David Pengelley's Books

Mathematical Masterpieces

Further Chronicles by the Explorers

By: Art Knoebel,Reinhard Laubenbacher,Jerry Lodder,David Pengelley

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Mathematical Masterpieces

Further Chronicles by the Explorers

By: Art Knoebel,Reinhard Laubenbacher,Jerry Lodder,David Pengelley

Intended for juniors and seniors majoring in mathematics, as well as anyone pursuing independent study, this book traces the historical development of four different mathematical concepts by presenting readers with the original sources. Each chapter showcases a masterpiece of mathematical achievement, anchored to a sequence of selected primary sources. The authors examine the interplay between the discrete and continuous, with a focus on sums of powers. They then delineate the development of algorithms by Newton, Simpson and Smale. Next they explore our modern understanding of curvature, and finally they look at the properties of prime numbers. The book includes exercises, numerous photographs, and an annotated bibliography.

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Page Count

346

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387330615

ISBN 13

9780387330617

Mathematical Expeditions

Chronicles by the Explorers

By: Reinhard Laubenbacher,David Pengelley

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Mathematical Expeditions

Chronicles by the Explorers

By: Reinhard Laubenbacher,David Pengelley

The stories of five mathematical journeys into new realms, pieced together from the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, others by more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realisation that still greater vistas remain to be explored. The authors tell these stories by guiding readers through the very words of the mathematicians at the heart of these events, providing an insightinto the art of approaching mathematical problems. The five chapters are completely independent, with varying levels of mathematical sophistication, and will attract students, instructors, and the intellectually curious reader. By working through some of the original sources and supplementary exercises, which discuss and solve -- or attempt to solve -- a great problem, this book helps readers discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics.

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Page Count

288

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461205239

ISBN 13

9781461205234

Number Theory Through the Eyes of Sophie Germain

An Inquiry Course

By: David Pengelley

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Number Theory Through the Eyes of Sophie Germain

An Inquiry Course

By: David Pengelley

Number Theory Through the Eyes of Sophie Germain: An Inquiry Course is an innovative textbook for an introductory number theory course. Sophie Germain (1776–1831) was largely self-taught in mathematics and, two centuries ago, in solitude, devised and implemented a plan to prove Fermat's Last Theorem. We have only recently completely understood this work from her unpublished letters and manuscripts. David Pengelley has been a driving force in unraveling this mystery and here he masterfully guides his readers along a path of discovery. Germain, because of her circumstances as the first woman to do important original mathematical research, was forced to learn most of what we now include in an undergraduate number theory course for herself. Pengelley has taken excerpts of her writings (and those of others) and, by asking his readers to decipher them, skillfully leads us through an inquiry-based course in elementary number theory. It is a detective story on multiple levels. What is Sophie Germain thinking? What do her mathematical writings mean? How do we understand what she knew and what she was trying to do, where she succeeded and where she didn't? Number Theory Through the Eyes of Sophie Germainis simultaneously a masterpiece of historical scholarship, a guide to reading and teaching from primary-source historical documents, an inquiry-based textbook for introductory number theory, and the riveting story of a major, but still unappreciated, mathematician. Work is required of the reader. Readers are carefully guided to discover and prove almost all results for themselves in a sequence of scaffolded exploratory tasks with hints, fully integrated with the narrative. The difficulty of the inquiry tasks varies considerably, but the author provides the reader with appropriately helpful guidance at every step. An introductory number theory course taught with this text would be a remarkable, potentially life-changing, experience. —Stephen Kennedy, Carleton College and MAA Press

