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Mathematics 4620: Projective Geometry
3.00 Credits
University of Missouri-St Louis
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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Mathematics 4620 - Projective Geometry
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Mathematics 4640: Introduction to Differential Geometry
3.00 Credits
University of Missouri-St Louis
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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Mathematics 4640 - Introduction to Differential Geometry
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Mathematics 4660: Foundations of Geometry
3.00 Credits
University of Missouri-St Louis
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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Mathematics 4660 - Foundations of Geometry
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Mathematics 4670: Introduction to Non-Euclidean Geometry
3.00 Credits
University of Missouri-St Louis
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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Mathematics 4670 - Introduction to Non-Euclidean Geometry
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Mathematics 4800: Introduction to Topology
3.00 Credits
University of Missouri-St Louis
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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Mathematics 4800 - Introduction to Topology
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Mathematics 4890: Topics in Mathematics
3.00 Credits
University of Missouri-St Louis
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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Mathematics 4890 - Topics in Mathematics
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Mathematics 5010: Theory of Ordinary Differential Equations
3.00 Credits
University of Missouri-St Louis
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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Mathematics 5010 - Theory of Ordinary Differential Equations
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Mathematics 5020: Classical Applied Mathematics
3.00 Credits
University of Missouri-St Louis
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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Mathematics 5020 - Classical Applied Mathematics
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Mathematics 5040: Calculus of Variations
3.00 Credits
University of Missouri-St Louis
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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Mathematics 5040 - Calculus of Variations
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Mathematics 5050: Computational Curves and Surfaces
3.00 Credits
University of Missouri-St Louis
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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Mathematics 5050 - Computational Curves and Surfaces
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