Author: Stephen Abbott Publisher: Princeton University Press ISBN: 0691206082 Category : Mathematics Languages : en Pages : 408
Book Description
"The proof stage is the story of the unexpected collaborations and resonances between theater and mathematics and how they have evolved since the turn of the twentieth century. Toward the end of the 1800s, unsettling discoveries about alternate geometries and the mathematical infinite began to reveal that, despite its reputation for absolute certainty, mathematical truth is not immutable. At the same time, new, experimental forms of theater were rapidly developing-some inspired by these very upheavals in mathematics. Both disciplines were, and are, characterized by a quest for truth and a shared ability to investigate their respective limitations. Stephen Abbott provides the first systematic, book-length treatment of the interactions between mathematics and theater that have occurred over the last 120 years. Drawing on the author's fifteen years of experience researching and teaching a course on the subject, the book examines how the two disciplines reveal novel insights about one another. Stages of Uncertainty follows the path of playwrights that engaged mathematics such as Alfred Jarry, Stanislav Witkeiwicz, Samuel Beckett, Bertolt Brecht, Felix Durrenmatt, Tom Stoppard, Micheal Frayn, and Simon McBurney. Intertwined with this history is the history of mathematics; along the way, Abbott describes the development of quantum mechanics, chaos theory, incompleteness, and alternative geometries that occurred as these plays were being written. The main arguments are that these two domains have deep resonances, including shared notions of uncertainty, self-reference, recursion, and orientation, and that theater has engaged deeply and innovatively with math for many years. Abbott reveals a unique portrait of mathematics, one that is unexpected and deeply human"--
Author: David Auburn Publisher: Dramatists Play Service Inc ISBN: 9780822217824 Category : Drama Languages : en Pages : 84
Book Description
THE STORY: On the eve of her twenty-fifth birthday, Catherine, a troubled young woman, has spent years caring for her brilliant but unstable father, a famous mathematician. Now, following his death, she must deal with her own volatile emotions; the
Author: Stephen Abbott Publisher: Princeton University Press ISBN: 0691243360 Category : Performing Arts Languages : en Pages : 408
Book Description
How playwrights from Alfred Jarry and Samuel Beckett to Tom Stoppard and Simon McBurney brought the power of abstract mathematics to the human stage The discovery of alternate geometries, paradoxes of the infinite, incompleteness, and chaos theory revealed that, despite its reputation for certainty, mathematical truth is not immutable, perfect, or even perfectible. Beginning in the last century, a handful of adventurous playwrights took inspiration from the fractures of modern mathematics to expand their own artistic boundaries. Originating in the early avant-garde, mathematics-infused theater reached a popular apex in Tom Stoppard’s 1993 play Arcadia. In The Proof Stage, mathematician Stephen Abbott explores this unlikely collaboration of theater and mathematics. He probes the impact of mathematics on such influential writers as Alfred Jarry, Samuel Beckett, Bertolt Brecht, and Stoppard, and delves into the life and mathematics of Alan Turing as they are rendered onstage. The result is an unexpected story about the mutually illuminating relationship between proofs and plays—from Euclid and Euripides to Gödel and Godot. Theater is uniquely poised to discover the soulful, human truths embedded in the austere theorems of mathematics, but this is a difficult feat. It took Stoppard twenty-five years of experimenting with the creative possibilities of mathematics before he succeeded in making fractal geometry and chaos theory integral to Arcadia’s emotional arc. In addition to charting Stoppard’s journey, Abbott examines the post-Arcadia wave of ambitious works by Michael Frayn, David Auburn, Simon McBurney, Snoo Wilson, John Mighton, and others. Collectively, these gifted playwrights transform the great philosophical upheavals of mathematics into profound and sometimes poignant revelations about the human journey.
Author: Andrew Wohlgemuth Publisher: Courier Corporation ISBN: 0486141683 Category : Mathematics Languages : en Pages : 385
Book Description
The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.
