John W. Dawson, Jr.'s Books

Why Prove it Again?

Alternative Proofs in Mathematical Practice

By: John W. Dawson, Jr.

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Why Prove it Again?

Alternative Proofs in Mathematical Practice

By: John W. Dawson, Jr.

This monograph considers several well-known mathematical theorems and asks the question, “Why prove it again?” while examining alternative proofs. It explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how they judge whether two proofs of a given result are different. While a number of books have examined alternative proofs of individual theorems, this is the first that presents comparative case studies of other methods for a variety of different theorems. The author begins by laying out the criteria for distinguishing among proofs and enumerates reasons why new proofs have, for so long, played a prominent role in mathematical practice. He then outlines various purposes that alternative proofs may serve. Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues’ Theorem, the Prime Number Theorem, and the proof of the irreducibility of cyclotomic polynomials. Why Prove It Again? will appeal to a broad range of readers, including historians and philosophers of mathematics, students, and practicing mathematicians. Additionally, teachers will find it to be a useful source of alternative methods of presenting material to their students.

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211

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Birkhäuser

Published Date

ISBN 10

3319173685

ISBN 13

9783319173689

Hitler's Scientists

Science, War, and the Devil's Pact

By: John Cornwell

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Hitler's Scientists

Science, War, and the Devil's Pact

By: John Cornwell

An eye-opening account of the rise of science in Germany through to Hitler’s regime, and the frightening Nazi experiments that occurred during the Reich A shocking account of Nazi science, and a compelling look at the the dramatic rise of German science in the nineteenth century, its preeminence in the early twentieth, and the frightening developments that led to its collapse in 1945, this is the compelling story of German scientists under Hitler’s regime. Weaving the history of science and technology with the fortunes of war and the stories of men and women whose discoveries brought both benefits and destruction to the world, Hitler's Scientists raises questions that are still urgent today. As science becomes embroiled in new generations of weapons of mass destruction and the war against terrorism, as advances in biotechnology outstrip traditional ethics, this powerful account of Nazi science forms a crucial commentary on the ethical role of science.

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577

Publisher

Penguin

Published Date

ISBN 10

1101640154

ISBN 13

9781101640159

Elements of Mathematics

From Euclid to Gödel

By: John Stillwell

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Elements of Mathematics

From Euclid to Gödel

By: John Stillwell

An exciting look at the world of elementary mathematics Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics—but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.

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440

Publisher

Princeton University Press

Published Date

ISBN 10

0691178542

ISBN 13

9780691178547

Roads to Infinity

The Mathematics of Truth and Proof

By: John Stillwell

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Roads to Infinity

The Mathematics of Truth and Proof

By: John Stillwell

Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is h

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202

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CRC Press

Published Date

ISBN 10

1439865507

ISBN 13

9781439865507

The Story of Proof

Logic and the History of Mathematics

By: John Stillwell

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The Story of Proof

Logic and the History of Mathematics

By: John Stillwell

How the concept of proof has enabled the creation of mathematical knowledge The Story of Proof investigates the evolution of the concept of proof—one of the most significant and defining features of mathematical thought—through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as “infinitesimal algebra,” and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved. Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field’s power and progress.

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457

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Princeton University Press

Published Date

ISBN 10

069123437X

ISBN 13

9780691234373

A Practical Logic of Cognitive Systems

The Reach of Abduction: Insight and Trial

By: Dov M. Gabbay,John Woods

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A Practical Logic of Cognitive Systems

