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MATH 5450: Calculus on Manifolds
3.00 Credits
University of North Texas
5450. Calculus on Manifolds. 3 hours. Introduction to differential geometry and topology. Topics include implicit and inverse function theorems, differentiable manifolds, tangent bundles, Riemannian manifolds, tensors, curvature, differential forms, integration on manifolds and Stokes' theorem. Prerequisite(s): consent of department.
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MATH 5460: Differential Equations
3.00 Credits
University of North Texas
5460. Differential Equations. 3 hours each. Calculation of solutions to systems of ordinary differential equations, study of algebraic and qualitative properties of solutions, study of partial differential equations of mathematical physics, iterative methods for numerical solutions of ordinary and partial differential equations and introduction to the finite element method. Prerequisite(s): MATH 5110-5120 and linear algebra.
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MATH 5460 - Differential Equations
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MATH 5470: Differential Equations
3.00 Credits
University of North Texas
5470. Differential Equations. 3 hours each. Calculation of solutions to systems of ordinary differential equations, study of algebraic and qualitative properties of solutions, study of partial differential equations of mathematical physics, iterative methods for numerical solutions of ordinary and partial differential equations and introduction to the finite element method. Prerequisite(s): MATH 5110-5120 and linear algebra.
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MATH 5470 - Differential Equations
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MATH 5500: Introduction to the Theory of Matrices
3.00 Credits
University of North Texas
5500. Introduction to the Theory of Matrices. 3 hours. Congruence (Hermitian); similarity; orthogonality, matrices with polynomial elements and minimal polynomials; Cayley-Hamilton theorem; bilinear and quadratic forms; eigenvalues. Only one course, MATH 5400, 5500, or 5600, may be used towards satisfying the coursework requirment for a graduate degree in Mathematics. (Meets with MATH 4450). Prerequisite(s): Consent of department.
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MATH 5520: Modern Algebra
3.00 Credits
University of North Texas
5520. Modern Algebra. 3 hours. Groups and their generalizations; homomorphism and isomorphism theories; direct sums and products; orderings; abelian groups and their invariants. Prerequisite(s): MATH 3510 or equivalent.
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MATH 5530: Selected Topics in Modern Algebra
3.00 Credits
University of North Texas
5530. Selected Topics in Modern Algebra. 3 hours. Ring and field extensions, Galois groups, ideals and valuation theory.
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MATH 5530 - Selected Topics in Modern Algebra
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MATH 5600: Introduction to Topology
3.00 Credits
University of North Texas
5600. Introduction to Topology. 3 hours. Point set topology; connectedness, compactness, continuous functions and metric spaces. Only one course, MATH 5400, 5500 or 5600, may be used towards staisfying the coursework requirement for a graduate degree in Mathematics. Prerequisite(s): Consent of department.
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MATH 5610: Topology.
3.00 Credits
University of North Texas
5610. Topology. 3 hours each. A rigorous development of abstract topological spaces, mappings, metric spaces, continua, product and quotient spaces; introduction to algebraic methods.
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MATH 5620: Topology
3.00 Credits
University of North Texas
5620. Topology. 3 hours each. A rigorous development of abstract topological spaces, mappings, metric spaces, continua, product and quotient spaces; introduction to algebraic methods.
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MATH 5700: Selected Topics in Contemporary Mathematics
3.00 Credits
University of North Texas
5700. Selected Topics in Contemporary Mathematics. 3 hours. Topics of current interest that vary from year to year. May be repeated for credit as topics vary. Prerequisite(s) : Consent of department.
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