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Page Count

216

Publisher

American Mathematical Society

Published Date

ISBN 10

1470472201

ISBN 13

9781470472207

The Reaches

By: David Drake

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The Reaches

By: David Drake

Thundering Space Adventure from the Best-Selling Author of Hammer's Slammers A thousand years ago, the human empire collapsed. Now mankind is reclaiming the galaxy, and ships hurtle between the stars, hoping to reap the rich opportunities of this new age of trade and exploration. But there are wars springing up, with new tyrants seizing whole planets, while other planets are rebelling against the powers that hold them captive. And lurking in the dark spaces between the stars are pirates, plundering all sides in the conflicts. It is the golden age of space travel, and it is possible for a brave man or woman to become very wealthy-or very dead. At the publisher's request, this title is sold without DRM (Digital Rights Management). A violent, hard-nosed swashbuckler, set forth with discernment and skill. ¾Kirkus Reviews Drake uses military language fluently to create vivid combat scenes. ¾Publishers Weekly Hard-hitting SF adventure-a tale that will appeal to fans of military SF. ¾Library Journal "A cleverly set up, Poul Anderson-style reprise of the early Elizabethan period, when trade and piracy were synonyms . . . enormously entertaining! ¾Detroit News

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1278

Publisher

Baen Publishing Enterprises

Published Date

ISBN 10

1618244140

ISBN 13

9781618244147

Preparing and Training for the Full Spectrum of Military Challenges

Insights from the Experiences of China, France, the United Kingdom, India, and Israel

By: David Eugene Johnson

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Preparing and Training for the Full Spectrum of Military Challenges

Insights from the Experiences of China, France, the United Kingdom, India, and Israel

By: David Eugene Johnson

The difficult and continually evolving operations in Iraq and Afghanistan show the complexities of what is now termed irregular warfare and highlight the need for new approaches to the security challenges with which the United States is now contending and will likely confront in the future. The research reported in this monograph focused on answering a rather straightforward, but thus far largely unanswered, question: What can the U.S. military learn from other militaries about how better to prepare for full-spectrum operations and deployments? To this end, RAND was asked by the OSD for Personnel and Readiness to examine the militaries of China, France, the UK, India, and Israel."--P. xiii.

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Page Count

315

Publisher

Rand Corporation

Published Date

ISBN 10

0833047817

ISBN 13

9780833047816

Law: The Basics

By: Gary Slapper,David Kelly

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Law: The Basics

By: Gary Slapper,David Kelly

An engaging introduction to one of the most complex areas of modern life. The book introduces both the main components of the legal system - including judges, juries and law-makers - and key areas of law - contract, civil negligence, and criminal law - to provide the uninitiated with an ideal introduction to law. Key questions to be considered include: How are laws made? How do judges decide cases? What is the exact role of the EU in the legal system? What are your rights and duties under contract law? What is a crime and what are criminal defences? Throughout the book, a wide range of contemporary cases are examined to relate key legal concepts to familiar examples and real world situations.

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Page Count

202

Publisher

Routledge

Published Date

ISBN 10

1136681876

ISBN 13

9781136681875

Fireships

By: David Drake

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Fireships

By: David Drake

In his acclaimed novels, "Igniting the Reaches" and "Through the Breach", David Drake took an epic journey to the farthest reaches of space, where pirates ruled a new age of expansion and opportunity. Now Drake returns to that savage time of untold possibility, wealth and danger.

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340

Publisher

Ace

Published Date

ISBN 10

0441004172

ISBN 13

9780441004171

Prime Numbers

The Most Mysterious Figures in Math

By: David Wells

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Prime Numbers

The Most Mysterious Figures in Math

By: David Wells

A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know--and much more that you never suspected--about prime numbers, including: * The unproven Riemann hypothesis and the power of the zeta function * The "Primes is in P" algorithm * The sieve of Eratosthenes of Cyrene * Fermat and Fibonacci numbers * The Great Internet Mersenne Prime Search * And much, much more