The Reach of Abduction: Insight and Trial

By: Dov M. Gabbay,John Woods

The present work is a continuation of the authors' acclaimed multi-volume APractical Logic of Cognitive Systems. After having investigated the notion ofrelevance in their previous volume, Gabbay and Woods now turn to abduction. Inthis highly original approach, abduction is construed as ignorance-preservinginference, in which conjecture plays a pivotal role. Abduction is a response to acognitive target that cannot be hit on the basis of what the agent currently knows.The abducer selects a hypothesis which were it true would enable the reasoner to attain his target. He concludes from this fact that the hypothesis may be conjectured. In allowing conjecture to stand in for the knowledge he fails to have, the abducer reveals himself to be a satisficer, since an abductive solution is not a solution from knowledge. Key to the authors' analysis is the requirement that a conjectured proposition is not just what a reasoner might allow himself to assume, but a proposition he must defeasibly release as a premiss for further inferences in the domain of enquiry in which the original abduction problem has arisen.The coverage of the book is extensive, from the philosophy of science tocomputer science and AI, from diagnostics to the law, from historical explanation to linguistic interpretation. One of the volume's strongest contributions is its exploration of the abductive character of criminal trials, with special attention given to the standard of proof beyond a reasonable doubt.Underlying their analysis of abductive reasoning is the authors' conception ofpractical agency. In this approach, practical agency is dominantly a matter of thecomparative modesty of an agent's cognitive agendas, together with comparatively scant resources available for their advancement. Seen in these ways, abduction has a significantly practical character, precisely because it is a form of inference that satisfices rather than maximizes its response to the agent's cognitive target.The Reach of Abduction will be necessary reading for researchers, graduatestudents and senior undergraduates in logic, computer science, AI, belief dynamics, argumentation theory, cognitive psychology and neuroscience, linguistics, forensic science, legal reasoning and related areas.Key features:- Reach of Abduction is fully integrated with a background logic of cognitive systems.- The most extensive coverage compared to competitive works.- Demonstrates not only that abduction is a form of ignorance preservinginference but that it is a mode of inference that is wholly rational.- Demonstrates the satisficing rather than maximizing character ofabduction.- The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticatedconceptual analysis and extensive logical modelling.· Reach of Abduction is fully integrated with a background logic of cognitive systems.· The most extensive coverage compared to competitive works· Demonstrates not only that abduction is a form of ignorance preservinginference but that it is a mode of inference that is wholly rational.· Demonstrates the satisficing rather than maximizing character ofabduction.· The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticatedconceptual analysis and extensive logical modelling.

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497

Publisher

Elsevier

Published Date

ISBN 10

0080460925

ISBN 13

9780080460925

Theology

Good, Bad, and Mysterious

By: John Warwick Montgomery

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Theology

Good, Bad, and Mysterious

By: John Warwick Montgomery

From the author’s Introduction: As this book’s subtitle has it, it’s a “potpourri.” That expression can be defined as “a mixture of dried petals and spices placed in a bowl to perfume a room.” But, having just published—at New Reformation Press—a little culinary masterpiece (A Gastronomic Vade-Mecum), I am thinking in terms of the secondary definition: “an unusual or interesting mixture of ingredients.” Either way, you will surely enjoy this collection of essays. They are unusual and interesting—and they will perfume your thinking as to ultimate issues. A sampling of essays in the present collection: • Resurrection and Legal Evidence • Did Jesus Physically Rise from the Dead? • Chronological Contradictions in the Gospels? • A More Consistent Application of Literary “Higher Criticism” • A Short and Easie Method with Postmodernists • Law & Morality: Friends or Foes? • Demon Possession: A Brief Commentary • Transhumanism? • Muslims As Two-Faced • The Stereotypic Clergyman • On Innovative Theologians • Racism in American Lutheranism • Do Christian Children lose Contact with Reality? • Those Who Have Not Heard the Gospel: A Construct • Terrorism and Revolution: Are They Ever Justified? Professor Montgomery, who is an American, British, and French citizen and who resides in Strasbourg, France, is a polymath, the author of more than 60 books in 5 languages, and a world-renowned defender of classic Christian faith. His credentials include: • Ph.D. (U. Chicago), D.Théol. (U. Strasbourg, France), LL.D. (Cardiff U., Wales), plus 8 other academic degrees. • Professor Emeritus of Law and Humanities, University of Bedfordshire (U.K.); Distinguished Professor-at-Large, 1517: The Legacy Project (California, U.S.A.); Director, International Academy of Apologetics, Evangelism and Human Rights (Strasbourg, France). • Barrister-at-Law (England and Wales); Avocat à la Cour (Paris); Member of the California, District of Columbia, Virginia, and Washington State bars, and the bar of the Supreme Court of the United States; Certified Fraud Examiner. • Honorary Chairman, Academic Board, International Institute for Religious Freedom, World Evangelical Fellowship. Websites: www.jwm.christendom.co.uk, www.apologeticsacademy.eu, www.newreformationpress.com/jwm-books, www.newreformationpress.com/jwm-audio

