Read and Download eBook Full
Author: Jonathan Borwein
Publisher: CRC Press
Published: 2008-10-27
Total Pages: 393
ISBN-13: 1439865361
DOWNLOAD EBOOKThis 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
Author: V. I. Arnold
Publisher: American Mathematical Soc.
Published: 2015-07-14
Total Pages: 170
ISBN-13: 0821894161
DOWNLOAD EBOOKOne 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).
Author: Jonathan M. Borwein
Publisher: CRC Press
Published: 2004-04-12
Total Pages: 372
ISBN-13: 1439864195
DOWNLOAD EBOOKNew 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
Author: Stephen Barr
Publisher: Courier Corporation
Published: 2012-12-04
Total Pages: 244
ISBN-13: 048615274X
DOWNLOAD EBOOKClassic, 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.
Author: Shangzhi Li
Publisher: World Scientific
Published: 2003
Total Pages: 234
ISBN-13: 9789812380500
DOWNLOAD EBOOKOwing 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.
Author: Jonathan M. Borwein
Publisher: A K Peters Ltd
Published: 2004
Total Pages: 288
ISBN-13: 9781568812113
DOWNLOAD EBOOKThis 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.
Author: Eddie Woo
Publisher: The Experiment
Published: 2019-09-03
Total Pages: 321
ISBN-13: 1615196129
DOWNLOAD EBOOK2021 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.
Author: Anne Watson
Publisher: Springer
Published: 2015-10-26
Total Pages: 339
ISBN-13: 331909629X
DOWNLOAD EBOOK*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.
Author: Michelle Crane (Editor)
Publisher:
Published: 2021
Total Pages:
ISBN-13: 9780744052725
DOWNLOAD EBOOKGet 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.
Author: Brian Sutton
Publisher: SIAM
Published: 2019-04-18
Total Pages: 448
ISBN-13: 1611975700
DOWNLOAD EBOOKThis 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.
