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Course Criteria
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3.00 Credits
Basic properties of groups, rings and fields, homomorphisms, normal subgroups, integral domains, ideals, algebraic extension fields, geometric constructions. Prerequisite: MATH 3308 or 3353.
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3.00 Credits
Elementary topology of the line and plane, metric spaces, and general topological spaces: continuity of mappings, connectedness, compactness, completeness and fixed-point theorems. Prerequisite: MATH 3308, MATH 3353 or instructor's permission.
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3.00 Credits
Numerical solution of linear and nonlinear equations, interpolation and approximation of functions, numerical integration, floating point arithmetic, and the numerical solution of initial value problems in ordinary differential equations. Student use of the computer is emphasized. Prerequisites: MATH 3315/CSE 3365 and MATH 2343; a programming course (e.g., C, FORTRAN or MATLAB).
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3.00 Credits
The efficient solution of dense and sparse linear systems, least squares problems and eigenvalue problems. Elementary and orthogonal matrix transformations provide a unified treatment. Programming will be in MATLAB with a focus on algorithms. Prerequisites: MATH 3353; MATH 3315/CSE 3365.
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3.00 Credits
Complex numbers, analytic functions, mapping by elementary functions, complex integration. Cauchy-Goursat theorem, Cauchy integral formulas. Taylor and Laurent series, residues, evaluation of improper integrals. Applications of conformal mapping and analytic functions. Prerequisite: MATH 3337.
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3.00 Credits
A mathematical introduction to sampling, data compression, multiresolution analysis, Fourier analysis and wavelet theory, including biorthogonal wavelets and spline wavelets. Prerequisites: MATH 3337, 3353 and 3315/CSE 3365.
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3.00 Credits
Elementary partial differential equations of applied mathematics: heat, wave, and Laplace's equations. Topics include physical derivations, separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, Bessel functions, Fourier transforms. Prerequisite: MATH 3337.
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3.00 Credits
Spectral theory of Hermitian matrices, Jordan normal form, Perron-Frobenius theory, convexity. Applications include image compression, Internet page rank methods, optimization, linear programming. Prerequisite: MATH 3353.
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3.00 Credits
Examines several basic notions pertaining to selfhood, including consciousness, cognition, motivation, personal identity and decision, as found in medieval texts.
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3.00 Credits
Survey of native Welsh literature (in translation) from the sixth to the 20th century. Primary focus is on medieval and Arthurian texts and their influence on the British and European literary imagination.
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