Proofs And Confirmations
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Proofs And Confirmations
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Author : David M. Bressoud
language : en
Publisher: Cambridge University Press
Release Date : 1999-08-13
Proofs And Confirmations written by David M. Bressoud and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-13 with Mathematics categories.
This is an introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. The author recounts the story of the search for and discovery of a proof of a formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While apparent that the conjecture must be true, the proof was elusive. Researchers became drawn to this problem, making connections to aspects of invariant theory, to symmetric functions, to hypergeometric and basic hypergeometric series, and, finally, to the six-vertex model of statistical mechanics. All these threads are brought together in Zeilberger's 1996 proof of the original conjecture. The book is accessible to anyone with a knowledge of linear algebra. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something new here.
Proofs And Confirmations
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Author : David M. Bressoud
language : en
Publisher: Cambridge University Press
Release Date : 1999-08-13
Proofs And Confirmations written by David M. Bressoud and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-13 with Mathematics categories.
This introduction to recent developments in algebraic combinatorics illustrates how research in mathematics actually progresses. The author recounts the dramatic search for and discovery of a proof of a counting formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While it was apparent that the conjecture must be true, the proof was elusive. As a result, researchers became drawn to this problem and made connections to aspects of the invariant theory of Jacobi, Sylvester, Cayley, MacMahon, Schur, and Young; to partitions and plane partitions; to symmetric functions; to hypergeometric and basic hypergeometric series; and, finally, to the six-vertex model of statistical mechanics. This volume is accessible to anyone with a knowledge of linear algebra, and it includes extensive exercises and Mathematica programs to help facilitate personal exploration. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something unique within Proofs and Confirmations.
A Course In Enumeration
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Author : Martin Aigner
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-28
A Course In Enumeration written by Martin Aigner 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 2007-06-28 with Mathematics categories.
Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. There are 666 exercises, and every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.
Explanation And Proof In Mathematics
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Author : Gila Hanna
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-04
Explanation And Proof In Mathematics written by Gila Hanna 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 2009-12-04 with Education categories.
In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece. Proof as bearers of mathematical knowledge. Bridging knowing and proving in mathematical reasoning. The role of mathematics in long-term cognitive development of reasoning. Proof as experiment in the work of Wittgenstein. Relationships between mathematical proof, problem-solving, and explanation. Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
Proof And Other Dilemmas
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Author : Bonnie Gold
language : en
Publisher: MAA
Release Date : 2008
Proof And Other Dilemmas written by Bonnie Gold and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
During the first 75 years of the twentieth century almost all work in the philosophy of mathematics concerned foundational questions. In the last quarter of the century, philosophers of mathematics began to return to basic questions concerning the philosophy of mathematics such as, what is the nature of mathematical knowledge and of mathematical objects, and how is mathematics related to science? Two new schools of philosophy of mathematics, social constructivism and structuralism, were added to the four traditional views (formalism, intuitionalism, logicism, and platonism). The advent of the computer led to proofs and the development of mathematics assisted by computer, and to questions of the role of the computer in mathematics. This book of 16 essays, all written specifically for this volume, is the first to explore this range of new developments in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers are not yet discussing. The other half, written by philsophers of mathematics, summarize the discussion in that community during the last 35 years. In each case, a connection is made to issues relevant to the teach of mathematics.
An Attempt To Explain And Establish The Doctrine Of Justification By Faith Only
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Author : James Thomas O'Brien
language : en
Publisher:
Release Date : 1863
An Attempt To Explain And Establish The Doctrine Of Justification By Faith Only written by James Thomas O'Brien and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1863 with Faith categories.
An Attempt To Explain And Establish The Doctrine Of Justification By Faith Only In Ten Sermons Upon The Nature And Effects Of Faith Etc
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Author : James Thomas O'BRIEN (Bishop of Ossory, Ferns and Leighlin.)
language : en
Publisher:
Release Date : 1862
An Attempt To Explain And Establish The Doctrine Of Justification By Faith Only In Ten Sermons Upon The Nature And Effects Of Faith Etc written by James Thomas O'BRIEN (Bishop of Ossory, Ferns and Leighlin.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1862 with categories.
Nature Mathematized
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Author : W.R. Shea
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nature Mathematized written by W.R. Shea 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 2012-12-06 with Science categories.
