Download or read book Mathematics by Experiment 2nd Edition written by Jonathan M. Borwein and published by A K Peters Ltd. This book was released on 2004 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new approach to mathematics---the utilization of advanced computing technology in mathematical research---is often called experimental mathematics. The computer provides the mathematician with a "laboratory" in which she can perform experiments---analyzing examples, testing out new ideas, or searching for patterns. This book presents the rationale and historical context of experimental mathematics, and includes a series of examples that best portray the experimental methodology. For more examples and insights, the book, "Experimentation in Mathematics: Computational Paths to Discovery" is a highly recommended companion.
Download or read book Mathematics by Experiment written by Jonathan Borwein and published by CRC Press. This book was released on 2008-10-27 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences", that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational P
Download or read book Experimental Mathematics written by V. I. Arnold and published by American Mathematical Soc.. This book was released on 2015-07-14 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
Download or read book Experimentation in Mathematics written by Jonathan M. Borwein and published by CRC Press. This book was released on 2004-04-12 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of
Download or read book Experiments in Topology written by Stephen Barr and published by Courier Corporation. This book was released on 2012-12-04 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.
Download or read book Mathematics Experiments written by Shangzhi Li and published by World Scientific. This book was released on 2003 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Owing to the advent of computers, experiments are becoming an increasingly important part of mathematics. This book provides guidance to students doing experiments in mathematics. The aim is to stimulate interest in mathematics through examples and experiments. Each experiment in the book starts with an interesting problem. The students are expected to work with these problems on computers, try to find the solutions themselves, and experience the scientific exploration in the process. The problems which the authors have chosen cover a wide spectrum in mathematics, ranging from calculus, number theory, coding and probability to geometry and chaos. They are introduced in a simple way and yet show great depth. The discussions are thorough but not lengthy. This book is useful not only to mathematics students, but also to students in all areas of sciences who are interested in learning some of the mathematical tools. It provides a hands-on approach to the most fundamental issues in mathematics -- an approach which may help to revolutionize the teaching of mathematics.
Download or read book It s a Numberful World written by Eddie Woo and published by The Experiment. This book was released on 2019-09-03 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2021 Mathical Honor Book Why aren’t left-handers extinct? What makes a rainbow round? How is a pancreas . . . like a pendulum? Publisher's note: It's a Numberful World was published in Australia under the title Woo's Wonderful World of Maths. These may not look like math questions, but they are—because they all have to do with patterns. And mathematics, at heart, is the study of patterns. That realization changed Eddie Woo’s life—by turning the “dry” subject he dreaded in high school into a boundless quest for discovery. Now an award-winning math teacher, Woo sees patterns everywhere: in the “branches” of blood vessels and lightning, in the growth of a savings account and a sunflower, even in his morning cup of tea! Here are twenty-six bite-size chapters on the hidden mathematical marvels that encrypt our email, enchant our senses, and even keep us alive—from the sine waves we hear as “music” to the mysterious golden ratio. This book will change your mind about what math can be. We are all born mathematicians—and It’s a Numberful World.
Download or read book Math Maker Lab written by Michelle Crane (Editor) and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Get hands-on with 27 creative projects and experiments that will turn you into a math whiz.Explore the exciting world of numbersWhether you're a math geek or prefer practical hands-on projects, this ebook combines creativity with calculations. You don't have to be a genius or even need a calculator. Each of the super-fun make-and-do projects in this ebook comes with simple step-by-step photographs and instructions that will help you whip up a cool math creation.Perfect for kids who are interested in STEM (science, technology, engineering, and math), Math Maker Lab features activities that cover many aspects of math, including numbers, measurement, and geometry. You'll combine art and math by drawing impossible objects, create beautiful patterns to make a times-table dream catcher, and perfect the ratio for making refreshing fruit drinks. Throughout the ebook, explanatory boxes show you how the math works and how the skills you've learned can be used in the real world.Math Maker Lab is the perfect for curious kids who are interested in taking the mystery out of math.
Download or read book Numerical Analysis written by Brian Sutton and published by SIAM. This book was released on 2019-04-18 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems?interpolation, integration, linear systems, zero finding, and differential equations?are considered, and some of the most important methods for their solution are demonstrated and analyzed. Notable features of this book include the development of Chebyshev methods alongside more classical ones; a dual emphasis on theory and experimentation; the use of linear algebra to solve problems from analysis, which enables students to gain a greater appreciation for both subjects; and many examples and exercises. Numerical Analysis: Theory and Experiments is designed to be the primary text for a junior- or senior-level undergraduate course in numerical analysis for mathematics majors. Scientists and engineers interested in numerical methods, particularly those seeking an accessible introduction to Chebyshev methods, will also be interested in this book.
Download or read book Optimal Design of Experiments written by Friedrich Pukelsheim and published by SIAM. This book was released on 2006-04-01 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples.
