s common errors and misconceptions in mathematics is a popular planning tool for primary trainees. It supports a deeper understanding of the difficulties encountered in mathematical development. This third edition has been updated to link to the new National Curriculum. New for this edition is a chapter on addressing errors misconceptions which explores how errors can best be identified and countered. The text examines misconceptions individually and in each case provides a description of the error alongside an explanation of why the error happens. The text also considers the role of the teacher in understanding and addressing children’s common mathematical misconceptions.

Children′s Errors in Mathematics

Alice Hansen,Doreen Drews,John Dudgeon,Fiona Lawton,Liz Surtees
Children s Errors in Mathematics Book PDF

Author : Alice Hansen,Doreen Drews,John Dudgeon,Fiona Lawton,Liz Surtees
Publisher : Learning Matters
Page : 345 pages
File Size : 53,5 Mb
Release : 2017-07-29
Category : Education
ISBN : 9781526422804

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Children′s Errors in Mathematics by Alice Hansen,Doreen Drews,John Dudgeon,Fiona Lawton,Liz Surtees Pdf

This practical and popular guide to children’s common errors and misconceptions in primary mathematics is an essential tool for teachers and trainees. It supports them in planning for and tackling potential errors and enhances their understanding of the difficulties encountered in mathematical development. This fourth edition explores how a Growth Mindset approach works alongside an awareness of children′s errors and how mistakes themselves are powerful learning tools. This edition includes 50 new identifiable misconceptions children have of mathematics. The text also considers the role of the teacher in understanding and addressing children’s common mathematical misconceptions. Key features: Linked to the new National Curriculum and covers every objective Provides an essential tool for planning primary mathematics lessons Explores how common misconceptions can be anticipated and addressed

Student Misconceptions and Errors in Physics and Mathematics

Teresa Neidorf,Alka Arora,Ebru Erberber,Yemurai Tsokodayi,Thanh Mai
Student Misconceptions and Errors in Physics and Mathematics Book PDF

Author : Teresa Neidorf,Alka Arora,Ebru Erberber,Yemurai Tsokodayi,Thanh Mai
Publisher : Springer Nature
Page : 173 pages
File Size : 50,5 Mb
Release : 2019-10-30
Category : Education
ISBN : 9783030301880

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Student Misconceptions and Errors in Physics and Mathematics by Teresa Neidorf,Alka Arora,Ebru Erberber,Yemurai Tsokodayi,Thanh Mai Pdf

This open access report explores the nature and extent of students’ misconceptions and misunderstandings related to core concepts in physics and mathematics and physics across grades four, eight and 12. Twenty years of data from the IEA’s Trends in International Mathematics and Science Study (TIMSS) and TIMSS Advanced assessments are analyzed, specifically for five countries (Italy, Norway, Russian Federation, Slovenia, and the United States) who participated in all or almost all TIMSS and TIMSS Advanced assessments between 1995 and 2015. The report focuses on students’ understandings related to gravitational force in physics and linear equations in mathematics. It identifies some specific misconceptions, errors, and misunderstandings demonstrated by the TIMSS Advanced grade 12 students for these core concepts, and shows how these can be traced back to poor foundational development of these concepts in earlier grades. Patterns in misconceptions and misunderstandings are reported by grade, country, and gender. In addition, specific misconceptions and misunderstandings are tracked over time, using trend items administered in multiple assessment cycles. The study and associated methodology may enable education systems to help identify specific needs in the curriculum, improve inform instruction across grades and also raise possibilities for future TIMSS assessment design and reporting that may provide more diagnostic outcomes.

Humble Pi

Matt Parker
Humble Pi Book PDF

Author : Matt Parker
Publisher : Penguin
Page : 338 pages
File Size : 46,5 Mb
Release : 2020-01-21
Category : Mathematics
ISBN : 9780593084700

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Humble Pi by Matt Parker Pdf

#1 INTERNATIONAL BESTSELLER AN ADAM SAVAGE BOOK CLUB PICK The book-length answer to anyone who ever put their hand up in math class and asked, “When am I ever going to use this in the real world?” “Fun, informative, and relentlessly entertaining, Humble Pi is a charming and very readable guide to some of humanity's all-time greatest miscalculations—that also gives you permission to feel a little better about some of your own mistakes.” —Ryan North, author of How to Invent Everything Our whole world is built on math, from the code running a website to the equations enabling the design of skyscrapers and bridges. Most of the time this math works quietly behind the scenes . . . until it doesn’t. All sorts of seemingly innocuous mathematical mistakes can have significant consequences. Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean. Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun.

Error Analysis in Numerical Processes

Solomon Grigorʹevich Mikhlin
Error Analysis in Numerical Processes Book PDF

Author : Solomon Grigorʹevich Mikhlin
Publisher : Unknown
Page : 292 pages
File Size : 54,8 Mb
Release : 1991-09-27
Category : Mathematics
ISBN : UOM:39015024770367

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Error Analysis in Numerical Processes by Solomon Grigorʹevich Mikhlin Pdf

Very Good,No Highlights or Markup,all pages are intact.

