For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.
Like a hunter who sees 'a bit of blood' on the trail, that's how Princeton mathematician Peter Sarnak describes the feeling of chasing an idea that seems to have a chance of success. If this is so, then the jungle of abstractions that is mathematics is full of frenzied hunters these days. They are out stalking big game: the resolution of 'The Riemann Hypothesis', seems to be in their sights. The Riemann Hypothesis is about the prime numbers, the fundamental numerical elements. Stated in 1859 by Professor Bernhard Riemann, it proposes a simple law which Riemann believed a 'very likely' explanation for the way in which the primes are distributed among the whole numbers, indivisible stars scattered without end throughout a boundless numerical universe. Just eight years later, at the tender age of thirty-nine Riemann would be dead from tuberculosis, cheated of the opportunity to settle his conjecture. For over a century, the Riemann Hypothesis has stumped the greatest of mathematical minds, but these days frustration has begun to give way to excitement. This unassuming comment is revealing astounding connections among nuclear physics, chaos and number theory, creating a frenzy of intellectual excitement amplified by the recent promise of a one million dollar bounty. The story of the quest to settle the Riemann Hypothesis is one of scientific exploration. It is peopled with solitary hermits and gregarious cheerleaders, cool calculators and wild-eyed visionaries, Nobel Prize-winners and Fields Medalists. To delve into the Riemann Hypothesis is to gain a window into the world of modern mathematics and the nature of mathematics research. Stalking the Riemann Hypothesis will open wide this window so that all may gaze through it in amazement.
For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.
The analysis of complex systems--from financial markets and voting patterns to ecosystems and food webs--can be daunting for newcomers to the subject, in part because existing methods often require expertise across multiple disciplines. This book shows how a single technique--the partition decoupling method--can serve as a useful first step for modeling and analyzing complex systems data. Accessible to a broad range of backgrounds and widely applicable to complex systems represented as high-dimensional or network data, this powerful methodology draws on core concepts in network modeling and analysis, cluster analysis, and a range of techniques for dimension reduction. The book explains these and other essential concepts and provides several real-world examples to illustrate how a data-driven approach can illuminate complex systems. Provides a comprehensive introduction to modeling and analysis of complex systems with minimal mathematical prerequisites Focuses on a single technique, thereby providing an easy entry point to the subject Explains analytic techniques using actual data from the social sciences Uses only linear algebra to model and analyze large data sets Includes problems and real-world examples An ideal textbook for students and invaluable resource for researchers with a wide range of backgrounds and preparation Proven in the classroom
Dan Zahavi offers an in-depth and up-to-date analysis of central and contested aspects of the philosophy of Edmund Husserl, the founder of phenomenology. What is ultimately at stake in Husserl's phenomenological analyses? Are they primarily to be understood as investigations of consciousness or are they equally about the world? What is distinctive about phenomenological transcendental philosophy, and what kind of metaphysical import, if any, might it have? Husserl's Legacy offers an interpretation of the more overarching aims and ambitions of Husserlian phenomenology and engages with some of the most contested and debated questions in phenomenology. Central to its interpretative efforts is the attempt to understand Husserl's transcendental idealism. Zahavi argues that Husserl was not a sophisticated introspectionist, not a phenomenalist, nor an internalist, not a quietist when it comes to metaphysical issues, and not opposed to all forms of naturalism. Husserl's Legacy argues that Husserl's phenomenology is as much about the world as it is about consciousness, and that a proper grasp of Husserl's transcendental idealism reveals the fundamental importance of facticity and intersubjectivity.
This book is aimed to explain the creation of artworks and their evaluation, and offers a new concept of aesthetics and beauty of artworks. Following and reconstructing Peircean realist epistemology, Aesthetics is one of the three normative sciences, along with Logic (Theoretic) and Ethics, which are the three different modes of representing reality. Aesthetics is the mode of artistic representation of reality, and the created artworks are judged beautiful when proven as an aesthetic true representation of reality. Artists aim to represent reality truly, and hence, beautifully, in order to enhance our knowledge of it and to afford us insights on how to better conduct our life in society.
A seventy-year-old Northwestern journalism professor, Loren Ghiglione, and two twenty-something Northwestern journalism students, Alyssa Karas and Dan Tham, climbed into a minivan and embarked on a three-month, twenty-eight state, 14,063-mile road trip in search of America’s identity. After interviewing 150 Americans about contemporary identity issues, they wrote this book, which is part oral history, part shoe-leather reporting, part search for America’s future, part memoir, and part travel journal. On their journey they retraced Mark Twain’s travels across America—from Hannibal, Missouri, to Chicago, New York, Boston, Philadelphia, Washington, DC, New Orleans, Salt Lake City, San Francisco, and Seattle. They hoped Twain’s insights into the late nineteenth-century soul of America would help them understand the America of today and the ways that our cultural fabric has shifted. Their interviews focused on issues of race, religion, gender, sexual orientation, and immigration status. The timely trip occurred as the United States was poised to replace president Barack Obama, an icon of multiculturalism and inclusion, with Donald Trump, whose white-identity agenda promoted exclusion and division. What they learned along the way paints an engaging portrait of the country during this crucial moment of ideological and political upheaval.