Author: Richard H. Hammack Publisher: ISBN: 9780989472111 Category : Mathematics Languages : en Pages : 314
Book Description
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Author: Martin Aigner Publisher: Springer Science & Business Media ISBN: 3662223430 Category : Mathematics Languages : en Pages : 194
Book Description
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author: Juan C. Bicarregui Publisher: Springer Science & Business Media ISBN: 1447115325 Category : Mathematics Languages : en Pages : 236
Book Description
Not so many years ago, it would have been difficult to find more than a handful of examples of the use of formal methods in industry. Today however, the industrial application of formal methods is becoming increasingly common in a variety of application areas, particularly those with a safety, security or financially critical aspects. Furthermore, in situations where a particularly high level of assurance is required, formal proof is broadly accepted as being of value. Perhaps the major benefit of formalisation is that it enables formal symbolic manip ulation of elements of a design and hence can provide developers with a variety of analyses which facilitate the detection of faults. Proof is just one of these possible formal activities, others, such as test case generation and animation, have also been shown to be effective bug finders. Proof can be used for both validation and verifi cation. Validation of a specification can be achieved by proving formal statements conjectured about the required behaviours of the system. Verification of the cor rectness of successive designs can be achieved by proof of a prescribed set of proof obligations generated from the specifications.
Author: Mywish K. Maredia Publisher: Intl Food Policy Res Inst ISBN: Category : Social Science Languages : en Pages : 48
Book Description
Assessing impacts of public investments has long captured the interest and attention of the development community. This paper presents the evolution of different methods and approaches used for ex ante appraisal, monitoring, project evaluation, and impact assessment over the last five decades. Among these tools, impact assessment (IA) conducted retrospectively comes closest to providing the proof of development effectiveness. It is defined as the systematic analysis of the significant or lasting changes in people's lives brought about by a given action or series of actions in relation to a counterfactual. There are three basic types of retrospective IAs: macro-level IAs that focus on the contribution of developmental efforts to an impact goal aggregated at a sector or a system level; micro-level impact evaluations (IEs) concerned with estimating the average effect of an intervention on outcomes at the beneficiary level; and micro-level ex post impact analysis concerned with total effects of a development effort after the outputs are scaled-up. Ex post IAs have evolved and expanded over the decades in both breadth and depth of analysis in response to evolving development themes and methodological advancements. The increased emphasis on learning from evaluations has also seen responses from both quantitative and qualitative camps of the evaluation community. The paper argues that generation of robust knowledge that feeds into making developmental policies and investment decisions requires a hierarchical and cumulative approach to "improving the proof" through rigorous and a variety of impact assessment methods applied incrementally at the project, program and system level. Subjecting as many development interventions as resources allow to rigorous impact assessment based on a common framework can help build a critical body of evidence on impacts of development interventions, which can then be subjected to meta-analyses to help assimilate results across different studies and build a knowledge base on what works and what does not.
Author: Jiahong He Publisher: Springer ISBN: 9811080259 Category : Law Languages : en Pages : 296
Book Description
This book offers the first theoretical approach to rules of evidence and the practice of judicial proof in China written in English by a Chinese professor. As Prof. He’s first representative work, based on over three decades of studying and researching evidence law, it clarifies concepts relevant to evidence law, highlights the value of studying evidence law, re-examines the domain of presumption, reviews central problems in obtaining evidence, and discusses the reasons for misjudged cases. In brief, the book not only presents all major aspects of Chinese rules of evidence in criminal justice, but also introduces readers to the latest developments from a global perspective.
Author: Stephen Abbott
Author: David Auburn
Author: Stephen Abbott
Author: Andrew Wohlgemuth
Author: Richard H. Hammack
Author: Martin Aigner
Author: Rebecca Goldstein
Author: Juan C. Bicarregui
Author: Mywish K. Maredia
Author: Jiahong He