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Course Criteria
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4.00 Credits
Film is a medium that combines a number of arts. It lies at the intersection of art and technology and of art and mass culture, and at the boundaries of the national and the global. Film is also a medium that coincides with and contributes to the invention of modern life. By exploring the expressive and representational achievements of cinema in the context of modernity and mass culture, students learn the concepts to grasp the different ways in which films create meaning, achieve their emotional impact, and respond in complex ways to the historical contexts in which they are made.
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4.00 Credits
A first course in discrete mathematics. Sets, algorithms, and induction. Combinatorics. Graphs and trees. Combinatorial circuits. Logic and Boolean algebra. Calculus Tracks Two calculus tracks are available: the standard track of Calculus I, II, and III (MATH-UA 121-123) and the Honors I, II track (MATH-UA 221, 222). Pursuing the honors track requires that the student know the material from Calculus I (MATH-UA 121), because the honors track covers material from Calculus II and III (MATH-UA 122, 123) as well as from Linear Algebra (MATH-UA 140). The honors courses MATH-UA 221, 222 count as the equivalent of two mathematics courses. Switching tracks is not encouraged. A student who intends to take the full calculus sequence should be prepared to continue on the same track for the whole sequence.
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4.00 Credits
Derivatives, antiderivatives, and integrals of functions of one variable. Applications include graphing, maximizing, and minimizing functions. Definite integrals and the fundamental theorem of calculus. Areas and volumes.
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4.00 Credits
Techniques of integration. Further applications. Plane analytic geometry. Polar coordinates and parametric equations. Infinite series, including power series.
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4.00 Credits
Functions of several variables. Vectors in the plane and space. Partial derivatives with applications. Double and triple integrals. Spherical and cylindrical coordinates. Surface and line integrals. Divergence, gradient, and curl. Theorem of Gauss and Stokes.
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4.00 Credits
The axioms of set theory; Boolean operations on sets; set-theoretic representation of relations, functions, and orderings; the natural numbers; theory of transfinite cardinal and ordinal numbers; the axiom of choice and its equivalents; and the foundations of analysis. May also cover such advanced topics as large cardinals or independence results.
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4.00 Credits
Systems of linear equations. Gaussian elimination, matrices, determinants, and Cramer's rule. Vectors, vector spaces, basis and dimension, linear transformations. Eigenvalues, eigenvectors, quadratic forms.
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4.00 Credits
Linear spaces, subspaces, and quotient spaces; linear dependence and independence; basis and dimension. Linear transformation and matrices, dual spaces and transposition. Solving linear equations. Determinants. Quadratic forms and their relation to local extrema of multivariable functions.
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4.00 Credits
Special theory, eigenvalues, and eigenvectors; Jordan canonical forms. Inner product and orthogonality. Self-adjoint mappings, matrix inequalities. Normed linear spaces and linear transformation between them. Positive matrices. Applications.
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4.00 Credits
Derivatives, antiderivatives, and integrals of functions of one real variable. Logarithmic and exponential functions. Applications to finance and economics; growth and decay models. Introduction to probability.
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