When Speech and Audio Signal Processing published in 1999, it stood out from its competition in its breadth of coverage and its accessible, intutiont-based style. This book was aimed at individual students and engineers excited about the broad span of audio processing and curious to understand the available techniques. Since then, with the advent of the iPod in 2001, the field of digital audio and music has exploded, leading to a much greater interest in the technical aspects of audio processing. This Second Edition will update and revise the original book to augment it with new material describing both the enabling technologies of digital music distribution (most significantly the MP3) and a range of exciting new research areas in automatic music content processing (such as automatic transcription, music similarity, etc.) that have emerged in the past five years, driven by the digital music revolution. New chapter topics include: Psychoacoustic Audio Coding, describing MP3 and related audio coding schemes based on psychoacoustic masking of quantization noise Music Transcription, including automatically deriving notes, beats, and chords from music signals. Music Information Retrieval, primarily focusing on audio-based genre classification, artist/style identification, and similarity estimation. Audio Source Separation, including multi-microphone beamforming, blind source separation, and the perception-inspired techniques usually referred to as Computational Auditory Scene Analysis (CASA).
We live in an electronic world, saturated with electronic sounds. Yet, electronic sounds aren’t a new phenomenon; they have long permeated our sonic landscape. What began as the otherworldly sounds of the film score for the 1956 film Forbidden Planet and the rarefied, new timbres of Stockhausen’s Kontakte a few years later, is now a common soundscape in technology, media, and an array of musical genres and subgenres. More people than ever before can produce and listen to electronic music, from isolated experimenters, classical and jazz musicians, to rock musicians, sound recordists, and the newer generations of electronic musicians making hip-hop, house, techno, and ambient music. Increasingly we are listening to electronic sounds, finding new meanings in them, experimenting with them, and rehearing them as listeners and makers. Live Wires explores how five key electronic technologies—the tape recorder, circuit, computer, microphone, and turntable—revolutionized musical thought. Featuring the work of major figures in electronic music—including everyone from Schaeffer, Varèse, Xenakis, Babbitt, and Oliveros to Eno, Keith Emerson, Grandmaster Flash, Juan Atkins, and Holly Herndon—Live Wires is an arresting discussion of the powerful musical ideas that are being recycled, rethought, and remixed by the most interesting electronic composers and musicians today.
Winner of the 2000 The Edward Goodwin Ballard Prize in Phenomenology In the rigorous and highly original Self-Awareness and Alterity, Dan Zahavi provides a sustained argument that phenomenology, especially in its Husserlian version, can contribute something decisive to the analysis of self-awareness. Taking on recent discussions within both analytical philosophy (Shoemaker, Castaneda, Nagel) and contemporary German philosophy (Henrich, Frank, Tugendhat), Zahavi argues that the phenomenological tradition has much more to offer when it comes to the problem of self-awareness than is normally assumed. As a contribution to the current philosophical debate concerning self-awareness, the book presents a comprehensive reconstruction of Husserl's theory of pre-reflective self-awareness, thereby criticizing a number of prevalent interpretations and a systematic discussion of a number of phenomenological insights related to this issue, including analyses of the temporal, intentional, reflexive, bodily, and social nature of the self.
In None so Fit to Break the Chains Dan Swain offers an interpretation of Marx's ethics that foregrounds his commitment to working class self-emancipation and uses it as a guiding thread to interpret the different aspects of Marx’s ethical thought.
Mission Driven Bureaucrats suggests that workers can often do better with more empowerment and less compliance-oriented management. Honig provides strategies for managers and suggestions for what everyday citizens can do to support the empowerment of bureaucrats in their governments.
It's a diabolical game of cat and mouse as top TEC agent Jack Logan tracks a scavenger through time and history . . . USA, 2007: There's a deadly thief on the loose, with stolen millions and a time machine that could virtually shut down the planet. Now the world's most covert agency--the Time Enforcement Commission--must find him before he destroys the world. TEC cop Jack Logan gets his first glimpse of the scavenger at the Empire State Building--just seconds before a B-25 slams into it on a summer morning in 1945. The felon escapes, and Logan survives to discover huge disturbances in the timestream--all connected to the scavenger's shopping list. From the fabled Lost Dutchman Mine to a Mississippi steamboat and a cyberfortress unsettingly close to the nation's capital, Logan races to apprehend the scavenger before he executes his chilling plan of global murder . . .
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