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MATH 4355: Groups and Rings
3.00 Credits
Southern Methodist University
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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MATH 4381: Introduction to General Topology
3.00 Credits
Southern Methodist University
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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MATH 5315: Introduction to Numerical Analysis
3.00 Credits
Southern Methodist University
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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MATH 5316: Introduction to Matrix Computation
3.00 Credits
Southern Methodist University
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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MATH 5331: Functions of a Complex Variable
3.00 Credits
Southern Methodist University
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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MATH 5332: Wavelet Transforms
3.00 Credits
Southern Methodist University
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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MATH 5334: Introduction to Partial Differential Equations
3.00 Credits
Southern Methodist University
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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MATH 5353: Linear Algebra
3.00 Credits
Southern Methodist University
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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MDVL 3321: The Birth of the Individual
3.00 Credits
Southern Methodist University
Examines several basic notions pertaining to selfhood, including consciousness, cognition, motivation, personal identity and decision, as found in medieval texts.
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MDVL 3323: Tales of Wales
3.00 Credits
Southern Methodist University
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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