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Course Criteria
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3.00 Credits
PQ: MATH 26200, 26300, 27000, 27200, and 27400; and consent of director or co-director of undergraduate studies. MATH 31700 covers smooth manifolds, tangent bundles, vector fields, Frobenius theorem, Sard's theorem, Whitney embedding theorem, and transversality. MATH 31800 considers fundamental group and covering spaces; Lie groups and Lie algebras; and principal bundles, connections, introduction to Riemannian geometry, geodesics, and curvature. Topics in MATH 31900 are cell complexes, homology, and cohomology; and Mayer-Vietoris theorem, Kunneth theorem, cup products, duality, and geometric applications. Autumn, Winter, Spring.
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3.00 Credits
PQ: MATH 25700-25800-25900, and consent of director or co-director of undergraduate studies. MATH 32500 deals with groups and commutative rings. MATH 32600 investigates elements of the theory of fields and of Galois theory, as well as noncommutative rings. MATH 32700 introduces other basic topics in algebra. Autumn, Winter, Spring.
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3.00 Credits
PQ: Linear algebra, finite fields, and a first course in group theory (Jordan-Holder and Sylow theorems) required; prior knowledge of algorithms not required. We consider the asymptotic complexity of some of the basic problems of computational group theory. The course demonstrates the relevance of a mix of mathematical techniques, ranging from combinatorial ideas, the elements of probability theory, and elementary group theory, to the theories of rapidly mixing Markov chains, applications of simply stated consequences of the Classification of Finite Simple Groups (CFSG), and, occasionally, detailed information about finite simple groups. No programming problems are assigned. L. Babai. Spring. Not offered 2009 C10; will be offered 201 0 -11.
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3.00 Credits
PQ: Consent of instructor. This course covers the basic mathematical theory behind numerical solution of partial differential equations. We investigate the convergence properties of finite element, finite difference and other discretization methods for solving partial differential equations, introducing Sobolev spaces and polynomial approximation theory. We emphasize error estimators, adaptivity, and optimal-order solvers for linear systems arising from PDEs. Special topics include PDEs of fluid mechanics, max-norm error estimates, and Bananch-space operator-interpolation techniques. T. Dupont. Spring.
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3.00 Credits
Background in music not required. Students must confirm enrollment by attending one of the first two sessions of class. This course meets the general education requirement in the dramatic, musical, and visual arts. This one-quarter course is designed to enrich the listening experience of students, particularly with respect to the art music of the Western European and American concert tradition. Students are introduced to the basic elements of music and the ways that they are integrated to create works in various styles. Particular emphasis is placed on musical form and on the potential for music to refer to and interact with aspects of the world outside. Autumn, Winter, Spring.
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3.00 Credits
Background in music not required. Students must confirm enrollment by attending one of the first two sessions of class. This course meets the general education requirement in the dramatic, musical, and visual arts. This course is a selected survey of classical, popular, and folk music traditions from around the world. The goals are not only to expand our skills as listeners but also to redefine what we consider music to be and, in the process, stimulate a fresh approach to our own diverse musical traditions. In addition, the role of music as ritual, aesthetic experience, mode of communication, and artistic expression is explored. Autumn, Winter, Spring.
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3.00 Credits
Background in music not required. Students must confirm enrollment by attending one of the first two sessions of class. This course meets the general education requirement in the dramatic, musical, and visual arts. In this variant of the introductory course in music, students explore the language of music through coordinated listening, analysis, and exercises in composition. A study of a wide diversity of musical styles serves as an incentive for student compositions in those styles. Autumn, Winter, Spring.
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3.00 Credits
Background in music not required. Students must confirm enrollment by attending one of the first two sessions of class. This course meets the general education requirement in the dramatic, musical, and visual arts. This course aims to develop students' analytical and critical tools by focusing on a select group of works drawn from the Western European and American concert tradition. The texts for the course are recordings. Through listening, written assignments, and class discussion, we explore topics such as compositional strategy, conditions of musical performance, interactions between music and text, and the relationship between music and ideology as they are manifested in complete compositions. Autumn, Winter, Spring.
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3.00 Credits
A. Robertson. Winter.
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3.00 Credits
Prior music course or ability to read music not required. Students must confirm enrollment by attending one of the first two sessions of class. This two-quarter sequence meets the general education requirement in civilization studies; it does not meet the general education requirement in the dramatic, musical, and visual arts. This two-quarter sequence explores musical works of broad cultural significance in Western civilization. We study pieces not only from the standpoint of musical style but also through the lenses of politics, intellectual history, economics, gender, cultural studies, and so on. Readings are taken both from our music textbook and from the writings of a number of figures such as St. Benedict of Nursia and Martin Luther. In addition to lectures, students discuss important issues in the readings and participate in music listening exercises in smaller sections.
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