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These prints mesh with a number of decor styles from abstract, modern, contemporary, traditional, vintage, bohemian, minimalist, or eclectic. We strive to accurately portray the color and brightness of the original paintings. we want to provide you with a replica that you will be proud to display. Color: White.

These prints mesh with a number of decor styles from abstract, modern, contemporary, traditional, vintage, bohemian, minimalist, or eclectic. We strive to accurately portray the color and brightness of the original paintings. we want to provide you with a replica that you will be proud to display. Color: White.

These prints mesh with a number of decor styles from abstract, modern, contemporary, traditional, vintage, bohemian, minimalist, or eclectic. We strive to accurately portray the color and brightness of the original paintings. we want to provide you with a replica that you will be proud to display. Color: White.

These prints mesh with a number of decor styles from abstract, modern, contemporary, traditional, vintage, bohemian, minimalist, or eclectic. We strive to accurately portray the color and brightness of the original paintings. we want to provide you with a replica that you will be proud to display. Color: White.

These prints mesh with a number of decor styles from abstract, modern, contemporary, traditional, vintage, bohemian, minimalist, or eclectic. We strive to accurately portray the color and brightness of the original paintings. we want to provide you with a replica that you will be proud to display. Color: White.

These prints mesh with a number of decor styles from abstract, modern, contemporary, traditional, vintage, bohemian, minimalist, or eclectic. We strive to accurately portray the color and brightness of the original paintings. we want to provide you with a replica that you will be proud to display. Color: White.

This wide-ranging study examines the role of the dream in medieval culture with reference to philosophical, legal and theological writings as well as literary and autobiographical works. Stephen Kruger studies the development of theories of dreaming, from the Neoplatonic and patristic writers to late medieval re-interpretations, and shows how these theories relate to autobiographical accounts and to more popular treatments of dreaming. He considers previously neglected material including one important dream vision by Nicole Oresme, and arrives at a new understanding of this literary genre, and of medieval attitudes to dreaming in general.

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This book examines whether mechanisms of accountability characteristic of democratic systems are sufficient to induce the representatives to act in the best interest of the represented. The first part of the volume focuses on the role of elections, distinguishing different ways in which they may cause representation. The second part is devoted to the role of checks and balances, between the government and the parliament as well as between the government and the bureaucracy. Overall, the essays combine theoretical discussions, game-theoretic models, case studies, and statistical analyses, within a shared analytical approach and a standardized terminology. The empirical material is drawn from the well established democracies as well as from new democracies.

"Music Theory And The Nashville Number System" is based on Grammy nominated hit songwriter Odie Blackmon's class at Vanderbilt University's Blair School of Music. Designed for songwriters, performers, musicians and audio engineers who know how to play chords on guitar or piano but haven't connected the dots of music theory or the Nashville Number System. Blackmon's book uses piano keyboard and guitar fretboard examples to prepare the student to communicate with other musicians, better understand how scales and chords works together, use chord extensions and inversions, see common patterns in chord progressions through number chart analysis, and read and write Nashville Number charts. Example charts are hand written by Blackmon and a host of Nashville's top studio players on hits they played.

Schumann's famous song cycle Dichterliebe of 1840 is one of the most enigmatic works in the Western musical repertoire. This book employs Romantic poetics and recent critical thought to help explain the mysterious magnetism of this essentially fragmentary work. A musico-poetic analysis demonstrates the voice of the "Other" and presents Schumann as the "second poet of the poem" when setting Heine's famous Lyrisches Intermezzo. Methodologically, the analysis attempts to synthesize philosophical, literary-critical, music-analytical and psycho-analytical modes of thought.

Algebraists have studied noncommutative fields (also called skew fields or division rings) less thoroughly than their commutative counterparts. Most existing accounts have been confined to division algebras, i.e. skew fields that are finite dimensional over their center. This work offers the first comprehensive account of skew fields. It is based on the author's LMS Lecture Note Volume "Skew Field Constructions". The axiomatic foundation and a precise description of the embedding problem precedes an account of algebraic and topological construction methods. The author presents his general embedding theory with full proofs, leading to the construction of skew fields. The author has simplified his treatment of equations over skew fields and has extended it by the use of matrix methods. A separate chapter describes valuations and orderings on skew fields, with a construction applicable to free fields. Numerous exercises test the reader's understanding, presenting further aspects and open problems in concise form. Notes and comments at the end of chapters provide historical background. The book will appeal to researchers in algebra, logic, and algebraic geometry, as well as graduate students in these fields.

Modern number theory, according to Hecke, dates from Gauss's quadratic reciprocity law. The various extensions of this law and the generalizations of the domains of study for number theory have led to a rich network of ideas, which has had effects throughout mathematics, in particular in algebra. This volume of the Encyclopaedia presents the main structures and results of algebraic number theory with emphasis on algebraic number fields and class field theory. Koch has written for the non-specialist. He assumes that the reader has a general understanding of modern algebra and elementary number theory. Mostly only the general properties of algebraic number fields and related structures are included. Special results appear only as examples which illustrate general features of the theory. A part of algebraic number theory serves as a basic science for other parts of mathematics, such as arithmetic algebraic geometry and the theory of modular forms. For this reason, the chapters on basic number theory, class field theory and Galois cohomology contain more detail than the others. This book is suitable for graduate students and research mathematicians who wish to become acquainted with the main ideas and methods of algebraic number theory.

This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

Tom Cohen questions the way history, ideology and politics are invoked in contemporary cultural studies. Enlisting the work of three seminal figures in literary theory--Walter Benjamin, Paul de Man, and M. Bakhtin--Cohen argues for a new politics of memory that moves beyond what he sees as our current paralyzing preoccupation with the present, and also for a new approach to the reading and analysis of cultural texts that breaks with the mimetic premises of traditional criticism.

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.

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The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a self-contained course in number theory, Fourier analysis and geometric discrepancy theory, and the relations between them, at the advanced undergraduate or beginning graduate level. It starts as a traditional course in elementary number theory, and introduces the reader to subsequent material on uniform distribution of infinite sequences, and discrepancy of finite sequences. Both modern and classical aspects of the theory are discussed, such as Weyl's criterion, Benford's law, the Koksma-Hlawka inequality, lattice point problems, and irregularities of distribution for convex bodies. Fourier analysis also features prominently, for which the theory is developed in parallel, including topics such as convergence of Fourier series, one-sided trigonometric approximation, the Poisson summation formula, exponential sums, decay of Fourier transforms, and Bessel functions.