Experimentation In Mathematics
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Experimentation In Mathematics
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Author : Jonathan M. Borwein
language : en
Publisher: A K Peters/CRC Press
Release Date : 2004-04-12
Experimentation In Mathematics written by Jonathan M. Borwein and has been published by A K Peters/CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-12 with Mathematics categories.
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 experimental research in the statement of new hypotheses and the discovery of new results that chart the road to future developments. Following the lead of Mathematics by Experiment: Plausible Reasoning in the 21st Century this book gives numerous additional case studies of experimental mathematics in action, ranging from sequences, series, products, integrals, Fourier series, zeta functions, partitions, primes and polynomials. Some advanced numerical techniques are also presented. To get a taste of the material presented in both books view the condensed version.
Mathematics By Experiment
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Author : Jonathan Borwein
language : en
Publisher: CRC Press
Release Date : 2008-10-27
Mathematics By Experiment written by Jonathan Borwein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-27 with Mathematics categories.
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
Experiments In Topology
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Author : Stephen Barr
language : en
Publisher: Courier Corporation
Release Date : 1989-01-01
Experiments In Topology written by Stephen Barr and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.
"A mathematician named Klein Thought the Moebius band was divine. Said he: 'If you glue The edges of two, You'll get a weird bottle like mine.' " — Stephen Barr In this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip. Beginning with a definition of topology and a discussion of Euler's theorem, Mr. Barr brings wit and clarity to these topics: New Surfaces (Orientability, Dimension, The Klein Bottle, etc.) The Shortest Moebius Strip The Conical Moebius Strip The Klein Bottle The Projective Plane (Symmetry) Map Coloring Networks (Koenigsberg Bridges, Betti Numbers, Knots) The Trial of the Punctured Torus Continuity and Discreteness ("Next Number," Continuity, Neighborhoods, Limit Points) Sets (Valid or Merely True? Venn Diagrams, Open and Closed Sets, Transformations, Mapping, Homotopy) With this book and a square sheet of paper, the reader can make paper Klein bottles, step by step; then, by intersecting or cutting the bottle, make Moebius strips. Conical Moebius strips, projective planes, the principle of map coloring, the classic problem of the Koenigsberg bridges, and many more aspects of topology are carefully and concisely illuminated by the author's informal and entertaining approach. Now in this inexpensive paperback edition, Experiments in Topology belongs in the library of any math enthusiast with a taste for brainteasing adventures
Laboratories In Mathematical Experimentation
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Author : Mount Holyoke College
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-03
Laboratories In Mathematical Experimentation written by Mount Holyoke College and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03 with Mathematics categories.
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.
Experimentation In Mathematics
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Author : Jonathan M. Borwein
language : en
Publisher: CRC Press
Release Date : 2004-04-12
Experimentation In Mathematics written by Jonathan M. Borwein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-12 with Mathematics categories.
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
Experimental Mathematics In Action
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Author : David Bailey
language : en
Publisher: CRC Press
Release Date : 2007-05-31
Experimental Mathematics In Action written by David Bailey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-31 with Mathematics categories.
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
Understanding Statistics And Experimental Design
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Author : Michael H. Herzog
language : en
Publisher: Springer
Release Date : 2019-08-13
Understanding Statistics And Experimental Design written by Michael H. Herzog and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-13 with Science categories.
This open access textbook provides the background needed to correctly use, interpret and understand statistics and statistical data in diverse settings. Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III provides insight into meta-statistics (statistics of statistics) and demonstrates why experiments often do not replicate. Finally, the textbook shows how complex statistics can be avoided by using clever experimental design. Both non-scientists and students in Biology, Biomedicine and Engineering will benefit from the book by learning the statistical basis of scientific claims and by discovering ways to evaluate the quality of scientific reports in academic journals and news outlets.
A Comprehensive Guide To Factorial Two Level Experimentation
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Author : Robert Mee
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-23
A Comprehensive Guide To Factorial Two Level Experimentation written by Robert Mee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-23 with Mathematics categories.
Factorial designs enable researchers to experiment with many factors. The 50 published examples re-analyzed in this guide attest to the prolific use of two-level factorial designs. As a testimony to this universal applicability, the examples come from diverse fields: Analytical Chemistry, Animal Science, Automotive Manufacturing, Ceramics and Coatings, Chromatography, Electroplating, Food Technology, Injection Molding, Marketing, Microarray Processing, Modeling and Neural Networks, Organic Chemistry, Product Testing, Quality Improvement, Semiconductor Manufacturing, and Transportation. Focusing on factorial experimentation with two-level factors makes this book unique, allowing the only comprehensive coverage of two-level design construction and analysis. Furthermore, since two-level factorial experiments are easily analyzed using multiple regression models, this focus on two-level designs makes the material understandable to a wide audience. This book is accessible to non-statisticians having a grasp of least squares estimation for multiple regression and exposure to analysis of variance. "This book contains a wealth of information, including recent results on the design of two-level factorials and various aspects of analysis... The examples are particularly clear and insightful." (William Notz, Ohio State University) "One of the strongest points of this book for an audience of practitioners is the excellent collection of published experiments, some of which didn’t ‘come out’ as expected... A statistically literate non-statistician who deals with experimental design will have plenty of motivation to read this book, and the payback for the effort will be substantial." (Max Morris, Iowa State University)
Numerical Analysis
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Author : Brian Sutton
language : en
Publisher: SIAM
Release Date : 2019-04-18
Numerical Analysis written by Brian Sutton and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-18 with Mathematics categories.
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.
Experimental Number Theory
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Author : Fernando Rodriguez Villegas
language : en
Publisher: Oxford University Press, USA
Release Date : 2007-05-24
Experimental Number Theory written by Fernando Rodriguez Villegas and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-24 with Mathematics categories.
This graduate text shows how the computer can be used as a tool for research in number theory through numerical experimentation. Examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, are provided along with exercises and selected solutions.