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Page Count

260

Publisher

Turner Publishing Company

Published Date

ISBN 10

1118045718

ISBN 13

9781118045718

Counterinsurgency in Crisis

Britain and the Challenges of Modern Warfare

By: Robert Egnell,David H. Ucko

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Counterinsurgency in Crisis

Britain and the Challenges of Modern Warfare

By: Robert Egnell,David H. Ucko

Long considered the masters of counterinsurgency, the British military encountered significant problems in Iraq and Afghanistan when confronted with insurgent violence. In their effort to apply the principles and doctrines of past campaigns, they failed to prevent Basra and Helmand from descending into lawlessness, criminality, and violence. By juxtaposing the deterioration of these situations against Britain's celebrated legacy of counterinsurgency, this investigation identifies both the contributions and limitations of traditional tactics in such settings, exposing a disconcerting gap between ambitions and resources, intent and commitment. Building upon this detailed account of the Basra and Helmand campaigns, this volume conducts an unprecedented assessment of British military institutional adaptation in response to operations gone awry. In calling attention to the enduring effectiveness of insurgent methods and the threat posed by undergoverned spaces, David H. Ucko and Robert Egnell underscore the need for military organizations to meet the irregular challenges of future wars in new ways.

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Page Count

249

Publisher

Columbia University Press

Published Date

ISBN 10

0231535414

ISBN 13

9780231535410

The Nature of War in the Information Age

Clausewitzian Future

By: David J. Lonsdale

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The Nature of War in the Information Age

Clausewitzian Future

By: David J. Lonsdale

Much of today's Revolution in Military Affairs (RMA) literature subscribes to the idea that the information age will witness a transformation in the very nature of war. In this book, David Lonsdale puts that notion to the test.

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285

Publisher

Routledge

Published Date

ISBN 10

1135757216

ISBN 13

9781135757212

EBOOK: Elementary Number Theory

By: David Burton

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EBOOK: Elementary Number Theory

By: David Burton

Elementary Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research. Written in David Burton’s engaging style, Elementary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.

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Page Count

453

Publisher

McGraw Hill

Published Date

ISBN 10

0077145089

ISBN 13

9780077145088

Proofs and Confirmations

The Story of the Alternating-Sign Matrix Conjecture

By: David M. Bressoud

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Proofs and Confirmations

The Story of the Alternating-Sign Matrix Conjecture

By: David M. Bressoud

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.

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Page Count

292

Publisher

Cambridge University Press

Published Date

ISBN 10

1316582752

ISBN 13

9781316582756

Steel's Naval Remembrancer

From the Commencement of the War in 1793 to the End of the Year 1800

By: David Steel

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Steel's Naval Remembrancer

From the Commencement of the War in 1793 to the End of the Year 1800

By: David Steel

A summary of ships lost and captured by the British Navy during the French Revolutionary Wars, first published in 1801.

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Cambridge University Press

Published Date

ISBN 10

1108023770

ISBN 13

9781108023771

In the Middle of the Fight

An Assessment of Medium-armored Forces in Past Military Operations

By: David Eugene Johnson,Adam Grissom,Olga Oliker

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In the Middle of the Fight

An Assessment of Medium-armored Forces in Past Military Operations

By: David Eugene Johnson,Adam Grissom,Olga Oliker

An analysis of the performance of medium-armored forces across the range of military operations since World War I yields insights with significant implications for U.S. Army decisions about fielding these units in the future. The authors find that medium-armored forces fare poorly against competent, heavily armored opponents, and that the Stryker and Future Combat Systems will not fill the void created by the retirement of the M551 Sheridan.

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Page Count

337

Publisher

Rand Corporation

Published Date

ISBN 10

0833044133

ISBN 13

9780833044136

China's Military Faces the Future

By: James Lilley,David L. Shambaugh

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China's Military Faces the Future

By: James Lilley,David L. Shambaugh

This is the most up-to-date assessment of all aspects of the People's Liberation Army. Leading specialists on the Chinese military cover military leadership, defense doctrine and military readiness, preparations for high-tech warfare, military expenditure, military logistics, the scientific and technological base for defense procurement, and China's security concerns in Northeast Asia.