Download or read book Discipline and Experience written by Peter Dear and published by University of Chicago Press. This book was released on 1995-11-25 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the Scientific Revolution has long been regarded as the beginning of modern science, there has been little consensus about its true character. While the application of mathematics to the study of the natural world has always been recognized as an important factor, the role of experiment has been less clearly understood. Peter Dear investigates the nature of the change that occurred during this period, focusing particular attention on evolving notions of experience and how these developed into the experimental work that is at the center of modern science. He examines seventeenth-century mathematical sciences—astronomy, optics, and mechanics—not as abstract ideas, but as vital enterprises that involved practices related to both experience and experiment. Dear illuminates how mathematicians and natural philosophers of the period—Mersenne, Descartes, Pascal, Barrow, Newton, Boyle, and the Jesuits—used experience in their argumentation, and how and why these approaches changed over the course of a century. Drawing on mathematical texts and works of natural philosophy from all over Europe, he describes a process of change that was gradual, halting, sometimes contradictory—far from the sharp break with intellectual tradition implied by the term "revolution."
Download or read book Task Design In Mathematics Education written by Anne Watson and published by Springer. This book was released on 2015-10-26 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: *THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* This open access book is the product of ICMI Study 22 Task Design in Mathematics Education. The study offers a state-of-the-art summary of relevant research and goes beyond that to develop new insights and new areas of knowledge and study about task design. The authors represent a wide range of countries and cultures and are leading researchers, teachers and designers. In particular, the authors develop explicit understandings of the opportunities and difficulties involved in designing and implementing tasks and of the interfaces between the teaching, researching and designing roles – recognising that these might be undertaken by the same person or by completely separate teams. Tasks generate the activity through which learners meet mathematical concepts, ideas, strategies and learn to use and develop mathematical thinking and modes of enquiry. Teaching includes the selection, modification, design, sequencing, installation, observation and evaluation of tasks. The book illustrates how task design is core to effective teaching, whether the task is a complex, extended, investigation or a small part of a lesson; whether it is part of a curriculum system, such as a textbook, or promotes free standing activity; whether the task comes from published source or is devised by the teacher or the student.
Download or read book Invited Lectures from the 13th International Congress on Mathematical Education written by Gabriele Kaiser and published by Springer. This book was released on 2018-02-06 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the Invited Lectures given at 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 – the biggest ICME so far - brought together about 3500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. The scholars came together to share their work on the improvement of mathematics education at all educational levels.. The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education. The Invited Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.
Download or read book Physics for Mathematicians written by Michael Spivak and published by . This book was released on 2010 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hands on Science and Math written by Beth Davis and published by Gryphon House Incorporated. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Encourage young investigators to feel, listen, smell, taste, and see their way to discovery by seamlessly infusing math and science throughout the school day As you incorporate all five senses into learning experiences, you will give little innovators the opportunity to observe and explore the world around them. The activities in Hands-On Science and Math: Fun, Fascinating Activities for Young Children will help you plan engaging science, technology, engineering, and math (STEM) lessons that will excite children and foster their critical thinking. Children can experience the thrill of scientific inquiry through simple experiments: Launching Recycled Rockets Shake and Freeze: Homemade Ice Cream Look Out Volcano Erupting The Mystery of Suspensions Go, Car, Go Simple Machines and Inclined Planes Designed to work with easy-to-find materials, the Hands-On Science and Math activities are inexpensive and uncomplicated, yet they lay the groundwork for understanding more complex STEM concepts later on. Award Winner Recipient of the following awards: 2015 Creative Child Magazine Preferred Choice Award 2015 Tillywig Toy Brain Child Award 2015 Academics' Choice Smart Book Award
Download or read book The Mathematics of Marriage written by John M. Gottman and published by MIT Press. This book was released on 2005-01-14 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Divorce rates are at an all-time high. But without a theoretical understanding of the processes related to marital stability and dissolution, it is difficult to design and evaluate new marriage interventions. The Mathematics of Marriage provides the foundation for a scientific theory of marital relations. The book does not rely on metaphors, but develops and applies a mathematical model using difference equations. The work is the fulfillment of the goal to build a mathematical framework for the general system theory of families first suggested by Ludwig Von Bertalanffy in the 1960s.The book also presents a complete introduction to the mathematics involved in theory building and testing, and details the development of experiments and models. In one "marriage experiment," for example, the authors explored the effects of lowering or raising a couple's heart rates. Armed with their mathematical model, they were able to do real experiments to determine which processes were affected by their interventions. Applying ideas such as phase space, null clines, influence functions, inertia, and uninfluenced and influenced stable steady states (attractors), the authors show how other researchers can use the methods to weigh their own data with positive and negative weights. While the focus is on modeling marriage, the techniques can be applied to other types of psychological phenomena as well.
Download or read book Visions of the Universe written by Alex Bellos and published by The Experiment. This book was released on 2016-11-29 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Peek “behind the scenes” of the universe—and see math in brilliant color! For curious minds throughout history, math was truly an art. In Visions of the Universe, you can pick up right where Isaac Newton, Blaise Pascal, and other luminaries left off—by coloring 58 exquisite patterns inspired by great discoveries in math: Intricate geometric designs like those that grace the mosques of Mecca Felix Klein’s astounding diagram—drawn in 1897—of light reflecting between five mirrored spheres A mind-bending puzzle so beautiful it once hung outside a Japanese temple, and more! Plus, in the Creating chapter, you’ll help complete 10 additional images by following simple steps that give spectacular results. No math knowledge is required: Anyone can be an artist in Numberland!
