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MTH 434: Set Theory and Topology I
3.00 Credits
Portland State University
Cardinal and ordinal numbers. The axiom of choice and equivalent formulations. Introduction to general topology with the notions of interior, closure, topological space, continuity, and homeomorphism. Construction techniques and properties of point-set topology, especially connectedness, compactness, and separation. Additional topics. Courses must be taken in sequence.
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MTH 434 - Set Theory and Topology I
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MTH 441: Introduction to Abstract Algebra I
3.00 Credits
Portland State University
Groups and rings with homomorphism theorems, vector spaces, modules, algebraic theory of fields and Galois theory, lattices, algebras. Courses must be taken in sequence.
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MTH 441 - Introduction to Abstract Algebra I
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MTH 451: Numerical Calculus I
3.00 Credits
Portland State University
Computer arithmetic. Solution of nonlinear equations. Interpolation. Numerical integration and differentiation. Solution of linear equation systems. Eigenvalue problem, least square, chebyshev, trigonometric and rational function approximation. Numerical solution of differential equations.
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MTH 451 - Numerical Calculus I
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MTH 461: Graph Theory I
3.00 Credits
Portland State University
Topics in graph theory, including connectivity, matchings, graph algorithms, network flows, graph matrices, isomorphisms, Eulerian and Hamiltonian graphs, spanning trees, decompositions, shortest paths, the matrix-tree theorem, colorings of graphs, planarity and embeddings, Kuratowski's theorem, matroids, and selected applications. Courses must be taken in sequence.
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MTH 461 - Graph Theory I
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MTH 482: Topics in Statistics for Mathematics Teachers
3.00 Credits
Portland State University
Introduction to methods of statistical analysis and methods for teaching statistics. Descriptive statistics, organization of data, sampling techniques, sampling distributions, methods of statistical inference, estimation, hypothesis testing, regression, and correlation. Computer-assisted analysis. With departmental approval may be repeated for credit.
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MTH 482 - Topics in Statistics for Mathematics Teachers
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MTH 510: Selected Topics
3.00 Credits
Portland State University
See department for course description.
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MTH 510 - Selected Topics
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MTH 511: Introduction to Real Analysis I
3.00 Credits
Portland State University
Sequences and series of functions; Lebesgue measure and integration; the Stone-Weierstrass and Baire category theorems; Fourier Series; elements of functional analysis. Courses must be taken in sequence.
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MTH 511 - Introduction to Real Analysis I
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MTH 527: Partial Differential Equations I
3.00 Credits
Portland State University
Solution techniques, qualitative analysis and applications: separation of variables, eigenfunction expansion, Sturm-Liouville problems, Green's functions, Fourier transform solutions, finite difference and finite element methods. Courses must be taken in sequence.
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MTH 527 - Partial Differential Equations I
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MTH 534: Set Theory and Topology I
3.00 Credits
Portland State University
Cardinal and ordinal numbers. The axiom of choice and equivalent formulations. Introduction to general topology with the notions of interior, closure, topological space, continuity, and homeomorphism. Construction techniques and properties of point-set topology, especially connectedness, compactness, and separation. Additional topics. Courses must be taken in sequence.
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MTH 534 - Set Theory and Topology I
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MTH 541: Introduction to Abstract Algebra I
3.00 Credits
Portland State University
Groups and rings with homomorphism theorems, vector spaces, modules, algebraic theory of fields and Galois theory, lattices, algebras. Courses must be taken in sequence.
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MTH 541 - Introduction to Abstract Algebra I
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