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Page Count

442

Publisher

Routledge

Published Date

ISBN 10

1315501031

ISBN 13

9781315501031

Phi, Pi, e and i

By: David Perkins

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Phi, Pi, e and i

By: David Perkins

Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (φ, π, e and i), each of which has recently been the individual subject of historical and mathematical expositions. But here we discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus. This material offers an excellent excuse to display the power of calculus to reveal elegant truths that are not often seen in college classes. These truths are described here via the work of such luminaries as Nilakantha, Liu Hui, Hemachandra, Khayyám, Newton, Wallis, and Euler. The book is written with the goal that an undergraduate student can read the book solo. With this goal in mind, the author provides endnotes throughout, in case the reader is unable to work out some of the missing steps. Those endnotes appear in the last chapter, Extra Help. Each chapter concludes with a series of exercises, all of which introduce new historical figures or content.

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Page Count

190

Publisher

The Mathematical Association of America

Published Date

ISBN 10

0883855895

ISBN 13

9780883855898

Insect Diapause

By: David L. Denlinger

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Insect Diapause

By: David L. Denlinger

Captures the full scope of the literature, integrating ecological and molecular mechanisms that enable insects to enter a dormant state.

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Page Count

465

Publisher

Cambridge University Press

Published Date

ISBN 10

1108497527

ISBN 13

9781108497527

Calculus and Its Origins

By: David Perkins

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Calculus and Its Origins

By: David Perkins

The story of how calculus came to be, accessible to anyone with a basic knowledge of geometry and algebra.

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Page Count

181

Publisher

MAA

Published Date

ISBN 10

0883855755

ISBN 13

9780883855751

Applied Partial Differential Equations

By: J. David Logan

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Applied Partial Differential Equations

By: J. David Logan

This text is written for the standard, one-semester, undergraduate course in elementary partial differential equations. The topics include derivations of some of the standard equations of mathematical physics (including the heat equation, the wave equation, and Laplace's equation) and methods for solving those equations on bounded and unbounded domains. Methods include eigenfunction expansions, or separation of variables, and methods based on Fourier and Laplace transforms.

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Page Count

228

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387209530

ISBN 13

9780387209531

Non-Lethal Weapons

The Law and Policy of Revolutionary Technologies for the Military and Law Enforcement

By: David A. Koplow

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Non-Lethal Weapons

The Law and Policy of Revolutionary Technologies for the Military and Law Enforcement

By: David A. Koplow

Too often, military and law enforcement authorities have found themselves constrained by inadequate weaponry. An emerging category of 'non-lethal weapons' carries promise for resolving this dilemma, proffering new capabilities for disabling opponents without inflicting death or permanent injury. This array of much more sophisticated technologies is being developed, and could emerge for use by soldiers and police in the near future. These augmented capabilities carry both immense promise and grave risks: they expand the power of law enforcement and military units, enabling them to accomplish assigned missions with greater finesse and reduced casualties. But they may also be misused - increasing maligned applications and inspiring leaders to over-rely upon a myth of 'bloodless combat'. This book explores the emerging world of non-lethal weapons by examining a series of case studies - recent real-world scenarios from five confrontations around the world where the availability of a modern arsenal might have made a difference.

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Page Count

167

Publisher

Cambridge University Press

Published Date

ISBN 10

1139456962

ISBN 13

9781139456968

A Radical Approach to Real Analysis

Second Edition

By: David Bressoud

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A Radical Approach to Real Analysis

Second Edition

By: David Bressoud

In this second edition of the MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on Infinite Summations, Differentiability and Continuity, and Convergence of Infinite Series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created. The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early 19th century. It follows Cauchy's attempts to establish a firm foundation for calculus and considers his failures as well as his successes. It culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof.

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Page Count

339

Publisher

American Mathematical Society

Published Date

ISBN 10

1470469049

ISBN 13

9781470469047

Ideals, Varieties, and Algorithms

An Introduction to Computational Algebraic Geometry and Commutative Algebra

By: David A Cox,John Little,Donal O'Shea

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Ideals, Varieties, and Algorithms

An Introduction to Computational Algebraic Geometry and Commutative Algebra

By: David A Cox,John Little,Donal O'Shea

This book details the heart and soul of modern commutative and algebraic geometry. It covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: a significantly updated section on Maple; updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR; and presents a shorter proof of the Extension Theorem.

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Page Count

565

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387356509

ISBN 13

9780387356501

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