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Course Criteria
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1.00 - 3.00 Credits
Topics selected from algebra, geometry, analysis, topology.
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3.00 Credits
The development of mathematics from its earliest beginnings through the first half of the twentieth century. Numeral systems, geometry, algebra, analysis and set theory.
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3.00 Credits
Axiom systems and models of Euclidean and Non-Euclidean geometry.
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3.00 Credits
Divisibility, primes; congruences, quadratic residues and reciprocity; Diophantine equations. Applications to cryptography.
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3.00 Credits
Abstract vector spaces, bases and dimensions, linear maps, eigenvalues and eigenvectors, inner product spaces, operators, spectral theorems, canonical forms.
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3.00 Credits
Complex variables; conformal mapping, contour integration.
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3.00 Credits
Derivation, well posedness, and qualitative properties of initial value and boundary value problems for the heat, wave and Laplace equations. Energy methods, causality, maximum principles, heat kernels, Fourier series, and potential theory.
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3.00 Credits
Continuation of MTH 513. Approximations of solutions, distributions and integral transform methods, spectral theory and scattering. Applications to physical problems. Nonlinear equations and phenomena.
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3.00 Credits
Linear systems, equilibrium and periodic solutions, stability analysis, bifurcation, phase plane analysis, boundary value problems, applications to engineering and physics.
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3.00 Credits
Bifurcation of equilibrium and periodic solutions, global theory of planar systems, planar maps, nonlinear vibrations, forced oscillations, chaotic solutions, Hamiltonian systems, applications to engineering and physics.
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