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Course Criteria
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3.00 Credits
Prerequisites: CMP SCI/MATH 3000, MATH 2000 and MATH 2450. Analytic approach to the study of projective spaces. Theorems of Desargues, Pascal, and Brianchon. Projective properties of conics.
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3.00 Credits
Prerequisite: CMP SCI/MATH 3000 and MATH 2000. Geometry of curves and surfaces in Euclidean three-space. Calculus on a surface. Intrinsic geometry of surfaces.
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3.00 Credits
Prerequisite: CMP SCI/MATH 3000 and MATH 2000 or consent of department. A development of portions of Euclidean geometry from a selected set of axioms, including a discussion of consistency, independence, categoricity, and completeness of the axioms.
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3.00 Credits
Prerequisite: CMP SCI/MATH 3000 and MATH 2000 or consent of the department. A summary of the history of the non- Euclidean geometries and a study of hyperbolic plane geometry.
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3.00 Credits
Prerequisite: CMP SCI/MATH 3000 and MATH 2000 or consent of the department. A study of topological spaces, including the concepts of limit, continuity, connectedness, compactness, etc. Special emphasis placed on, and examples taken from, the space of real numbers.
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3.00 Credits
Prerequisite: Consent of instructor. A seminar on special topics in mathematics to be determined by the interests of the instructor. May be repeated for credit provided different topics are studied.
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3.00 Credits
Prerequisite: MATH 4100.? A theoretical treatment of ordinary differential equations including the existence and uniqueness of solutions of differential equations and systems of differential equations. The course treats such topics as systems of linear differential equations, eigenvalue problems, autonomous systems, and boundary value problems.
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3.00 Credits
Prerequisites: MATH 4100, 4160, and 4450 or consent of instructor. The course gives the deriviation of equations of mathematical physics such as Navier-Stokes' equations, Euler's equations, equations of elastic materials, and equations of electrodynamics, using scaling and conservation principles. The course also includes elements of the calculus of variations, the Euler-Lagrange equations and Hamiltonian theory.
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3.00 Credits
Prerequisites: MATH 2020, 4100 and 4450. Classical functionals, minimization of functionals, Euler-Lagrange equations, appropriate function spaces, weak solutions, existence of solutions, approximation theory, practical applications and finite element approach to solutions will be covered.
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3.00 Credits
Prerequisite: MATH 4100, 4230 and 4450, or consent of instructor. Construction of curves and surfaces using subdivision algorithms. Iterative refinement of discrete data in an easily programmable manner. Discussion of issues of convergence, shape control, relation to spline functions with uniform knots, multi resolution analysis, and wavelets.
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