Advanced review of principal elements of Spanish grammar. For majors, minors, and others who plan to continue with Spanish beyond SPANISH 240.

Advanced review of principal elements of Spanish grammar. For majors, minors, and others who plan to continue with Spanish beyond SPANISH 240.

Advanced review of principal elements of Spanish grammar. For majors, minors, and others who plan to continue with Spanish beyond SPANISH 240.

Advanced review of principal elements of Spanish grammar. For majors, minors, and others who plan to continue with Spanish beyond SPANISH 240.

This course is designed primarily for MM Jazz Composition and Arranging students. It is open as an elective to graduate students in other areas who possess a thorough knowledge of composition and orchestration, and software notation skills. This is a project based course on writing music for visual media. It involves the study of the work of industry standard compositions in three visual media areas, TV commercials, cartoons, and film.

Inverse and implicit functions theorems, rank of a map. Regular and critical values. Sard's theorem. Differentiable manifolds, submanifolds, embeddings, immersions and diffeomorphisms. Tangent space and bundle, differential of a map. Partitions of unity, orientation, transversality embed-dings in Rn. Vector fields, local flows. Lie bracket, Frobenius theorem. Lie groups, matrix Lie groups, left invariant vector fields, tensor fields, differential form, integration, closed and exact forms. DeRham's cohomology, vector bundles, connections, curvature.

By any measure, and at all levels, American politics is deeply polarized along partisan lines, often asymmetrically so. This tribal division along partisan lines has changed the tone of political discourse, impacted the ability of our government to function, and even spread into apolitical facets of American life. This class will delve into the origins, psychology and social dynamics of this hyper-polarization. We will seek to understand the nature of this division and examine its implications for government, society and the future of American democracy.

By any measure, and at all levels, American politics is deeply polarized along partisan lines, often asymmetrically so. This tribal division along partisan lines has changed the tone of political discourse, impacted the ability of our government to function, and even spread into apolitical facets of American life. This class will delve into the origins, psychology and social dynamics of this hyper-polarization. We will seek to understand the nature of this division and examine its implications for government, society and the future of American democracy.