• MATH 559: Seminar: Algebra

  1.00 - 3.00 Credits

  The University of Tennessee - Knoxville

  
  Repeatability: May be repeated. Maximum 12 hours.
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• MATH 561: Topology I

  3.00 Credits

  The University of Tennessee - Knoxville

  
  Topological spaces and continuous functions, separation axioms, product and quotient topologies, connectedness, compactness, complete metric spaces.Recommended Background: One year of advanced calculus.
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• MATH 562: Topology II

  3.00 Credits

  The University of Tennessee - Knoxville

  
  Continuation of 561. Fundamental group and covering spaces.(DE) Prerequisite(s): 561.
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• MATH 567: Riemannian Geometry I

  3.00 Credits

  The University of Tennessee - Knoxville

  
  Riemannian and Lorentzian manifolds. Variations of arc length, Jacobi fields, comparison theorems. Constant curvature spaces. Curvature and topology of manifolds.Recommended Background: One year of advanced calculus.
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• MATH 568: Riemannian Geometry II

  3.00 Credits

  The University of Tennessee - Knoxville

  
  Continuation of 567.(DE) Prerequisite(s): 567.
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• MATH 569: Seminar: Topology/Geometry

  1.00 - 3.00 Credits

  The University of Tennessee - Knoxville

  
  Repeatability: May be repeated. Maximum 12 hours.
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• MATH 571: Numerical Mathematics I

  3.00 Credits

  The University of Tennessee - Knoxville

  
  Direct and iterative methods for linear systems. The algebraic eigenvalue problem and the singular decomposition theorem. Newton and quasi-Newton methods for systems of nonlinear equations.Cross-listed: (Same as Computer Science 571.)Recommended Background: Courses in advanced calculus and basic numerical analysis.
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• MATH 572: Numerical Mathematics II

  3.00 Credits

  The University of Tennessee - Knoxville

  
  Numerical techniques for initial value problems of ordinary differential equations. Two-point boundary value problems. Finite difference and finite element methods for selected partial differential equations. Fast Poisson solvers.Cross-listed: (Same as Computer Science 572.)(DE) Prerequisite(s): 571.
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• MATH 574: Finite Element Methods

  3.00 Credits

  The University of Tennessee - Knoxville

  
  Finite element techniques for solution of boundary and initial-boundary value problems. Variational formulation. Finite dimensional subspaces and their approximating properties; rates of convergence. Computer implementation.Cross-listed: (Same as Computer Science 574.)Recommended Background: Courses in partial differential equations, linear algebra and numerical analysis.
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• MATH 577: Optimization

  3.00 Credits

  The University of Tennessee - Knoxville

  
  Mathematical foundations of constrained and unconstrained optimization. Lagrange multipliers, the Farkas lemma, the Kuhn-Tucker-Karush theorem. Analysis of major algorithms and applications to real world problems.Recommended Background: Courses in numerical algorithms, linear algebra and advanced calculus.
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