Magnificent Mistakes in Mathematics

Alfred S. Posamentier,Ingmar Lehmann
Magnificent Mistakes in Mathematics Book PDF

Author : Alfred S. Posamentier,Ingmar Lehmann
Publisher : Prometheus Books
Page : 298 pages
File Size : 52,8 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9781616147488

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Magnificent Mistakes in Mathematics by Alfred S. Posamentier,Ingmar Lehmann Pdf

Two veteran math educators demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts. In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced using large wooden numerals to decorate the cupola of a hall in the Palais de la Découverte in Paris. However, in 1946, with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the 528th decimal place. Today, supercomputers have determined the value of pi to trillions of decimal places. This is just one of the amusing and intriguing stories about mistakes in mathematics in this layperson's guide to mathematical principles. In another example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even known to Euclid - that of "betweenness." And if we disregard the time-honored Pythagorean theorem, this is a misuse of the concept of infinity. Even using correct procedures can sometimes lead to absurd - but enlightening - results. Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science.

Error Correcting Codes

D J. Baylis
Error Correcting Codes Book PDF

Author : D J. Baylis
Publisher : Routledge
Page : 113 pages
File Size : 52,7 Mb
Release : 2018-05-11
Category : Mathematics
ISBN : 9781351449830

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Error Correcting Codes by D J. Baylis Pdf

Assuming little previous mathematical knowledge, Error Correcting Codes provides a sound introduction to key areas of the subject. Topics have been chosen for their importance and practical significance, which Baylis demonstrates in a rigorous but gentle mathematical style.Coverage includes optimal codes; linear and non-linear codes; general techniques of decoding errors and erasures; error detection; syndrome decoding, and much more. Error Correcting Codes contains not only straight maths, but also exercises on more investigational problem solving. Chapters on number theory and polynomial algebra are included to support linear codes and cyclic codes, and an extensive reminder of relevant topics in linear algebra is given. Exercises are placed within the main body of the text to encourage active participation by the reader, with comprehensive solutions provided.Error Correcting Codes will appeal to undergraduate students in pure and applied mathematical fields, software engineering, communications engineering, computer science and information technology, and to organizations with substantial research and development in those areas.

Children'S Mathematics 4-15: Learning From Errors And Misconceptions

Ryan, Julie,Williams, Julian
Children S Mathematics 4 15 Learning From Errors And Misconceptions Book PDF

Author : Ryan, Julie,Williams, Julian
Publisher : McGraw-Hill Education (UK)
Page : 262 pages
File Size : 40,7 Mb
Release : 2007-04-01
Category : Education
ISBN : 9780335220427

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Children'S Mathematics 4-15: Learning From Errors And Misconceptions by Ryan, Julie,Williams, Julian Pdf

This work uses data from the authors' own research on children's performance, errors and misconceptions across the mathematics curriculum. It develops concepts for teachers to use in organising their understanding and knowledge of children's mathematics, and concludes with theoretical accounts of learning and teaching.

Deterministic and Stochastic Error Bounds in Numerical Analysis

Erich Novak
Deterministic and Stochastic Error Bounds in Numerical Analysis Book PDF

Author : Erich Novak
Publisher : Springer
Page : 118 pages
File Size : 51,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540459873

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Deterministic and Stochastic Error Bounds in Numerical Analysis by Erich Novak Pdf

In these notes different deterministic and stochastic error bounds of numerical analysis are investigated. For many computational problems we have only partial information (such as n function values) and consequently they can only be solved with uncertainty in the answer. Optimal methods and optimal error bounds are sought if only the type of information is indicated. First, worst case error bounds and their relation to the theory of n-widths are considered; special problems such approximation, optimization, and integration for different function classes are studied and adaptive and nonadaptive methods are compared. Deterministic (worst case) error bounds are often unrealistic and should be complemented by different average error bounds. The error of Monte Carlo methods and the average error of deterministic methods are discussed as are the conceptual difficulties of different average errors. An appendix deals with the existence and uniqueness of optimal methods. This book is an introduction to the area and also a research monograph containing new results. It is addressd to a general mathematical audience as well as specialists in the areas of numerical analysis and approximation theory (especially optimal recovery and information-based complexity).

The Error of Truth

Steven J. Osterlind
The Error of Truth Book PDF

Author : Steven J. Osterlind
Publisher : Oxford University Press
Page : 352 pages
File Size : 45,9 Mb
Release : 2019-01-24
Category : Science
ISBN : 9780192567390

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The Error of Truth by Steven J. Osterlind Pdf

