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Course Criteria
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3.00 Credits
Differential geometry uses tools from calculus and linear algebra to study the geometric properties of smooth curves and surfaces in Euclidean spaces. Topis include: arc length, surface area, geodesics, curvature, first and second fundamental forms, Gauss-Bonnett formula. Graduate students will be assigned additional assignments and/or project.
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3.00 Credits
Topics in complex variables including functions, limits, derivatives, integrals, the Cauchy-Riemann conditions, series representation of functions, Cauchy Integral formula, and elementary conformal mappings.
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3.00 Credits
Topics in complex variables including functions, limits, derivatives, integrals, the Cauchy-Riemann conditions, series representation of functions,Cauchy Integral formula, and elementary conformal mappings.
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3.00 Credits
An introduction to metric spaces, topological spaces, connectedness and compactness of topological spaces, and continuous functions on topological spaces. Graduate students enrolled in this course will complete one or more assignments that the undergraduate students will not be required to complete.
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3.00 Credits
An introduction to metric spaces, topological spaces, connectedness and compactness of topological spaces, and continuous functions on topological spaces. Graduate students enrolled in this course will complete one or more assignments that the undergraduate students will not be required to complete.
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3.00 Credits
Fractals an nonlinear systems involving feedback and iteration. Classical fractals, limits and self-similarity. Fractal dimensions. Encoding of fractals. Decoding of fractals. Iterated function systems.
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3.00 Credits
Fractals as nonlinear systems involving feedback and iteration. Classical fractals, limits and self-similarity. Fractal dimensions. Encoding of fractals. Decoding of fractals. Iterated function systems.
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3.00 Credits
The study of the theory and techniques used for the computer generation of curves and surfaces. Topics include Bernstein/Bezier and B-spline curves and surfaces, transformations and projections, affine spaces and maps, geometric continuity, curvature, subdivision and interpolation. This course is recommended for students in mathematics, engineering and computer science. Graduate students will be given an extra assignment not required of undergraduate students.
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3.00 Credits
The study of the theory and techniques used for the computer generation of curves and surfaces. Topics include Bernstein/Bezier and B-spline curves and surfaces, transformations and projections, affine spaces and maps, geometric continuity, curvature, subdivision and interpolation. This course is recommended for students in mathematics, engineering and computer science. Graduate students will be given an extra assignment not required of undergraduate students.
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3.00 Credits
A survey of mathematical topics useful in the study of areas of applied sciences such as physics, engineering and computer science. Topics include: linear algebra and matrices, ordinary differential equations, partial differential equations, Fourier series, vector calculus, complex variables, numerical methods, probability and graph theory. For non-math majors only. Graduate students will be given an extra assignment not required of undergraduate students.
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