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253

Publisher

Wipf and Stock Publishers

Published Date

ISBN 10

1725294427

ISBN 13

9781725294424

The Civil War Years in Utah

The Kingdom of God and the Territory That Did Not Fight

By: John Gary Maxwell

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The Civil War Years in Utah

The Kingdom of God and the Territory That Did Not Fight

By: John Gary Maxwell

In 1832 Joseph Smith, Jr., the Mormons’ first prophet, foretold of a great war beginning in South Carolina. In the combatants’ mutual destruction, God’s purposes would be served, and Mormon men would rise to form a geographical, political, and theocratic “Kingdom of God” to encompass the earth. Three decades later, when Smith’s prophecy failed with the end of the American Civil War, the United States left torn but intact, the Mormons’ perspective on the conflict—and their inactivity in it—required palliative revision. In The Civil War Years in Utah, the first full account of the events that occurred in Utah Territory during the Civil War, John Gary Maxwell contradicts the patriotic mythology of Mormon leaders’ version of this dark chapter in Utah history. While the Civil War spread death, tragedy, and sorrow across the continent, Utah Territory remained virtually untouched. Although the Church of Jesus Christ of Latter-day Saints—and its faithful—proudly praise the service of an 1862 Mormon cavalry company during the Civil War, Maxwell’s research exposes the relatively inconsequential contribution of these Nauvoo Legion soldiers. Active for a mere ninety days, they patrolled overland trails and telegraph lines. Furthermore, Maxwell finds indisputable evidence of Southern allegiance among Mormon leaders, despite their claim of staunch, long-standing loyalty to the Union. Men at the highest levels of Mormon hierarchy were in close personal contact with Confederate operatives. In seeking sovereignty, Maxwell contends, the Saints engaged in blatant and treasonous conflict with Union authorities, the California and Nevada Volunteers, and federal policies, repeatedly skirting open warfare with the U.S. government. Collective memory of this consequential period in American history, Maxwell argues, has been ill-served by a one-sided perspective. This engaging and long-overdue reappraisal finally fills in the gaps, telling the full story of the Civil War years in Utah Territory.

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373

Publisher

University of Oklahoma Press

Published Date

ISBN 10

0806155272

ISBN 13

9780806155272

Theatre in Dublin, 1745–1820

A Calendar of Performances

By: John C. Greene

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Theatre in Dublin, 1745–1820

A Calendar of Performances

By: John C. Greene

Theatre in Dublin,1745–1820: A Calendar of Performances is the first comprehensive, daily compendium of more than 18,000 performances that took place in Dublin’s many professional theatres, music halls, pleasure gardens, and circus amphitheatres between Thomas Sheridan’s becoming the manager at Smock Alley Theatre in 1745 and the dissolution of the Crow Street Theatre in 1820. The daily performance calendar for each of the seventy-five seasons recorded here records and organizes all surviving documentary evidence pertinent to each evening’s entertainments, derived from all known sources, but especially from playbills and newspaper advertisements. Each theatre’s daily entry includes all preludes, mainpieces, interludes, and afterpieces with casts and assigned roles, followed by singing and singers, dancing and dancers, and specialty entertainments. Financial data, program changes, rehearsal notices, authorship and premiere information are included in each component’s entry, as is the text of contemporary correspondence and editorial contextualization and commentary, followed by other additional commentary, such as the many hundreds of printed puffs, notices, and performance reviews. In the cases of the programs of music halls, pleasure gardens, and circuses, the playbills have generally been transcribed verbatim. The calendar for each season is preceded by an analytical headnote that presents several categories of information including, among other things, an alphabetical listing of all members of each company, whether actors, musicians, specialty artists, or house servants, who are known to have been employed at each venue. Limited biographical commentary is included, particularly about performers of Irish origin, who had significant stage careers but who did not perform in London. Each headnote presents the seasons’s offerings of entertainments of each theatrical type (prelude, mainpiece, interlude, afterpiece) analyzed according to genre, including a list of the number of plays in each genre and according to period in which they were first performed. The headnote also notes the number of different plays by Shakespeare staged during each season and gives particular attention to entertainments of “special Irish interest.” The various kinds of benefit performance and command performances are also noted. Finally, this Calendar of Performances contains an appendix that furnishes a season-by-season listing of the plays that were new to the London patent theatres, and, later, of the important “minors.” This information is provided in order for us to understand the interrelatedness of the London and Dublin repertories.

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Page Count

801

Publisher

Lehigh University Press

Published Date

ISBN 10

1611461154

ISBN 13

9781611461152

Book's by John W. Dawson, Jr.

Why Prove it Again?

Why Prove it Again?

Hitler's Scientists

Hitler's Scientists

Elements of Mathematics

Elements of Mathematics

Roads to Infinity

Roads to Infinity

The Story of Proof

The Story of Proof

A Practical Logic of Cognitive Systems

A Practical Logic of Cognitive Systems

Theology

Theology

The Civil War Years in Utah

The Civil War Years in Utah

Theatre in Dublin, 1745–1820

Theatre in Dublin, 1745–1820

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