These remarks preface two volumes consisting of the proceedings of the Third International Conference on the History and Philosophy of Science of the International Union of History and Philosophy of Science. The conference was held under the auspices of the Union, The Social Sciences and Humanities Research Council of Canada, and the Canadian Society for History and Philosophy of Science. The meetings took place in Montreal, Canada, 25--29 August 1980, with Concordia University as host institution. The program of the conference was arranged by a Joint Commission of the International Union of History and Philosophy of Science consisting of Robert E. Butts (Canada), John Murdoch (U. S. A. ), Vladimir Kirsanov (U. S. S. R. ), and Paul Weingartner (Austria). The Local Arrangements Committee consisted of Stanley G. French, Chair (Concordia), Michel Paradis, treasurer (McGill), Franyois Duchesneau (Universite de Montreal), Robert Nadeau (Universite du Quebec a Montreal), and William Shea (McGill University). Both committees are indebted to Dr. G. R. Paterson, then President of the Canadian Society for History and Philosophy of Science, who shared his expertise in many ways. Dr. French and his staff worked diligently and efficiently on behalf of all participants. The city of Montreal was, as always, the subtle mixture of extravagance, charm, warmth and excitement that retains her status as the jewel of Canadian cities. The funding of major international conferences is always a problem.
Forensic Investigations
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Author : Brent E. Turvey
language : en
Publisher: Academic Press
Release Date : 2017-01-05
Forensic Investigations written by Brent E. Turvey and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-05 with Law categories.
The terms forensic investigator and forensic investigation are part of our cultural identity. They can be found in the news, on television, and in film. They are invoked, generally, to imply that highly trained personnel will be collecting some form of physical evidence with eventual scientific results that cannot be questioned or bargained with. In other words, they are invoked to imply the reliability, certainty, and authority of a scientific inquiry. Using cases from the authors' extensive files, Forensic Investigations: An Introduction provides an overview of major subjects related to forensic inquiry and evidence examination. It will prepare Criminal Justice and Criminology students in forensic programs for more specialized courses and provide a valuable resource to newly employed forensic practitioners. Written by practicing and testifying forensic professionals from law enforcement, academia, mental health and the forensic sciences, this work offers a balanced scientific approach, based on the established literature, for broad appeal. The purpose of this book is to help students and professionals rid themselves of the myths and misconceptions they have accumulated regarding forensic investigators and the subsequent forensic investigations they help to conduct. It will help the reader understand the role of the forensic investigator; the nature and variety of forensic investigations that take place in the justice system; and the mechanisms by which such investigations become worthy as evidence in court. Its goals are no loftier than that. However, they could not be more necessary to our understanding of what justice is, how it is most reliably achieved, and how it can be corrupted by those who are burdened with apathy and alternative motives. - A primary text for instructors teaching forensic courses related to criminal and forensic investigation - Written by forensic professionals, currently in practice and testifying in court - Offers applied protocols for a broad range of forensic investigations - Augments theoretical constructs with recent, and relevant case studies and forensic reports - Based on the most recent scientific research, practice, and protocols related to forensic inquiry
Forensic Fraud
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Author : Brent E. Turvey
language : en
Publisher: Academic Press
Release Date : 2013-03-18
Forensic Fraud written by Brent E. Turvey and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-18 with Social Science categories.
Forensic Fraud is the culmination of 12 years of research by author Brent E. Turvey. A practicing forensic scientist since 1996, Turvey has rendered this first of its kind study into the widespread problem of forensic fraud in the United States. It defines the nature and scope of the problem, the cultural attitudes and beliefs of those involved, and establishes clear systemic contributors. Backed up by scrupulous research and hard data, community reforms are proposed and discussed in light of the recently published National Academy of Sciences report on forensic science. An adaptation of Dr. Turvey's doctoral dissertation, this volume relentlessly cites chapter and verse in support of its conclusions that law enforcement cultural and scientific values are incompatible, and that the problem of forensic fraud is systemic in nature. It begins with an overview of forensic fraud as a sub-type of occupational fraud, it explores the extent of fraud in both law enforcement and scientific employment settings, it establishes and then contrasts the core values of law enforcement and scientific cultures and then it provides a comprehensive review of the scientific literature regarding forensic fraud. The final chapters present data from Dr. Turvey's original research into more than 100 fraudulent examiners between 2000 and 2010, consideration of significant findings, and a review of proposed reforms to the forensic science community based on what was learned. It closes with a chapter on the numerous crime lab scandals, and closures that occurred between 2010 and 2012 – an update on the deteriorating state of the forensic science community in the United States subsequent to data collection efforts in the present research. Forensic Fraud is intended for use as a professional reference manual by those working in the criminal system who encounter the phenomenon and want to understand its context and origins. It is intended to help forensic scientist and their supervisors to recognize, manage and expel it; to provide policy makers with the necessary understaffing for acknowledging and mitigating it; and to provide agents of the courts with the knowledge, and confidence, to adjudicate it. It is also useful for those at the university level seeking a strong secondary text for courses on forensic science, law and evidence, or miscarriages of justice. - First of its kind overview of the cultural instigators of forensic fraud - First of its kind research into the nature and impact of forensic fraud, with data (2000-2010) - First of its kind typology of forensic fraud, for use in future case examination in research - Numerous profiles of forensic fraudsters - Review of major crime lab scandals between 2010 and 2012