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Author : David H. Bailey
Publisher :
ISBN 13 : 9781935638247
Total Pages : 364 pages
Book Rating : 4.6/5 (382 download)
Download or read book Exploratory Experimentation in Mathematics written by David H. Bailey and published by . This book was released on 2012 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 21 pages
Book Rating : 4.:/5 (727 download)
Download or read book Exploratory Experimentation and Computation written by and published by . This book was released on 2010 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We believe the mathematical research community is facing a great challenge to re-evaluate the role of proof in light of recent developments. On one hand, the growing power of current computer systems, of modern mathematical computing packages, and of the growing capacity to data-mine on the Internet, has provided marvelous resources to the research mathematician. On the other hand, the enormous complexity of many modern capstone results such as the Poincare conjecture, Fermat's last theorem, and the classification of finite simple groups has raised questions as to how we can better ensure the integrity of modern mathematics. Yet as the need and prospects for inductive mathematics blossom, the requirement to ensure the role of proof is properly founded remains undiminished.
Author : Jonathan M. Borwein
Publisher : CRC Press
ISBN 13 : 1439864195
Total Pages : 372 pages
Book Rating : 4.4/5 (398 download)
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
Author : Jonathan Borwein
Publisher : CRC Press
ISBN 13 : 1439865361
Total Pages : 393 pages
Book Rating : 4.4/5 (398 download)
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 393 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
Author : Jonathan M. Borwein
Publisher : PSIpress
ISBN 13 : 193563805X
Total Pages : 309 pages
Book Rating : 4.9/5 (356 download)
Download or read book Experimental and Computational Mathematics written by Jonathan M. Borwein and published by PSIpress. This book was released on 2010 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: A quiet revolution in mathematical computing and scientific visualization took place in the latter half of the 20th century. These developments have dramatically enhanced modes of mathematical insight and opportunities for "exploratory" computational experimentation. This volume collects the experimental and computational contributions of Jonathan and Peter Borwein over the past quarter century.
Author : Benjamin Hutz
Publisher : American Mathematical Soc.
ISBN 13 : 1470430975
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)
Download or read book An Experimental Introduction to Number Theory written by Benjamin Hutz and published by American Mathematical Soc.. This book was released on 2018-04-17 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.
Author : David Bailey
Publisher : CRC Press
ISBN 13 : 1439864330
Total Pages : 337 pages
Book Rating : 4.4/5 (398 download)
Download or read book Experimental Mathematics in Action written by David Bailey and published by CRC Press. This book was released on 2007-05-31 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the continued advance of computing power and accessibility, the view that "real mathematicians don't compute" no longer has any traction for a newer generation of mathematicians. The goal in this book is to present a coherent variety of accessible examples of modern mathematics where intelligent computing plays a significant role and in so doi
Author : Falai Chen
Publisher : World Scientific Publishing Company
ISBN 13 : 9813102438
Total Pages : 228 pages
Book Rating : 4.8/5 (131 download)
Download or read book Mathematics Experiments written by Falai Chen and published by World Scientific Publishing Company. This book was released on 2003-02-18 with total page 228 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.
Author : Gila Hanna
Publisher : Springer Science & Business Media
ISBN 13 : 9400721293
Total Pages : 468 pages
Book Rating : 4.4/5 (7 download)
Download or read book Proof and Proving in Mathematics Education written by Gila Hanna and published by Springer Science & Business Media. This book was released on 2012-06-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: *THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
Author : Stephen Barr
Publisher : Courier Corporation
ISBN 13 : 048615274X
Total Pages : 244 pages
Book Rating : 4.4/5 (861 download)
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.
Author : V. I. Arnold
Publisher : American Mathematical Soc.
ISBN 13 : 0821894161
Total Pages : 170 pages
Book Rating : 4.8/5 (218 download)
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).
Author : Jonathan Borwein
Publisher : CRC Press
ISBN 13 : 1439876916
Total Pages : 170 pages
Book Rating : 4.4/5 (398 download)
Download or read book The Computer as Crucible written by Jonathan Borwein and published by CRC Press. This book was released on 2008-10-28 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces to create this introduction to experimental mathematics. They cover a variety of topics and examples to give the reader a good sense of the current sta
Author : Mount Holyoke College
Publisher : Springer Science & Business Media
ISBN 13 : 9780387949222
Total Pages : 308 pages
Book Rating : 4.9/5 (492 download)
Download or read book Laboratories in Mathematical Experimentation written by Mount Holyoke College and published by Springer Science & Business Media. This book was released on 1997-03 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text is composed of a set of sixteen laboratory investigations which allow the student to explore rich and diverse ideas and concepts in mathematics. The approach is hands-on, experimental, an approach that is very much in the spirit of modern pedagogy. The course is typically offered in one semester, at the sophomore (second year) level of college. It requires completion of one year of calculus. The course provides a transition to the study of higher, abstract mathematics. The text is written independent of any software. Supplements will be available on the projects' web site.
Author : Russell Marcus
Publisher : Bloomsbury Publishing
ISBN 13 : 1472529480
Total Pages : 849 pages
Book Rating : 4.4/5 (725 download)
Download or read book An Historical Introduction to the Philosophy of Mathematics: A Reader written by Russell Marcus and published by Bloomsbury Publishing. This book was released on 2016-02-11 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.
Author : Friedrich Steinle
Publisher : University of Pittsburgh Press
ISBN 13 : 0822981378
Total Pages : 468 pages
Book Rating : 4.8/5 (229 download)
Download or read book Exploratory Experiments written by Friedrich Steinle and published by University of Pittsburgh Press. This book was released on 2016-09-02 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translated by Alex Levine The nineteenth century was a formative period for electromagnetism and electrodynamics. Hans Christian Orsted's groundbreaking discovery of the interaction between electricity and magnetism in 1820 inspired a wave of research, led to the science of electrodynamics, and resulted in the development of electromagnetic theory. Remarkably, in response, Andre-Marie Ampere and Michael Faraday developed two incompatible, competing theories. Although their approaches and conceptual frameworks were fundamentally different, together their work launched a technological revolution—laying the foundation for our modern scientific understanding of electricity—and one of the most important debates in physics, between electrodynamic action-at-a-distance and field theories. In this foundational study, Friedrich Steinle compares the influential work of Ampere and Faraday to reveal the prominent role of exploratory experimentation in the development of science. While this exploratory phase was responsible for decisive conceptual innovations, it has yet to be examined in such great detail. Focusing on Ampere's and Faraday's research practices, reconstructed from previously unknown archival materials, including laboratory notes, diaries, letters, and interactions with instrument makers, this book considers both the historic and epistemological basis of exploratory experimentation and its importance to scientific development.
Author :
Publisher :
ISBN 13 :
Total Pages : 318 pages
Book Rating : 4.3/5 (436 download)
Download or read book Proceedings of the ... Conference on the Design of Experiments written by and published by . This book was released on 1988 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bharath Sriraman
Publisher : Springer Nature
ISBN 13 : 3031408462
Total Pages : 3221 pages
Book Rating : 4.0/5 (314 download)
Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
