Download or read book Magnificent Mistakes in Mathematics written by Alfred S. Posamentier and published by Prometheus Books. This book was released on 2013-08-13 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Mathematics of Errors written by Nicolas Bouleau and published by Springer Nature. This book was released on 2022-03-27 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Humble Pi written by Matt Parker and published by Penguin. This book was released on 2021-01-19 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: #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.

Download or read book Student Misconceptions and Errors in Physics and Mathematics written by Teresa Neidorf and published by Springer Nature. This book was released on 2019-10-30 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Children s Errors in Mathematics written by Alice Hansen and published by Learning Matters. This book was released on 2014-06-23 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Error Correction Coding written by Todd K. Moon and published by John Wiley & Sons. This book was released on 2005-06-06 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: An unparalleled learning tool and guide to error correction coding Error correction coding techniques allow the detection and correction of errors occurring during the transmission of data in digital communication systems. These techniques are nearly universally employed in modern communication systems, and are thus an important component of the modern information economy. Error Correction Coding: Mathematical Methods and Algorithms provides a comprehensive introduction to both the theoretical and practical aspects of error correction coding, with a presentation suitable for a wide variety of audiences, including graduate students in electrical engineering, mathematics, or computer science. The pedagogy is arranged so that the mathematical concepts are presented incrementally, followed immediately by applications to coding. A large number of exercises expand and deepen students' understanding. A unique feature of the book is a set of programming laboratories, supplemented with over 250 programs and functions on an associated Web site, which provides hands-on experience and a better understanding of the material. These laboratories lead students through the implementation and evaluation of Hamming codes, CRC codes, BCH and R-S codes, convolutional codes, turbo codes, and LDPC codes. This text offers both "classical" coding theory-such as Hamming, BCH, Reed-Solomon, Reed-Muller, and convolutional codes-as well as modern codes and decoding methods, including turbo codes, LDPC codes, repeat-accumulate codes, space time codes, factor graphs, soft-decision decoding, Guruswami-Sudan decoding, EXIT charts, and iterative decoding. Theoretical complements on performance and bounds are presented. Coding is also put into its communications and information theoretic context and connections are drawn to public key cryptosystems. Ideal as a classroom resource and a professional reference, this thorough guide will benefit electrical and computer engineers, mathematicians, students, researchers, and scientists.

Download or read book The Error of Truth written by Steven J. Osterlind and published by Oxford University Press. This book was released on 2019-01-24 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Error Correcting Codes written by D J. Baylis and published by Routledge. This book was released on 2018-05-11 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Rounding Errors in Algebraic Processes written by James Hardy Wilkinson and published by Courier Corporation. This book was released on 1994-01-01 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary introduction to problem of cumulative effect of rounding errors in a very large number of arithmetical calculations—particularly applicable to computer operations. Simple representative analyses illustrate techniques. Topics include fundamental arithmetic operations, computations involving polynomials and matrix computations. Results deal exclusively with digital computers but are equally applicable to desk calculators. Bibliography.

Download or read book An Introduction to Error Analysis written by John Robert Taylor and published by Univ Science Books. This book was released on 1997-01-01 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems after each chapter

Download or read book The End of Error written by John L. Gustafson and published by CRC Press. This book was released on 2017-06-26 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Children S Mathematics 4 15 Learning From Errors And Misconceptions written by Ryan, Julie and published by McGraw-Hill Education (UK). This book was released on 2007-04-01 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Integral and Discrete Transforms with Applications and Error Analysis written by Abdul Jerri and published by CRC Press. This book was released on 2021-11-19 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines.

Download or read book Theory of the Combination of Observations Least Subject to Errors written by Carl Friedrich Gauss and published by SIAM. This book was released on 1995-01-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: English translation of Gauss' two memoirs which contain his final, definitive treatment of least squares and wealth of additional material.

Download or read book Problem Solving Strategies written by Arthur Engel and published by Springer Science & Business Media. This book was released on 2008-01-19 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Things to Make and Do in the Fourth Dimension written by Matt Parker and published by Farrar, Straus and Giroux. This book was released on 2014-12-02 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book from the stand-up mathematician that makes math fun again! Math is boring, says the mathematician and comedian Matt Parker. Part of the problem may be the way the subject is taught, but it's also true that we all, to a greater or lesser extent, find math difficult and counterintuitive. This counterintuitiveness is actually part of the point, argues Parker: the extraordinary thing about math is that it allows us to access logic and ideas beyond what our brains can instinctively do—through its logical tools we are able to reach beyond our innate abilities and grasp more and more abstract concepts. In the absorbing and exhilarating Things to Make and Do in the Fourth Dimension, Parker sets out to convince his readers to revisit the very math that put them off the subject as fourteen-year-olds. Starting with the foundations of math familiar from school (numbers, geometry, and algebra), he reveals how it is possible to climb all the way up to the topology and to four-dimensional shapes, and from there to infinity—and slightly beyond. Both playful and sophisticated, Things to Make and Do in the Fourth Dimension is filled with captivating games and puzzles, a buffet of optional hands-on activities that entices us to take pleasure in math that is normally only available to those studying at a university level. Things to Make and Do in the Fourth Dimension invites us to re-learn much of what we missed in school and, this time, to be utterly enthralled by it.

Download or read book Common Mistakes in Teaching Elementary Math And How to Avoid Them written by Fuchang Liu and published by Routledge. This book was released on 2017-03-27 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn the most effective ways to teach elementary math, no matter how much experience you have with the subject. In this book, Fuchang Liu takes you through many common mistakes in math instruction and explains the misunderstandings behind them. He points out practices that should be avoided, helping you to adjust your lessons so that all students can achieve success. You’ll discover how to... - Increase your confidence with core math principles and reasoning - Set your students on the path toward eventually developing more complex math skills - Improve student achievement by approaching problems in logical yet creative ways - Overcome common challenges faced by students and teachers - Teach problem solving for different learning styles Every chapter reconsiders well-established ways of teaching all areas of elementary math, from addition and subtraction to statistics and graphs. Helpful examples and tips are scattered throughout the book, offering revisions to the way these topics are often presented in the classroom. Also included are group study ideas for principals and instructional coaches so your school or district can work on the book together. With this practical guide, you’ll be ready to help students truly develop their math understanding.