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What does the sublime sound like? Harmonious, discordant, noisy, rustling, silent? Miranda Eva Stanyon rereads and resounds this crucial aesthetic category in English and German literatures of the long eighteenth century from a musical perspective and shows how sonorous sublimes lay at the heart of a central and transformative discourse. For Enlightenment and Romantic era listeners, the musical sublime represented a sonic encounter of the most extreme kind, one that tested what humans were capable of feeling, imagining, thinking, and therefore becoming.The sublime and music have not always sung from the same hymn sheet, Stanyon observes. She charts an antagonistic intimacy between the two, from the sublime's rise to prominence in the later seventeenth century, through the upheavals associated with Kant in the late eighteenth century, and their reverberations in the nineteenth. Offering readings of canonical texts by Longinus, Dryden, Burke, Klopstock, Herder, Coleridge, De Quincey, and others alongside lesser-known figures, she shows how the literary sublime was inextricable from musical culture, from folksongs and ballads to psalmody, polychoral sacred music, and opera. Deeply interdisciplinary, Resounding the Sublime draws literature into dialogue with sound studies, musicology, and intellectual and cultural history to offer new perspectives on the sublime as a phenomenon which crossed media, disciplines, and cultures.An interdisciplinary study of sound in history, the book recovers varieties of the sublime crucial for understanding both the period it covers and the genealogy of modern and postmodern aesthetic discourses. In resounding the sublime, Stanyon reveals a phenomenon which was always already resonant. The sublime emerges not only as the aesthetic of the violently powerful, a-rational, or unrepresentable, but as a variegated discourse with competing dissonant, harmonious, rustling, noisy, and silent strains, one in which music and sound illustrate deep divisions over issues of power, reason, and representation.

Aesthetics in literature --- English literature --- German literature --- Music in literature --- Sublime, The --- Sublime, The, in literature --- Sublime, The, in music --- Music --- History and criticism --- History

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Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mirror symmetry). As such, the book will appeal to experts with a wide range of backgrounds.

Mathematics. --- Algebra. --- Field theory (Physics). --- Dynamics. --- Ergodic theory. --- Differential geometry. --- Dynamical Systems and Ergodic Theory. --- Differential Geometry. --- Field Theory and Polynomials. --- Differential geometry --- Ergodic transformations --- Dynamical systems --- Kinetics --- Classical field theory --- Continuum physics --- Math --- Differentiable dynamical systems. --- Global differential geometry. --- Physics --- Continuum mechanics --- Geometry, Differential --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Geometry, Algebraic. --- Mathematics --- Mathematical analysis --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics

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Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mirror symmetry). As such, the book will appeal to experts with a wide range of backgrounds.

Algebra --- Differential geometry. Global analysis --- Ergodic theory. Information theory --- Mathematics --- Classical mechanics. Field theory --- algebra --- differentiaal geometrie --- wiskunde --- fysica --- mechanica --- dynamica --- informatietheorie