Quantitative thinking is our inclination to view natural and everyday phenomena through a lens of measurable events, with forecasts, odds, predictions, and likelihood playing a dominant part. The Error of Truth recounts the astonishing and unexpected tale of how quantitative thinking came to be, and its rise to primacy in the nineteenth and early twentieth centuries. Additionally, it considers how seeing the world through a quantitative lens has shaped our perception of the world we live in, and explores the lives of the individuals behind its early establishment. This worldview was unlike anything humankind had before, and it came about because of a momentous human achievement: we had learned how to measure uncertainty. Probability as a science was conceptualised. As a result of probability theory, we now had correlations, reliable predictions, regressions, the bellshaped curve for studying social phenomena, and the psychometrics of educational testing. Significantly, these developments happened during a relatively short period in world history— roughly, the 130-year period from 1790 to 1920, from about the close of the Napoleonic era, through the Enlightenment and the Industrial Revolutions, to the end of World War I. At which time, transportation had advanced rapidly, due to the invention of the steam engine, and literacy rates had increased exponentially. This brief period in time was ready for fresh intellectual activity, and it gave a kind of impetus for the probability inventions. Quantification is now everywhere in our daily lives, such as in the ubiquitous microchip in smartphones, cars, and appliances; in the Bayesian logic of artificial intelligence, as well as applications in business, engineering, medicine, economics, and elsewhere. Probability is the foundation of quantitative thinking. The Error of Truth tells its story— when, why, and how it happened.

An Introduction to Error Analysis

John Robert Taylor
An Introduction to Error Analysis Book PDF

Author : John Robert Taylor
Publisher : Univ Science Books
Page : 327 pages
File Size : 41,9 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 0935702423

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An Introduction to Error Analysis by John Robert Taylor Pdf

Problems after each chapter

Propagation of Errors

Mike Peralta
Propagation of Errors Book PDF

Author : Mike Peralta
Publisher : CreateSpace
Page : 198 pages
File Size : 43,9 Mb
Release : 2012-01-30
Category : Mathematics
ISBN : 1469985861

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Propagation of Errors by Mike Peralta Pdf

“The Best Propagation-of-Errors Book Out There” Great care was taken to fully derive what the technique of Propagation of Errors (POE) Analysis is based on. I would have loved to have this book as both an undergrad and grad student. (And as a professional scientist and engineer as well). And now this is finally available. As a student I was required to use (first order linear) POE to analyze measurement errors in my physical experiments. However it was never derived or explained. This book now derives the POE analysis. Not just to first order linear but also the correlated and second order case as well. With this POE book we now have “The Grand Slam” of POE books. In this second edition, exercises are now included so the book can be used in a class or lab setting. What is Propagation of Errors? Experimental measurements always have some degree of error. If these measurements are used to calculate other results, through mathematical expressions, these errors will propagate through to these other results. As you will see in this book, the usual POE expression is first order and is linear in the parameters. Most of the time, the first order linear POE is all that is needed. However, sometimes the second order treatment is necessary. First order linear POE can be found in many fine books, but second order is rarely treated, and so that may be the highlight of this book for those who wish to really understand propagation-of-errors. Notes about the Second Edition: • Chapter 2 has been split into Chapters 2, 3, and 4. • Chapter 3 was added to focus on Propagation of Errors when some or all of the random variables are correlated. This will be found to be very influential in many cases – especially when measuring procedures take advantage of tracking or matched resistors for example. • Chapter 4 was added to include and expand on the Second Order Propagation of Errors Case. • Exercises were added to Chapters 2, 3, and 4. This will now encourage this material to be used as a textbook.

Error Patterns in Computation

Robert B. Ashlock
Error Patterns in Computation Book PDF

Author : Robert B. Ashlock
Publisher : Unknown
Page : 256 pages
File Size : 53,5 Mb
Release : 1990
Category : Arithmetic
ISBN : CORNELL:31924052333204

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Error Patterns in Computation by Robert B. Ashlock Pdf

As your students learn about mathematical operations and methods of computation, they may adopt erroneous procedures and misconceptions, despite your best efforts. This engaging book was written to model how you, the teacher, can make thoughtful analyses of your student's work, and in doing so, discover patterns in the errors they make. The text considers reasons why students may have learned erroneous procedures and presents strategies for helping those students. You will come away from the reading with a clear vision of how you can use student error patterns to gain more specific knowledge of their strengths on which to base your future instruction. Book jacket.

The End of Error

John L. Gustafson
The End of Error Book PDF

Author : John L. Gustafson
Publisher : CRC Press
Page : 536 pages
File Size : 54,5 Mb
Release : 2017-06-26
Category : Computers
ISBN : 9781351665605

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The End of Error by John L. Gustafson Pdf

The Future of Numerical Computing Written by one of the foremost experts in high-performance computing and the inventor of Gustafson’s Law, The End of Error: Unum Computing explains a new approach to computer arithmetic: the universal number (unum). The unum encompasses all IEEE floating-point formats as well as fixed-point and exact integer arithmetic. This new number type obtains more accurate answers than floating-point arithmetic yet uses fewer bits in many cases, saving memory, bandwidth, energy, and power. A Complete Revamp of Computer Arithmetic from the Ground Up Richly illustrated in color, this groundbreaking book represents a fundamental change in how to perform calculations automatically. It illustrates how this novel approach can solve problems that have vexed engineers and scientists for decades, including problems that have been historically limited to serial processing. Suitable for Anyone Using Computers for Calculations The book is accessible to anyone who uses computers for technical calculations, with much of the book only requiring high school math. The author makes the mathematics interesting through numerous analogies. He clearly defines jargon and uses color-coded boxes for mathematical formulas, computer code, important descriptions, and exercises.